results for quantum machine learning

- The quantum autoencoder is a recent paradigm in the field of quantum machine learning, which may enable an enhanced use of resources in quantum technologies. To this end, quantum neural networks with less nodes in the inner than in the outer layers were considered. Here, we propose a useful connection between approximate quantum adders and quantum autoencoders. Specifically, this link allows us to employ optimized approximate quantum adders, obtained with genetic algorithms, for the implementation of quantum autoencoders for a variety of initial states. Furthermore, we can also directly optimize the quantum autoencoders via genetic algorithms. Our approach opens a different path for the design of quantum autoencoders in controllable quantum platforms.
- Sep 21 2017 quant-ph arXiv:1709.06678v1Fundamental questions in chemistry and physics may never be answered due to the exponential complexity of the underlying quantum phenomena. A desire to overcome this challenge has sparked a new industry of quantum technologies with the promise that engineered quantum systems can address these hard problems. A key step towards demonstrating such a system will be performing a computation beyond the capabilities of any classical computer, achieving so-called quantum supremacy. Here, using 9 superconducting qubits, we demonstrate an immediate path towards quantum supremacy. By individually tuning the qubit parameters, we are able to generate thousands of unique Hamiltonian evolutions and probe the output probabilities. The measured probabilities obey a universal distribution, consistent with uniformly sampling the full Hilbert-space. As the number of qubits in the algorithm is varied, the system continues to explore the exponentially growing number of states. Combining these large datasets with techniques from machine learning allows us to construct a model which accurately predicts the measured probabilities. We demonstrate an application of these algorithms by systematically increasing the disorder and observing a transition from delocalized states to localized states. By extending these results to a system of 50 qubits, we hope to address scientific questions that are beyond the capabilities of any classical computer.
- We develop a machine learning method to construct accurate ground-state wave functions of strongly interacting and entangled quantum spin as well as fermionic models on lattices. A restricted Boltzmann machine algorithm in the form of an artificial neural network is combined with a conventional variational Monte Carlo method with pair product (geminal) wave functions and quantum number projections. The combined method substantially improves the accuracy beyond that ever achieved by each method separately, in the Heisenberg as well as Hubbard models on square lattices, thus proving its power as a highly accurate quantum many-body solver.
- Sep 19 2017 quant-ph arXiv:1709.05381v1NP-hard optimization problems scale very rapidly with problem size, becoming unsolvable with brute force methods, even with supercomputing resources. Typically, such problems have been approximated with heuristics. However, these methods still take a long time and are not guaranteed to find an optimal solution. Quantum computing offers the possibility of producing significant speed-up and improved solution quality. Current quantum annealing (QA) devices are designed to solve difficult optimization problems, but they are limited by hardware size and qubit connectivity restrictions. We present a novel heterogeneous computing stack that combines QA and classical machine learning, allowing the use of QA on problems larger than the hardware limits of the quantum device. These results represent experiments on a real-world problem represented by the weighted k-clique problem. Through this experiment, we provide insight into the state of quantum machine learning.
- We develop a variational method to obtain many-body ground states of the Bose-Hubbard model using feedforward artificial neural networks. A fully-connected network with a single hidden layer works better than a fully-connected network with multiple hidden layers, and a multi-layer convolutional network is more efficient than a fully-connected network. AdaGrad and Adam are optimization methods that work well. Moreover, we show that many-body ground states with different numbers of atoms can be generated by a single network.
- In this letter, we apply the artificial neural network in a supervised manner to map out the quantum phase diagram of disordered topological superconductor in class DIII. Given the disorder that keeps the discrete symmetries of the ensemble as a whole, translational symmetry which is broken in the quasiparticle distribution individually is recovered statistically by taking an ensemble average. By using this, we classify the phases by the artificial neural network that learned the quasiparticle distribution in the clean limit, and show that the result is totally consistent with the calculation by the transfer matrix method or noncommutative geometry approach. If all three phases, namely the $\mathbb{Z}_2$, trivial, and the thermal metal phases appear in the clean limit, the machine can classify them with high confidence over the entire phase diagram. If only the former two phases are present, we find that the machine remains confused in the certain region, leading us to conclude the detection of the unknown phase which is eventually identified as the thermal metal phase. In our method, only the first moment of the quasiparticle distribution is used for input, but application to a wider variety of systems is expected by the inclusion of higher moments.
- Entanglement not only plays a crucial role in quantum technologies, but is key to our understanding of quantum correlations in many-body systems. However, in an experiment, the only way of measuring entanglement in a generic mixed state is through reconstructive quantum tomography, requiring an exponential number of measurements in the system size. Here, we propose an operational scheme to measure the entanglement --- as given by the negativity --- between arbitrary subsystems of size $N_A$ and $N_B$, with $\mathcal{O}(N_A + N_B)$ measurements, and without any prior knowledge of the state. We propose how to experimentally measure the partially transposed moments of a density matrix, and using just the first few of these, extract the negativity via Chebyshev approximation or machine learning techniques. Our procedure will allow entanglement measurements in a wide variety of systems, including strongly interacting many body systems in both equilibrium and non-equilibrium regimes.
- Sep 18 2017 quant-ph arXiv:1709.05015v2Quantum walks on graphs have shown prioritized benefits and applications in wide areas. In some scenarios, however, it may be more natural and accurate to mandate high-order relationships for hypergraphs, due to the density of information stored inherently. Therefore, we can explore the potential of quantum walks on hypergraphs. In this paper, by presenting the one-to-one correspondence between regular uniform hypergraphs and bipartite graphs, we construct a model for quantum walks on bipartite graphs of regular uniform hypergraphs with Szegedy's quantum walks, which gives rise to a quadratic speed-up. Furthermore, we deliver spectral properties of the transition matrix, given that the cardinalities of the two disjoint sets are different in the bipartite graph. Our model provides the foundation for building quantum algorithms on the strength of quantum walks, suah as quantum walks search, quantized Google's PageRank and quantum machine learning, based on hypergraphs.
- Sep 13 2017 quant-ph arXiv:1709.03617v1This paper introduces the forest algorithm, an algorithm that can detect entanglement through the use of decision trees generated by machine learning. Tests against similar tomography-based detection algorithms using experimental data and numerical simulations indicate that, once trained, the proposed algorithm outperforms previous approaches. The results identify entanglement detection as another area of quantum information where machine learning can play a helpful role.
- Quantum information technologies, and intelligent learning systems, are both emergent technologies that will likely have a transforming impact on our society. The respective underlying fields of research -- quantum information (QI) versus machine learning (ML) and artificial intelligence (AI) -- have their own specific challenges, which have hitherto been investigated largely independently. However, in a growing body of recent work, researchers have been probing the question to what extent these fields can learn and benefit from each other. QML explores the interaction between quantum computing and ML, investigating how results and techniques from one field can be used to solve the problems of the other. Recently, we have witnessed breakthroughs in both directions of influence. For instance, quantum computing is finding a vital application in providing speed-ups in ML, critical in our "big data" world. Conversely, ML already permeates cutting-edge technologies, and may become instrumental in advanced quantum technologies. Aside from quantum speed-up in data analysis, or classical ML optimization used in quantum experiments, quantum enhancements have also been demonstrated for interactive learning, highlighting the potential of quantum-enhanced learning agents. Finally, works exploring the use of AI for the very design of quantum experiments, and for performing parts of genuine research autonomously, have reported their first successes. Beyond the topics of mutual enhancement, researchers have also broached the fundamental issue of quantum generalizations of ML/AI concepts. This deals with questions of the very meaning of learning and intelligence in a world that is described by quantum mechanics. In this review, we describe the main ideas, recent developments, and progress in a broad spectrum of research investigating machine learning and artificial intelligence in the quantum domain.
- Sep 08 2017 physics.soc-ph cond-mat.quant-gas cs.CY physics.atom-ph physics.data-an quant-ph arXiv:1709.02230v1Despite recent advances driven by machine learning algorithms, experts agree that such algorithms are still often unable to match the experience-based and intuitive problem solving skills of humans in highly complex settings. Recent studies have demonstrated how the intuition of lay people in citizen science games [1] and the experience of fusion-scientists [2] have assisted automated search algorithms by restricting the size of the active search space leading to optimized results. Humans, thus, have an uncanny ability to detect patterns and solution strategies based on observations, calculations, or physical insight. Here we explore the fundamental question: Are these strategies truly distinct or merely labels we attach to different points in a high dimensional continuum of solutions? In the latter case, our human desire to identify patterns may lead us to terminate search too early. We demonstrate that this is the case in a theoretical study of single atom transport in an optical tweezer, where more than 200,000 citizen scientists helped probe the Quantum Speed Limit [1]. With this insight, we develop a novel global entirely deterministic search methodology yielding dramatically improved results. We demonstrate that this "bridging" of solution strategies can also be applied to closed-loop optimization of the production of Bose-Einstein condensates. Here we find improved solutions using two implementations of a novel remote interface. First, a team of theoretical optimal control researchers employ a Remote version of their dCRAB optimization algorithm (RedCRAB), and secondly a gamified interface allowed 600 citizen scientists from around the world to participate in the optimization. Finally, the "real world" nature of such problems allow for an entirely novel approach to the study of human problem solving, enabling us to run a hypothesis-driven social science experiment "in the wild".
- Generative modeling, which learns joint probability distribution from training data and generates samples according to it, is an important task in machine learning and artificial intelligence. Inspired by probabilistic interpretation of quantum physics, we propose a generative model using matrix product states, which is a tensor network originally proposed for describing (particularly one-dimensional) entangled quantum states. Our model enjoys efficient learning by utilizing the density matrix renormalization group method which allows dynamic adjusting dimensions of the tensors, and offers an efficient direct sampling approach, Zipper, for generative tasks. We apply our method to generative modeling of several standard datasets including the principled Bars and Stripes, random binary patterns and the MNIST handwritten digits, to illustrate ability of our model, and discuss features as well as drawbacks of our model over popular generative models such as Hopfield model, Boltzmann machines and generative adversarial networks. Our work shed light on many interesting directions for future exploration on the development of quantum-inspired algorithms for unsupervised machine learning, which is of possibility of being realized by a quantum device.
- Motivated by the close relations of the renormalization group with both the holography duality and the deep learning, we propose that the holographic geometry can emerge from deep learning the entanglement feature of a quantum many-body state. We develop a concrete algorithm, call the entanglement feature learning (EFL), based on the random tensor network (RTN) model for the tensor network holography. We show that each RTN can be mapped to a Boltzmann machine, trained by the entanglement entropies over all subregions of a given quantum many-body state. The goal is to construct the optimal RTN that best reproduce the entanglement feature. The RTN geometry can then be interpreted as the emergent holographic geometry. We demonstrate the EFL algorithm on 1D free fermion system and observe the emergence of the hyperbolic geometry (AdS$_3$ spatial geometry) as we tune the fermion system towards the gapless critical point (CFT$_2$ point).
- We report a proof-of-principle experimental demonstration of a quantum speed-up for learning agents utilizing a small-scale quantum information processor based on radiofrequency-driven trapped ions. The decision-making process of a quantum learning agent within the projective simulation paradigm for machine learning is modeled in a system of two qubits. The latter are realized in the hyperfine levels of two frequency-addressed ions exposed to a static magnetic field gradient. The deliberation algorithm is implemented using single-qubit rotations and two-qubit conditional quantum dynamics. We show that the deliberation time of this quantum learning agent is quadratically improved with respect to comparable classical learning agents. The performance of this quantum-enhanced learning agent highlights the potential of scalable ion trap quantum processors taking advantage of machine learning.
- Fundamental open questions about the two-dimensional Holstein model of electrons coupled to quantum phonons are addressed by continuous-time quantum Monte Carlo simulations. The critical temperature of the charge-density-wave transition is determined by a finite-size scaling of a renormalization-group-invariant correlation ratio. $T_c$ is finite for any nonzero coupling for classical phonons, and suppressed by quantum lattice fluctuations. The phase transition---also detectable via the fidelity susceptibility and machine learning---is demonstrated to be in the universality class of the two-dimensional Ising model. We discuss the possibility of $T_c=0$ at weak coupling and present evidence for a spin-gapped, bipolaronic metal above $T_c$.
- With quantum computing technologies nearing the era of commercialization and quantum supremacy, machine learning (ML) appears as one of the promising "killer" applications. Despite significant effort, there has been a disconnect between most quantum machine learning proposals, the needs of ML practitioners, and the capabilities of near-term quantum devices to demonstrate quantum enhancement in the near future. In this contribution to the focus collection on "What would you do with 1000 qubits?", we provide concrete examples of intractable ML tasks that could be enhanced with near-term devices. We argue that to reach this target, the focus should be on areas where ML researchers are still struggling, such as generative models in unsupervised or semisupervised learning, instead of the popular and much more tractable ML techniques. We also highlight the case of classical datasets with potential quantum-like statistical correlations where quantum models could be more suitable. We focus on hybrid quantum-classical approaches and illustrate some of the key challenges we foresee for near-term implementations. Finally, we introduce the quantum-assisted Helmholtz machine (QAHM); an attempt to use near-term quantum devices to tackle high-resolution datasets on continuous variables. Instead of using quantum computers to assist deep learning, as previous approaches do, the QAHM uses deep learning to extract a low-dimensional binary representation of data, suitable for relatively small quantum processors which can assist the training of an unsupervised generative model. Although we illustrate this concept on a quantum annealer, other quantum platforms could benefit as well from this hybrid quantum-classical framework.
- In this Letter we supervisedly train neural networks to distinguish different topological phases in the context of topological band insulators. After training with Hamiltonians of one-dimensional insulators with chiral symmetry, the neural network can predict their topological winding numbers with nearly 100% accuracy, even for Hamiltonians with larger winding numbers that are not included in the training data. These results show a remarkable success that the neural network can capture the global and nonlinear topological features of quantum phases from local inputs. By opening up the neural network, we confirm that the network does learn the discrete version of the winding number formula. We also make a couple of remarks regrading the role of the symmetry and the opposite effect of regularization techniques when applying machine learning to physical systems.
- Machine learning has been presented as one of the key applications for near-term quantum technologies, given its high commercial value and wide range of applicability. In this work, we introduce the quantum-assisted Helmholtz machine: a hybrid quantum-classical framework with the potential of tackling high-dimensional real-world machine learning datasets on continuous variables. Instead of using quantum computers to only assist deep learning, as previous approaches have suggested, we use deep learning to extract a low-dimensional binary representation of data, suitable for relatively small quantum processors which can assist the training of an unsupervised generative model. To demonstrate this concept on a real-world dataset, we used 1644 quantum bits of a noisy non-fault-tolerant quantum device, the D-Wave 2000Q, to assist the training of a sub-sampled version of the MNIST handwritten digit dataset with 16 x 16 continuous valued pixels. Although we illustrate this concept on a quantum annealer, adaptations to other quantum platforms, such as ion-trap technologies or superconducting gate-model architectures, could be explored within this flexible framework.
- Aug 25 2017 physics.gen-ph hep-th arXiv:1708.07408v1In this essay we conjecture that quantum fields such as the Higgs field is related to a restricted Boltzmann machine for deep neural networks. An accelerating Rindler observer in a flat spacetime sees the quantum fields having a thermal distribution from the quantum entanglement, and a renormalization group process for the thermal fields on a lattice is similar to a deep learning algorithm. This correspondence can be generalized for the KMS states of quantum fields in a curved spacetime like a black hole.
- Aug 22 2017 cond-mat.mtrl-sci arXiv:1708.06017v1Machine learning (ML) of quantum mechanical properties shows promise for accelerating chemical discovery. For transition metal chemistry where accurate calculations are computationally costly and available training data sets are small, the molecular representation becomes a critical ingredient in ML model predictive accuracy. We introduce a series of revised autocorrelation functions (RACs) that encode relationships between the heuristic atomic properties (e.g., size, connectivity, and electronegativity) on a molecular graph. We alter the starting point, scope, and nature of the quantities evaluated in standard ACs to make these RACs amenable to inorganic chemistry. On an organic molecule set, we first demonstrate superior standard AC performance to other presently-available topological descriptors for ML model training, with mean unsigned errors (MUEs) for atomization energies on set-aside test molecules as low as 6 kcal/mol. For inorganic chemistry, our RACs yield 1 kcal/mol ML MUEs on set-aside test molecules in spin-state splitting in comparison to 15-20x higher errors from feature sets that encode whole-molecule structural information. Systematic feature selection methods including univariate filtering, recursive feature elimination, and direct optimization (e.g., random forest and LASSO) are compared. Random-forest- or LASSO-selected subsets 4-5x smaller than RAC-155 produce sub- to 1-kcal/mol spin-splitting MUEs, with good transferability to metal-ligand bond length prediction (0.004-5 Å MUE) and redox potential on a smaller data set (0.2-0.3 eV MUE). Evaluation of feature selection results across property sets reveals the relative importance of local, electronic descriptors (e.g., electronegativity, atomic number) in spin-splitting and distal, steric effects in redox potential and bond lengths.
- Aug 22 2017 quant-ph arXiv:1708.05753v1Clustering is a powerful machine learning technique that groups "similar" data points based on their characteristics. Many clustering algorithms work by approximating the minimization of an objective function, namely the sum of within-the-cluster distances between points. The straightforward approach involves examining all the possible assignments of points to each of the clusters. This approach guarantees the solution will be a global minimum, however the number of possible assignments scales quickly with the number of data points and becomes computationally intractable even for very small datasets. In order to circumvent this issue, cost function minima are found using popular local-search based heuristic approaches such as k-means and hierarchical clustering. Due to their greedy nature, such techniques do not guarantee that a global minimum will be found and can lead to sub-optimal clustering assignments. Other classes of global-search based techniques, such as simulated annealing, tabu search, and genetic algorithms may offer better quality results but can be too time consuming to implement. In this work, we describe how quantum annealing can be used to carry out clustering. We map the clustering objective to a quadratic binary optimization (QUBO) problem and discuss two clustering algorithms which are then implemented on commercially-available quantum annealing hardware, as well as on a purely classical solver "qbsolv." The first algorithm assigns N data points to K clusters, and the second one can be used to perform binary clustering in a hierarchical manner. We present our results in the form of benchmarks against well-known k-means clustering and discuss the advantages and disadvantages of the proposed techniques.
- We employ several unsupervised machine learning techniques, including autoencoders, random trees embedding, and t-distributed stochastic neighboring ensemble (t-SNE), to reduce the dimensionality of, and therefore classify, raw (auxiliary) spin configurations generated, through Monte Carlo simulations of small clusters, for the Ising and Fermi-Hubbard models at finite temperatures. Results from a convolutional autoencoder for the three-dimensional Ising model can be shown to produce the magnetization and the susceptibility as a function of temperature with a high degree of accuracy. Quantum fluctuations distort this picture and prevent us from making such connections between the output of the autoencoder and physical observables for the Hubbard model. However, we are able to define an indicator based on the output of the t-SNE algorithm that shows a near perfect agreement with the antiferromagnetic structure factor of the model in two and three spatial dimensions in the weak-coupling regime. t-SNE also predicts a transition to the canted antiferromagnetic phase for the three-dimensional model when a strong magnetic field is present. We show that these techniques cannot be expected to work away from half filling when the "sign problem" in quantum Monte Carlo simulations is present.
- Aug 02 2017 quant-ph cond-mat.mes-hall arXiv:1708.00238v1In the near future, more and more laborious tasks will be replaced by machines. In the context of quantum control, the question is, can machines replace human beings to design reliable quantum control methods? Here we investigate the performance of machine learning in composing composite pulse sequences which are indispensable for a universal control of singlet-triplet spin qubits. Subject to the control constraints, one can in principle construct a sequence of composite pulses to achieve an arbitrary rotation of a singlet-triplet spin qubits. In absence of noise, they are required to perform arbitrary single-qubit operations due to the special control constraint of a singlet-triplet qubit; Furthermore, even in a noisy environment, it is possible to develop sophisticated pulse sequences to dynamically compensate the errors. However, tailoring these sequences is in general a resource-consuming process, where a numerical search for the solution of certain non-linear equations is required. Here we demonstrate that these composite-pulse sequences can be efficiently generated by a well-trained, double-layer neural network. For sequences designed for the noise-free case, the trained neural network is capable of producing almost exactly the same pulses developed in the literature. For more complicated noise-correcting sequences, the neural network produced pulses with a slightly different line-shape, but the robustness against noises remains about the same. These results indicate that the neural network can be a judicious and powerful alternative to existing techniques, in developing pulse sequences for universal fault-tolerant quantum computation.
- Aug 01 2017 quant-ph arXiv:1707.09524v2In recent years, quantum computing has been shown to be powerful in efficiently solving various machine learning problems, one of the most representative examples being linear regression. However, all the previous quantum linear regression algorithms only consider the ordinary linear regression (OLR), which is very unsatisfactory in practice when encountering multicollinearity of independent variables and overfitting. In this letter, we address a more general version of OLR---ridge regression---on quantum computer, which can effectively circumvent these two difficulties by introducing an amount, called regularization parameter ($\alpha$), of regularization of fitting parameters into optimization. In particular, we suggest two quantum algorithms for tackling two main and fundamental problems in ridge regression, namely estimating the optimal fitting parameters and choosing a good $\alpha$. The first algorithm generates a quantum state to encode the optimal fitting parameters in its amplitudes, and the second one adopts $K$-fold cross validation to choose a good $\alpha$ with which ridge regression achieves good predictive performance. Both algorithms are shown exponentially faster than their classical counterparts when the design matrix admits low-rank approximation and is of low condition number.
- With the extensive applications of machine learning, the issue of private or sensitive data in the training examples becomes more and more serious: during the training process, personal information or habits may be disclosed to unexpected persons or organisations, which can cause serious privacy problems or even financial loss. In this paper, we present a quantum privacy-preserving algorithm for machine learning with perceptron. There are mainly two steps to protect original training examples. Firstly when checking the current classifier, quantum tests are employed to detect data user's possible dishonesty. Secondly when updating the current classifier, private random noise is used to protect the original data. The advantages of our algorithm are: (1) it protects training examples better than the known classical methods; (2) it requires no quantum database and thus is easy to implement.
- Aug 01 2017 cond-mat.dis-nn cond-mat.quant-gas arXiv:1707.09723v1Motivated by the recent successful application of artificial neural networks to quantum many-body problems [G. Carleo and M. Troyer, Science \bf 355, 602 (2017)], a method to calculate the ground state of the Bose-Hubbard model using a feedforward neural network is proposed. The results are in good agreement with those obtained by exact diagonalization and the Gutzwiller approximation. The method of neural-network quantum states is promising for solving quantum many-body problems of ultracold atoms in optical lattices.
- Recently, increased computational power and data availability, as well as algorithmic advances, have led machine learning techniques to impressive results in regression, classification, data-generation and reinforcement learning tasks. Despite these successes, the proximity to the physical limits of chip fabrication alongside the increasing size of datasets are motivating a growing number of researchers to explore the possibility of harnessing the power of quantum computation to speed-up classical machine learning algorithms. Here we review the literature in quantum machine learning and discuss perspectives for a mixed readership of classical machine learning and quantum computation experts. Particular emphasis will be placed on clarifying the limitations of quantum algorithms, how they compare with their best classical counterparts and why quantum resources are expected to provide advantages for learning problems. Learning in the presence of noise and certain computationally hard problems in machine learning are identified as promising directions for the field. Practical questions, like how to upload classical data into quantum form, will also be addressed.
- Jul 21 2017 physics.chem-ph stat.ML arXiv:1707.06338v1Understanding the relationship between the structure of light-harvesting systems and their excitation energy transfer properties is of fundamental importance in many applications including the development of next generation photovoltaics. Natural light harvesting in photosynthesis shows remarkable excitation energy transfer properties, which suggests that pigment-protein complexes could serve as blueprints for the design of nature inspired devices. Mechanistic insights into energy transport dynamics can be gained by leveraging numerically involved propagation schemes such as the hierarchical equations of motion (HEOM). Solving these equations, however, is computationally costly due to the adverse scaling with the number of pigments. Therefore virtual high-throughput screening, which has become a powerful tool in material discovery, is less readily applicable for the search of novel excitonic devices. We propose the use of artificial neural networks to bypass the computational limitations of established techniques for exploring the structure-dynamics relation in excitonic systems. Once trained, our neural networks reduce computational costs by several orders of magnitudes. Our predicted transfer times and transfer efficiencies exhibit similar or even higher accuracies than frequently used approximate methods such as secular Redfield theory
- Jul 14 2017 physics.chem-ph arXiv:1707.04146v3Given sufficient examples, recently introduced machine learning models enable rapid, yet accurate, predictions of properties of new molecules. Extrapolation to larger molecules with differing composition is prohibitive due to all the specific chemistries which would be required for training. We address this problem by exploiting redundancies due to chemical similarity of repeating building blocks each represented by an effective \underline atom in \underline molecule: The "am-on". In analogy to the DNA sequence in a gene encoding its function, constituting amons encode a query molecule's properties. The use of amons affords highly accurate machine learning predictions of quantum properties of arbitrary query molecules in real time. We investigate this approach for predicting energies of various covalently and non-covalently bonded systems. After training on the few amons detected, very low prediction errors can be reached, on par with experimental uncertainty. Systems studied include two dozen large biomolecules, eleven thousand medium sized organic molecules, large common polymers, water clusters, doped $h$BN sheets, bulk silicon, and Watson-Crick DNA base pairs. Conceptually, the amons extend Mendeleev's table to account for the chemical environments of elements. They represent an important stepping stone to machine learning based virtual chemical space exploration campaigns.
- Jul 05 2017 quant-ph arXiv:1707.00986v3A network of driven nonlinear oscillators without dissipation has recently been proposed for solving combinatorial optimization problems via quantum adiabatic evolution through its bifurcation point. Here we investigate the behavior of the quantum bifurcation machine in the presence of dissipation. Our numerical study suggests that the output probability distribution of the dissipative quantum bifurcation machine is Boltzmann-like, where the energy in the Boltzmann distribution corresponds to the cost function of the optimization problem. We explain the Boltzmann distribution by generalizing the concept of quantum heating in a single oscillator to the case of multiple coupled oscillators. The present result also suggests that such driven dissipative nonlinear oscillator networks can be applied to Boltzmann sampling, which is used, e.g., for Boltzmann machine learning in the field of artificial intelligence.
- The application of state-of-the-art machine learning techniques to statistical physic problems has seen a surge of interest for their ability to discriminate phases of matter by extracting essential features in the many-body wavefunction or the ensemble of correlators sampled in Monte Carlo simulations. Here we introduce a gener- alization of supervised machine learning approaches that allows to accurately map out phase diagrams of inter- acting many-body systems without any prior knowledge, e.g. of their general topology or the number of distinct phases. To substantiate the versatility of this approach, which combines convolutional neural networks with quantum Monte Carlo sampling, we map out the phase diagrams of interacting boson and fermion models both at zero and finite temperatures and show that first-order, second-order, and Kosterlitz-Thouless phase transitions can all be identified. We explicitly demonstrate that our approach is capable of identifying the phase transition to non-trivial many-body phases such as superfluids or topologically ordered phases without supervision.
- Jul 04 2017 quant-ph arXiv:1707.00360v1With the significant advancement in quantum computation in the past couple of decades, the exploration of machine-learning subroutines using quantum strategies has become increasingly popular. Gaussian process regression is a widely used technique in supervised classical machine learning. Here we introduce an algorithm for Gaussian process regression using continuous-variable quantum systems that can be realized with technology based on photonic quantum computers. Our algorithm shows that by using a continuous-variable quantum computer a dramatic speed-up in computing Gaussian process regression can be achieved, i.e., the possibility of exponentially reducing the time to compute. Furthermore, our results also include a continuous-variable quantum-assisted singular value decomposition method of non-sparse low rank matrices and forms an important subroutine in our Gaussian process regression algorithm.
- Determining the best method for training a machine learning algorithm is critical to maximizing its ability to classify data. In this paper, we compare the standard "fully supervised" approach (that relies on knowledge of event-by-event truth-level labels) with a recent proposal that instead utilizes class ratios as the only discriminating information provided during training. This so-called "weakly supervised" technique has access to less information than the fully supervised method and yet is still able to yield impressive discriminating power. In addition, weak supervision seems particularly well suited to particle physics since quantum mechanics is incompatible with the notion of mapping an individual event onto any single Feynman diagram. We examine the technique in detail -- both analytically and numerically -- with a focus on the robustness to issues of mischaracterizing the training samples. Weakly supervised networks turn out to be remarkably insensitive to systematic mismodeling. Furthermore, we demonstrate that the event level outputs for weakly versus fully supervised networks are probing different kinematics, even though the numerical quality metrics are essentially identical. This implies that it should be possible to improve the overall classification ability by combining the output from the two types of networks. For concreteness, we apply this technology to a signature of beyond the Standard Model physics to demonstrate that all these impressive features continue to hold in a scenario of relevance to the LHC.
- Jun 27 2017 cond-mat.stat-mech cond-mat.quant-gas arXiv:1706.07977v2This work aims at the goal whether the artificial intelligence can recognize phase transition without the prior human knowledge. If this becomes successful, it can be applied to, for instance, analyze data from quantum simulation of unsolved physical models. Toward this goal, we first need to apply the machine learning algorithm to well-understood models and see whether the outputs are consistent with our prior knowledge, which serves as the benchmark of this approach. In this work, we feed the compute with data generated by the classical Monte Carlo simulation for the XY model in frustrated triangular and union jack lattices, which has two order parameters and exhibits two phase transitions. We show that the outputs of the principle component analysis agree very well with our understanding of different orders in different phases, and the temperature dependences of the major components detect the nature and the locations of the phase transitions. Our work offers promise for using machine learning techniques to study sophisticated statistical models, and our results can be further improved by using principle component analysis with kernel tricks and the neural network method.
- Jun 27 2017 quant-ph cond-mat.dis-nn arXiv:1706.08470v2Quantum annealers aim at solving non-convex optimization problems by exploiting cooperative tunneling effects to escape local minima. The underlying idea consists in designing a classical energy function whose ground states are the sought optimal solutions of the original optimization problem and add a controllable quantum transverse field to generate tunneling processes. A key challenge is to identify classes of non-convex optimization problems for which quantum annealing remains efficient while thermal annealing fails. We show that this happens for a wide class of problems which are central to machine learning. Their energy landscapes is dominated by local minima that cause exponential slow down of classical thermal annealers while quantum annealing converges efficiently to rare dense regions of optimal solutions.
- Quantum computing for machine learning attracts increasing attention and recent technological developments suggest that especially adiabatic quantum computing may soon be of practical interest. In this paper, we therefore consider this paradigm and discuss how to adopt it to the problem of binary clustering. Numerical simulations demonstrate the feasibility of our approach and illustrate how systems of qubits adiabatically evolve towards a solution.
- Jun 20 2017 quant-ph physics.chem-ph arXiv:1706.05413v2The NSF Workshop in Quantum Information and Computation for Chemistry assembled experts from directly quantum-oriented fields such as algorithms, chemistry, machine learning, optics, simulation, and metrology, as well as experts in related fields such as condensed matter physics, biochemistry, physical chemistry, inorganic and organic chemistry, and spectroscopy. The goal of the workshop was to summarize recent progress in research at the interface of quantum information science and chemistry as well as to discuss the promising research challenges and opportunities in the field. Furthermore, the workshop hoped to identify target areas where cross fertilization among these fields would result in the largest payoff for developments in theory, algorithms, and experimental techniques. The ideas can be broadly categorized in two distinct areas of research that obviously have interactions and are not separated cleanly. The first area is quantum information for chemistry, or how quantum information tools, both experimental and theoretical can aid in our understanding of a wide range of problems pertaining to chemistry. The second area is chemistry for quantum information, which aims to discuss the several aspects where research in the chemical sciences can aid progress in quantum information science and technology. The results of the workshop are summarized in this report.
- Given a quantum (or statistical) system with a very large number of degrees of freedom and a preferred tensor product factorization of the Hilbert space (or of a space of distributions) we describe how it can be approximated with a very low-dimensional field theory with geometric degrees of freedom. The geometric approximation procedure consists of three steps. The first step is to construct weighted graphs (we call information graphs) with vertices representing subsystems (e.g. qubits or random variables) and edges representing mutual information (or the flow of information) between subsystems. The second step is to deform the adjacency matrices of the information graphs to that of a (locally) low-dimensional lattice using the graph flow equations introduced in the paper. (Note that the graph flow produces very sparse adjacency matrices and thus might also be used, for example, in machine learning or network science where the task of graph sparsification is of a central importance.) The third step is to define an emergent metric and to derive an effective description of the metric and possibly other degrees of freedom. To illustrate the procedure we analyze (numerically and analytically) two information graph flows with geometric attractors (towards locally one- and two-dimensional lattices) and metric perturbations obeying a geometric flow equation. Our analysis also suggests a possible approach to (a non-perturbative) quantum gravity in which the geometry (a secondary object) emerges directly from a quantum state (a primary object) due to the flow of the information graphs.
- Jun 07 2017 quant-ph arXiv:1706.01561v1The primary questions in the emerging field of quantum machine learning (QML) are, "Is it possible to achieve quantum speed-up of machine learning?" and "What quantum effects contribute to the speed-up and how?" Satisfactory answers to such questions have recently been provided by the quantum support vector machine (QSVM), which classifies many quantum data vectors by exploiting their quantum parallelism. However, it is demanded to realize a full-scale quantum computer that can process big data to learn quantum-mechanically, while nearly all the real-world data the users recognize are measured data, classical say. Then, the following important question arises: "Can quantum learning speed-up be attained even with the user-recognizable (classical) data?" Here, we provide an affirmative answer to the afore-mentioned question by performing proof-of-principle experiments.
- How useful can machine learning be in a quantum laboratory? Here we raise the question of the potential of intelligent machines in the context of scientific research. We investigate this question by using the projective simulation model, a physics-oriented approach to artificial intelligence. In our approach, the projective simulation system is challenged to design complex photonic quantum experiments that produce high-dimensional entangled multiphoton states, which are of high interest in modern quantum experiments. The artificial intelligence system learns to create a variety of entangled states, in number surpassing the best previously studied automated approaches, and improves the efficiency of their realization. In the process, the system autonomously (re)discovers experimental techniques which are only becoming standard in modern quantum optical experiments - a trait which was not explicitly demanded from the system but emerged through the process of learning. Such features highlight the possibility that machines could have a significantly more creative role in future research.
- Recent theoretical and experimental results suggest the possibility of using current and near-future quantum hardware in challenging sampling tasks. In this paper, we introduce free energy-based reinforcement learning (FERL) as an application of quantum hardware. We propose a method for processing a quantum annealer's measured qubit spin configurations in approximating the free energy of a quantum Boltzmann machine (QBM). We then apply this method to perform reinforcement learning on the grid-world problem using the D-Wave 2000Q quantum annealer. The experimental results show that our technique is a promising method for harnessing the power of quantum sampling in reinforcement learning tasks.
- Jun 02 2017 cond-mat.mtrl-sci physics.chem-ph arXiv:1706.00179v1Determining the stability of molecules and condensed phases is the cornerstone of atomistic modelling, underpinning our understanding of chemical and materials properties and transformations. Here we show that a machine learning model, based on a local description of chemical environments and Bayesian statistical learning, provides a unified framework to predict atomic-scale properties. It captures the quantum mechanical effects governing the complex surface reconstructions of silicon, predicts the stability of different classes of molecules with chemical accuracy, and distinguishes active and inactive protein ligands with more than 99% reliability. The universality and the systematic nature of our framework provides new insight into the potential energy surface of materials and molecules.
- In this paper, we propose the classification method based on a learning paradigm we are going to call Quantum Low Entropy based Associative Reasoning or QLEAR learning. The approach is based on the idea that classification can be understood as supervised clustering, where a quantum entropy in the context of the quantum probabilistic model, will be used as a "capturer" (measure, or external index), of the "natural structure" of the data. By using quantum entropy we do not make any assumption about linear separability of the data that are going to be classified. The basic idea is to find close neighbors to a query sample and then use relative change in the quantum entropy as a measure of similarity of the newly arrived sample with the representatives of interest. In other words, method is based on calculation of quantum entropy of the referent system and its relative change with the addition of the newly arrived sample. Referent system consists of vectors that represent individual classes and that are the most similar, in Euclidean distance sense, to the vector that is analyzed. Here, we analyze the classification problem in the context of measuring similarities to prototype examples of categories. While nearest neighbor classifiers are natural in this setting, they suffer from the problem of high variance (in bias-variance decomposition) in the case of limited sampling. Alternatively, one could use machine learning techniques (like support vector machines) but they involve time-consuming optimization. Here we propose a hybrid of nearest neighbor and machine learning technique which deals naturally with the multi-class setting, has reasonable computational complexity both in training and at run time, and yields excellent results in practice.
- May 23 2017 quant-ph cond-mat.dis-nn arXiv:1705.07855v2A fault-tolerant quantum computation requires an efficient means to detect and correct errors that accumulate in encoded quantum information. In the context of machine learning, neural networks are a promising new approach to quantum error correction. Here we show that a recurrent neural network can be trained, using only experimentally accessible data, to detect errors in a widely used topological code, the surface code, with a performance above that of the established minimum-weight perfect matching (or blossom) decoder. The performance gain is achieved because the neural network decoder can detect correlations between bit-flip (X) and phase-flip (Z) errors. The machine learning algorithm adapts to the physical system, hence no noise model is needed to achieve optimal performance. The long short-term memory cell of the recurrent neural network maintains this performance over a large number of error correction cycles, making it a practical decoder for forthcoming experimental realizations of the surface code.
- May 18 2017 physics.chem-ph arXiv:1705.05907v1Machine learning has emerged as an invaluable tool in many research areas. In the present work, we harness this power to predict highly accurate molecular infrared spectra with unprecedented computational efficiency. To account for vibrational anharmonic and dynamical effects -- typically neglected by conventional quantum chemistry approaches -- we base our machine learning strategy on ab initio molecular dynamics simulations. While these simulations are usually extremely time consuming even for small molecules, we overcome these limitations by leveraging the power of a variety of machine learning techniques, not only accelerating simulations by several orders of magnitude, but also greatly extending the size of systems that can be treated. To this end, we develop a molecular dipole moment model based on environment dependent neural network charges and combine it with the neural network potentials of Behler and Parrinello. Contrary to the prevalent big data philosophy, we are able to obtain very accurate machine learning models for the prediction of infrared spectra based on only a few hundreds of electronic structure reference points. This is made possible through the introduction of a fully automated sampling scheme and the use of molecular forces during neural network potential training. We demonstrate the power of our machine learning approach by applying it to model the infrared spectra of a methanol molecule, n-alkanes containing up to 200 atoms and the protonated alanine tripeptide, which at the same time represents the first application of machine learning techniques to simulate the dynamics of a peptide. In all these case studies we find excellent agreement between the infrared spectra predicted via machine learning models and the respective theoretical and experimental spectra.
- Over the past two decades, the feedforward neural network (FNN) optimization has been a key interest among the researchers and practitioners of multiple disciplines. The FNN optimization is often viewed from the various perspectives: the optimization of weights, network architecture, activation nodes, learning parameters, learning environment, etc. Researchers adopted such different viewpoints mainly to improve the FNN's generalization ability. The gradient-descent algorithm such as backpropagation has been widely applied to optimize the FNNs. Its success is evident from the FNN's application to numerous real-world problems. However, due to the limitations of the gradient-based optimization methods, the metaheuristic algorithms including the evolutionary algorithms, swarm intelligence, etc., are still being widely explored by the researchers aiming to obtain generalized FNN for a given problem. This article attempts to summarize a broad spectrum of FNN optimization methodologies including conventional and metaheuristic approaches. This article also tries to connect various research directions emerged out of the FNN optimization practices, such as evolving neural network (NN), cooperative coevolution NN, complex-valued NN, deep learning, extreme learning machine, quantum NN, etc. Additionally, it provides interesting research challenges for future research to cope-up with the present information processing era.
- Correlated many-body problems ubiquitously appear in various fields of physics such as condensed matter physics, nuclear physics, and statistical physics. However, due to the interplay of the large number of degrees of freedom, it is generically impossible to treat these problems from first principles. Thus the construction of a proper model, namely effective Hamiltonian, is essential. Here, we propose a simple scheme of constructing Hamiltonians from given energy or entanglement spectra with machine learning. We apply the proposed scheme to the Hubbard model at the half-filling, and compare the obtained effective low-energy spin-1/2 model with several analytic results based on the high order perturbation theory which have been inconsistent with each other. We also show that our approach can be used to construct the entanglement Hamiltonian of a quantum many-body state from its entanglement spectrum as well. We exemplify this using the ground states of the $S=1/2$ two-leg Heisenberg ladders. We observe a qualitative difference between the entanglement Hamiltonians of the two phases (the Haldane phase and the Rung Singlet phase) of the model due to the different origin of the entanglement. In the Haldane phase, we find that the entanglement Hamiltonian is non-local by nature, and the locality can be restored by introducing the anisotropy and turning the system into the large-$D$ phase. Possible applications to the study of strongly-correlated systems and the model construction from experimental data are discussed.
- This work demonstrates how to accelerate dense linear algebra computations using CLBlast, an open-source OpenCL BLAS library providing optimized routines for a wide variety of devices. It is targeted at machine learning and HPC applications and thus provides a fast matrix-multiplication routine (GEMM) to accelerate the core of many applications (e.g. deep learning, iterative solvers, astrophysics, computational fluid dynamics, quantum chemistry). CLBlast has four main advantages over other BLAS libraries: 1) it is optimized for and tested on a large variety of OpenCL devices including less commonly used devices such as embedded and low-power GPUs, 2) it can be explicitly tuned for specific problem-sizes on specific hardware platforms, 3) it can perform operations in half-precision floating-point FP16 saving precious bandwidth, time and energy, 4) and it can combine multiple operations in a single batched routine, accelerating smaller problems significantly. This paper describes the library and demonstrates the advantages of CLBlast experimentally for different use-cases on a wide variety of OpenCL hardware.
- After decades of progress and effort, obtaining a phase diagram for a strongly-correlated topological system still remains a challenge. Although in principle one could turn to Wilson loops and long-range entanglement, evaluating these non-local observables at many points in phase space can be prohibitively costly. With growing excitement over topological quantum computation comes the need for an efficient approach for obtaining topological phase diagrams. Here we turn to machine learning using quantum loop topography (QLT), a notion we have recently introduced. Specifically, we propose a construction of QLT that is sensitive to quasi-particle statistics. We then use mutual statistics between the spinons and visions to detect a $\mathbb Z_2$ quantum spin liquid in a multi-parameter phase space. We successfully obtain the quantum phase boundary between the topological and trivial phases using a simple feed forward neural network. Furthermore we demonstrate how our approach can speed up evaluation of the phase diagram by orders of magnitude. Such statistics-based machine learning of topological phases opens new efficient routes to studying topological phase diagrams in strongly correlated systems.
- Second-Harmonic Scatteringh (SHS) experiments provide a unique approach to probe non-centrosymmetric environments in aqueous media, from bulk solutions to interfaces, living cells and tissue. A central assumption made in analyzing SHS experiments is that the each molecule scatters light according to a constant molecular hyperpolarizability tensor $\boldsymbol{\beta}^{(2)}$. Here, we investigate the dependence of the molecular hyperpolarizability of water on its environment and internal geometric distortions, in order to test the hypothesis of constant $\boldsymbol{\beta}^{(2)}$. We use quantum chemistry calculations of the hyperpolarizability of a molecule embedded in point-charge environments obtained from simulations of bulk water. We demonstrate that both the heterogeneity of the solvent configurations and the quantum mechanical fluctuations of the molecular geometry introduce large variations in the non-linear optical response of water. This finding has the potential to change the way SHS experiments are interpreted: in particular, isotopic differences between H$_2$O and D$_2$O could explain recent second-harmonic scattering observations. Finally, we show that a simple machine-learning framework can predict accurately the fluctuations of the molecular hyperpolarizability. This model accounts for the microscopic inhomogeneity of the solvent and represents a first step towards quantitative modelling of SHS experiments.
- May 04 2017 quant-ph arXiv:1705.01523v3The problem of determining whether a given quantum state is entangled lies at the heart of quantum information processing, which is known to be an NP-hard problem in general. Despite the proposed many methods such as the positive partial transpose (PPT) criterion and the k-symmetric extendibility criterion to tackle this problem in practice, none of them enables a general, effective solution to the problem even for small dimensions. Explicitly, separable states form a high-dimensional convex set, which exhibits a vastly complicated structure. In this work, we build a new separability-entanglement classifier underpinned by machine learning techniques. Our method outperforms the existing methods in generic cases in terms of both speed and accuracy, opening up the avenues to explore quantum entanglement via the machine learning approach.
- Quantum information science has profoundly changed the ways we understand, store, and process information. A major challenge in this field is to look for an efficient means for classifying quantum state. For instance, one may want to determine if a given quantum state is entangled or not. However, the process of a complete characterization of quantum states, known as quantum state tomography, is a resource-consuming operation in general. An attractive proposal would be the use of Bell's inequalities as an entanglement witness, where only partial information of the quantum state is needed. The problem is that entanglement is necessary but not sufficient for violating Bell's inequalities, making it an unreliable state classifier. Here we aim at solving this problem by the methods of machine learning. More precisely, given a family of quantum states, we randomly picked a subset of it to construct a quantum-state classifier, accepting only partial information of each quantum state. Our results indicated that these transformed Bell-type inequalities can perform significantly better than the original Bell's inequalities in classifying entangled states. We further extended our analysis to three-qubit and four-qubit systems, performing classification of quantum states into multiple species. These results demonstrate how the tools in machine learning can be applied to solving problems in quantum information science.
- Apr 21 2017 quant-ph arXiv:1704.06174v2Solving linear systems of equations is a frequently encountered problem in machine learning and optimisation. Given a matrix $A$ and a vector $\mathbf b$ the task is to find the vector $\mathbf x$ such that $A \mathbf x = \mathbf b$. We describe a quantum algorithm that achieves a sparsity-independent runtime scaling of $\mathcal{O}(\kappa^2 \|A\|_F \text{polylog}(n)/\epsilon)$, where $n\times n$ is the dimensionality of $A$ with Frobenius norm $\|A\|_F$, $\kappa$ denotes the condition number of $A$, and $\epsilon$ is the desired precision parameter. When applied to a dense matrix with spectral norm bounded by a constant, the runtime of the proposed algorithm is bounded by $\mathcal{O}(\kappa^2\sqrt{n} \text{polylog}(n)/\epsilon)$, which is a quadratic improvement over known quantum linear system algorithms. Our algorithm is built upon a singular value estimation subroutine, which makes use of a memory architecture that allows for efficient preparation of quantum states that correspond to the rows and row Frobenius norms of $A$.
- Maximum likelihood estimation (MLE) is one of the most important methods in machine learning, and the expectation-maximization (EM) algorithm is often used to obtain maximum likelihood estimates. However, EM heavily depends on initial configurations and fails to find the global optimum. On the other hand, in the field of physics, quantum annealing (QA) was proposed as a novel optimization approach. Motivated by QA, we propose a quantum annealing extension of EM, which we call the deterministic quantum annealing expectation-maximization (DQAEM) algorithm. We also discuss its advantage in terms of the path integral formulation. Furthermore, by employing numerical simulations, we illustrate how it works in MLE and show that DQAEM outperforms EM.
- Apr 18 2017 quant-ph arXiv:1704.04992v3Quantum Machine Learning is an exciting new area that was initiated by the breakthrough quantum algorithm of Harrow, Hassidim, Lloyd \citeHHL09 for solving linear systems of equations and has since seen many interesting developments \citeLMR14, LMR13a, LMR14a, KP16. In this work, we start by providing a quantum linear system solver that outperforms the current ones for large families of matrices and provides exponential savings for any low-rank (even dense) matrix. Our algorithm uses an improved procedure for Singular Value Estimation which can be used to perform efficiently linear algebra operations, including matrix inversion and multiplication. Then, we provide the first quantum method for performing gradient descent for cases where the gradient is an affine function. Performing $\tau$ steps of the quantum gradient descent requires time $O(\tau C_S)$, where $C_S$ is the cost of performing quantumly one step of the gradient descent, which can be exponentially smaller than the cost of performing the step classically. We provide two applications of our quantum gradient descent algorithm: first, for solving positive semidefinite linear systems, and, second, for performing stochastic gradient descent for the weighted least squares problem.
- Quantum machine learning witnesses an increasing amount of quantum algorithms for data-driven decision making, a problem with potential applications ranging from automated image recognition to medical diagnosis. Many of those algorithms are implementations of quantum classifiers, or models for the classification of data inputs with a quantum computer. Following the success of collective decision making with ensembles in classical machine learning, this paper introduces the concept of quantum ensembles of quantum classifiers. Creating the ensemble corresponds to a state preparation routine, after which the quantum classifiers are evaluated in parallel and their combined decision is accessed by a single-qubit measurement. This framework naturally allows for exponentially large ensembles in which -- similar to Bayesian learning -- the individual classifiers do not have to be trained. As an example, we analyse an exponentially large quantum ensemble in which each classifier is weighed according to its performance in classifying the training data, leading to new results for quantum as well as classical machine learning.
- D-Wave quantum annealers represent a novel computational architecture and have attracted significant interest, but have been used for few real-world computations. Machine learning has been identified as an area where quantum annealing may be useful. Here, we show that the D-Wave 2X can be effectively used as part of an unsupervised machine learning method. This method can be used to analyze large datasets. The D-Wave only limits the number of features that can be extracted from the dataset. We apply this method to learn the features from a set of facial images.
- Deep convolutional networks have witnessed unprecedented success in various machine learning applications. Formal understanding on what makes these networks so successful is gradually unfolding, but for the most part there are still significant mysteries to unravel. The inductive bias, which reflects prior knowledge embedded in the network architecture, is one of them. In this work, we establish a fundamental connection between the fields of quantum physics and deep learning. We use this connection for asserting novel theoretical observations regarding the role that the number of channels in each layer of the convolutional network fulfills in the overall inductive bias. Specifically, we show an equivalence between the function realized by a deep convolutional arithmetic circuit (ConvAC) and a quantum many-body wave function, which relies on their common underlying tensorial structure. This facilitates the use of quantum entanglement measures as well-defined quantifiers of a deep network's expressive ability to model intricate correlation structures of its inputs. Most importantly, the construction of a deep ConvAC in terms of a Tensor Network is made available. This description enables us to carry a graph-theoretic analysis of a convolutional network, with which we demonstrate a direct control over the inductive bias of the deep network via its channel numbers, that are related to the min-cut in the underlying graph. This result is relevant to any practitioner designing a network for a specific task. We theoretically analyze ConvACs, and empirically validate our findings on more common ConvNets which involve ReLU activations and max pooling. Beyond the results described above, the description of a deep convolutional network in well-defined graph-theoretic tools and the formal connection to quantum entanglement, are two interdisciplinary bridges that are brought forth by this work.
- Apr 03 2017 quant-ph arXiv:1703.10793v2Lately, much attention has been given to quantum algorithms that solve pattern recognition tasks in machine learning. Many of these quantum machine learning algorithms try to implement classical models on large-scale universal quantum computers that have access to non-trivial subroutines such as Hamiltonian simulation, amplitude amplification and phase estimation. We approach the problem from the opposite direction and analyse a distance-based classifier that is realised by a simple quantum interference circuit. After state preparation, the circuit only consists of a Hadamard gate as well as two single-qubit measurements, and computes the distance between data points in quantum parallel. We demonstrate the proof-of-principle using the IBM Quantum Experience and analyse the performance of the classifier with numerical simulations, showing that it classifies surprisingly well for simple benchmark tasks.
- We present a feature functional theory - binding predictor (FFT-BP) for the protein-ligand binding affinity prediction. The underpinning assumptions of FFT-BP are as follows: i) representability: there exists a microscopic feature vector that can uniquely characterize and distinguish one protein-ligand complex from another; ii) feature-function relationship: the macroscopic features, including binding free energy, of a complex is a functional of microscopic feature vectors; and iii) similarity: molecules with similar microscopic features have similar macroscopic features, such as binding affinity. Physical models, such as implicit solvent models and quantum theory, are utilized to extract microscopic features, while machine learning algorithms are employed to rank the similarity among protein-ligand complexes. A large variety of numerical validations and tests confirms the accuracy and robustness of the proposed FFT-BP model. The root mean square errors (RMSEs) of FFT-BP blind predictions of a benchmark set of 100 complexes, the PDBBind v2007 core set of 195 complexes and the PDBBind v2015 core set of 195 complexes are 1.99, 2.02 and 1.92 kcal/mol, respectively. Their corresponding Pearson correlation coefficients are 0.75, 0.80, and 0.78, respectively.
- Mar 17 2017 quant-ph arXiv:1703.05402v1Efficiently characterising quantum systems, verifying operations of quantum devices and validating underpinning physical models, are central challenges for the development of quantum technologies and for our continued understanding of foundational physics. Machine-learning enhanced by quantum simulators has been proposed as a route to improve the computational cost of performing these studies. Here we interface two different quantum systems through a classical channel - a silicon-photonics quantum simulator and an electron spin in a diamond nitrogen-vacancy centre - and use the former to learn the latter's Hamiltonian via Bayesian inference. We learn the salient Hamiltonian parameter with an uncertainty of approximately $10^{-5}$. Furthermore, an observed saturation in the learning algorithm suggests deficiencies in the underlying Hamiltonian model, which we exploit to further improve the model itself. We go on to implement an interactive version of the protocol and experimentally show its ability to characterise the operation of the quantum photonic device. This work demonstrates powerful new quantum-enhanced techniques for investigating foundational physical models and characterising quantum technologies.
- The experimental realization of increasingly complex synthetic quantum systems calls for the development of general theoretical methods, to validate and fully exploit quantum resources. Quantum-state tomography (QST) aims at reconstructing the full quantum state from simple measurements, and therefore provides a key tool to obtain reliable analytics. Brute-force approaches to QST, however, demand resources growing exponentially with the number of constituents, making it unfeasible except for small systems. Here we show that machine learning techniques can be efficiently used for QST of highly-entangled states in arbitrary dimension. Remarkably, the resulting approach allows one to reconstruct traditionally challenging many-body quantities - such as the entanglement entropy - from simple, experimentally accessible measurements. This approach can benefit existing and future generations of devices ranging from quantum computers to ultra-cold atom quantum simulators.
- Molecular machine learning has been maturing rapidly over the last few years. Improved methods and the presence of larger datasets have enabled machine learning algorithms to make increasingly accurate predictions about molecular properties. However, algorithmic progress has been limited due to the lack of a standard benchmark to compare the efficacy of proposed methods; most new algorithms are benchmarked on different datasets making it challenging to gauge the quality of proposed methods. This work introduces MoleculeNet, a large scale benchmark for molecular machine learning. MoleculeNet curates multiple public datasets, establishes metrics for evaluation, and offers high quality open-source implementations of multiple previously proposed molecular featurization and learning algorithms (released as part of the DeepChem open source library). MoleculeNet benchmarks demonstrate that learnable representations, and in particular graph convolutional networks, are powerful tools for molecular machine learning and broadly offer the best performance. However, for quantum mechanical and biophysical datasets, the use of physics-aware featurizations can be significantly more important than choice of particular learning algorithm.
- Feb 21 2017 cond-mat.mtrl-sci physics.chem-ph arXiv:1702.05771v1High-throughput computational screening has emerged as a critical component of materials discovery. Direct density functional theory (DFT) simulation of inorganic materials and molecular transition metal complexes is often used to describe subtle trends in inorganic bonding and spin-state ordering, but these calculations are computationally costly and properties are sensitive to the exchange-correlation functional employed. To begin to overcome these challenges, we trained artificial neural networks (ANNs) to predict quantum-mechanically-derived properties, including spin-state ordering, sensitivity to Hartree-Fock exchange, and spin- state specific bond lengths in transition metal complexes. Our ANN is trained on a small set of inorganic-chemistry-appropriate empirical inputs that are both maximally transferable and do not require precise three-dimensional structural information for prediction. Using these descriptors, our ANN predicts spin-state splittings of single-site transition metal complexes (i.e., Cr-Ni) at arbitrary amounts of Hartree-Fock exchange to within 3 kcal/mol accuracy of DFT calculations. Our exchange-sensitivity ANN enables improved predictions on a diverse test set of experimentally-characterized transition metal complexes by extrapolation from semi-local DFT to hybrid DFT. The ANN also outperforms other machine learning models (i.e., support vector regression and kernel ridge regression), demonstrating particularly improved performance in transferability, as measured by prediction errors on the diverse test set. We establish the value of new uncertainty quantification tools to estimate ANN prediction uncertainty in computational chemistry, and we provide additional heuristics for identification of when a compound of interest is likely to be poorly predicted by the ANN.
- Feb 21 2017 physics.chem-ph arXiv:1702.05532v2We investigate the impact of choosing regressors and molecular representations for the construction of fast machine learning (ML) models of thirteen electronic ground-state properties of organic molecules. The performance of each regressor/representation/property combination is assessed using learning curves which report out-of-sample errors as a function of training set size with up to $\sim$117k distinct molecules. Molecular structures and properties at hybrid density functional theory (DFT) level of theory used for training and testing come from the QM9 database [Ramakrishnan et al, \em Scientific Data \bf 1 140022 (2014)] and include dipole moment, polarizability, HOMO/LUMO energies and gap, electronic spatial extent, zero point vibrational energy, enthalpies and free energies of atomization, heat capacity and the highest fundamental vibrational frequency. Various representations from the literature have been studied (Coulomb matrix, bag of bonds, BAML and ECFP4, molecular graphs (MG)), as well as newly developed distribution based variants including histograms of distances (HD), and angles (HDA/MARAD), and dihedrals (HDAD). Regressors include linear models (Bayesian ridge regression (BR) and linear regression with elastic net regularization (EN)), random forest (RF), kernel ridge regression (KRR) and two types of neural net works, graph convolutions (GC) and gated graph networks (GG). We present numerical evidence that ML model predictions deviate from DFT less than DFT deviates from experiment for all properties. Furthermore, our out-of-sample prediction errors with respect to hybrid DFT reference are on par with, or close to, chemical accuracy. Our findings suggest that ML models could be more accurate than hybrid DFT if explicitly electron correlated quantum (or experimental) data was available.
- This paper surveys quantum learning theory: the theoretical aspects of machine learning using quantum computers. We describe the main results known for three models of learning: exact learning from membership queries, and Probably Approximately Correct (PAC) and agnostic learning from classical or quantum examples.
- Jan 19 2017 cond-mat.dis-nn quant-ph arXiv:1701.05039v1The challenge of quantum many-body problems comes from the difficulty to represent large-scale quantum states, which in general requires an exponentially large number of parameters. Recently, a connection has been made between quantum many-body states and the neural network representation (\textitarXiv:1606.02318). An important open question is what characterizes the representational power of deep and shallow neural networks, which is of fundamental interest due to popularity of the deep learning methods. Here, we give a rigorous proof that a deep neural network can efficiently represent most physical states, including those generated by any polynomial size quantum circuits or ground states of many body Hamiltonians with polynomial-size gaps, while a shallow network through a restricted Boltzmann machine cannot efficiently represent those states unless the polynomial hierarchy in computational complexity theory collapses.
- Superconducting circuit technologies have recently achieved quantum protocols involving closed feedback loops. Quantum artificial intelligence and quantum machine learning are emerging fields inside quantum technologies which may enable quantum devices to acquire information from the outer world and improve themselves via a learning process. Here we propose the implementation of basic protocols in quantum reinforcement learning, with superconducting circuits employing feedback-loop control. We introduce diverse scenarios for proof-of-principle experiments with state-of-the-art superconducting circuit technologies and analyze their feasibility in presence of imperfections. The field of quantum artificial intelligence implemented with superconducting circuits paves the way for enhanced quantum control and quantum computation protocols.
- Restricted Boltzmann machine (RBM) is one of the fundamental building blocks of deep learning. RBM finds wide applications in dimensional reduction, feature extraction, and recommender systems via modeling the probability distributions of a variety of input data including natural images, speech signals, and customer ratings, etc. We build a bridge between RBM and tensor network states (TNS) widely used in quantum many-body physics research. We devise efficient algorithms to translate an RBM into the commonly used TNS. Conversely, we give sufficient and necessary conditions to determine whether a TNS can be transformed into an RBM of given architectures. Revealing these general and constructive connections can cross-fertilize both deep learning and quantum-many body physics. Notably, by exploiting the entanglement entropy bound of TNS, we can rigorously quantify the expressive power of RBM on complex datasets. Insights into TNS and its entanglement capacity can guide the design of more powerful deep learning architectures. On the other hand, RBM can represent quantum many-body states with fewer parameters compared to TNS, which may allow more efficient classical simulations.
- Machine learning, one of today's most rapidly growing interdisciplinary fields, promises an unprecedented perspective for solving intricate quantum many-body problems. Understanding the physical aspects of the representative artificial neural-network states is recently becoming highly desirable in the applications of machine learning techniques to quantum many-body physics. Here, we study the quantum entanglement properties of neural-network states, with a focus on the restricted-Boltzmann-machine (RBM) architecture. We prove that the entanglement of all short-range RBM states satisfies an area law for arbitrary dimensions and bipartition geometry. For long-range RBM states we show by using an exact construction that such states could exhibit volume-law entanglement, implying a notable capability of RBM in representing efficiently quantum states with massive entanglement. We further examine generic RBM states with random weight parameters. We find that their averaged entanglement entropy obeys volume-law scaling and meantime strongly deviates from the Page-entropy of the completely random pure states. We show that their entanglement spectrum has no universal part associated with random matrix theory and bears a Poisson-type level statistics. Using reinforcement learning, we demonstrate that RBM is capable of finding the ground state (with power-law entanglement) of a model Hamiltonian with long-range interaction. In addition, we show, through a concrete example of the one-dimensional symmetry-protected topological cluster states, that the RBM representation may also be used as a tool to analytically compute the entanglement spectrum. Our results uncover the unparalleled power of artificial neural networks in representing quantum many-body states, which paves a novel way to bridge computer science based machine learning techniques to outstanding quantum condensed matter physics problems.