- We construct a linear system non-local game which can be played perfectly using a limit of finite-dimensional quantum strategies, but which cannot be played perfectly on any finite-dimensional Hilbert space, or even with any tensor-product strategy. In particular, this shows that the set of (tensor-product) quantum correlations is not closed. The constructed non-local game provides another counterexample to the "middle" Tsirelson problem, with a shorter proof than our previous paper (though at the loss of the universal embedding theorem). We also show that it is undecidable to determine if a linear system game can be played perfectly with a limit of finite-dimensional quantum strategies.
- Mar 28 2017 cond-mat.str-el quant-ph arXiv:1703.09188v1Matrix Product Vectors form the appropriate framework to study and classify one-dimensional quantum systems. In this work, we develop the structure theory of Matrix Product Unitary operators (MPUs) which appear e.g. in the description of time evolutions of one-dimensional systems. We prove that all MPUs have a strict causal cone, making them Quantum Cellular Automata (QCAs), and derive a canonical form for MPUs which relates different MPU representations of the same unitary through a local gauge. We use this canonical form to prove an Index Theorem for MPUs which gives the precise conditions under which two MPUs are adiabatically connected, providing an alternative derivation to that of [Commun. Math. Phys. 310, 419 (2012), arXiv:0910.3675] for QCAs. We also discuss the effect of symmetries on the MPU classification. In particular, we characterize the tensors corresponding to MPU that are invariant under conjugation, time reversal, or transposition. In the first case, we give a full characterization of all equivalence classes. Finally, we give several examples of MPU possessing different symmetries.
- Mar 24 2017 quant-ph arXiv:1703.07847v1We present an infinite family of protocols to distill magic states for $T$-gates that has a low space overhead and uses an asymptotic number of input magic states to achieve a given target error that is conjectured to be optimal. The space overhead, defined as the ratio between the physical qubits to the number of output magic states, is asymptotically constant, while both the number of input magic states used per output state and the $T$-gate depth of the circuit scale linearly in the logarithm of the target error $\delta$ (up to $\log \log 1/\delta$). Unlike other distillation protocols, this protocol achieves this performance without concatenation and the input magic states are injected at various steps in the circuit rather than all at the start of the circuit. The protocol can be modified to distill magic states for other gates at the third level of the Clifford hierarchy, with the same asymptotic performance. The protocol relies on the construction of weakly self-dual CSS codes with many logical qubits and large distance, allowing us to implement control-SWAPs on multiple qubits. We call this code the "inner code". The control-SWAPs are then used to measure properties of the magic state and detect errors, using another code that we call the "outer code". Alternatively, we use weakly-self dual CSS codes which implement controlled Hadamards for the inner code, reducing circuit depth. We present several specific small examples of this protocol.
- Mar 24 2017 quant-ph arXiv:1703.08118v1A central result in the study of Quantum Hamiltonian Complexity is that the k-Local hamiltonian problem is QMA-complete. In that problem, we must decide if the lowest eigenvalue of a Hamiltonian is bounded below some value, or above another, promised one of these is true. Given the ground state of the Hamiltonian, a quantum computer can determine this question, even if the ground state itself may not be efficiently quantum preparable. Kitaev's proof of QMA-completeness encodes a unitary quantum circuit in QMA into the ground space of a Hamiltonian. However, we now have quantum computing models based on measurement instead of unitary evolution, furthermore we can use post-selected measurement as an additional computational tool. In this work, we generalise Kitaev's construction to allow for non-unitary evolution including post-selection. Furthermore, we consider a type of post-selection under which the construction is consistent, which we call tame post-selection. We consider the computational complexity consequences of this construction and then consider how the probability of an event upon which we are post-selecting affects the gap between the ground state energy and the energy of the first excited state of its corresponding Hamiltonian. We provide numerical evidence that the two are not immediately related, by giving a family of circuits where the probability of an event upon which we post-select is exponentially small, but the gap in the energy levels of the Hamiltonian decreases as a polynomial.
- Mar 27 2017 quant-ph arXiv:1703.08179v1We demonstrate that small quantum memories, realized via quantum error correction in multi-qubit devices, can benefit substantially by choosing a quantum code that is tailored to the relevant error model of the system. For a biased noise model, with independent bit and phase flips occurring at different rates, we show that a single code greatly outperforms the well-studied Steane code across the full range of parameters of the noise model, including for unbiased noise. In fact, this tailored code performs almost optimally when compared with 10,000 randomly selected stabilizer codes of comparable experimental complexity. Tailored codes can even outperform the Steane code with realistic experimental noise, and without any increase in the experimental complexity, as we demonstrate by comparison in the observed error model in a recent 7-qubit trapped ion experiment.
- We study 't Hooft anomalies of discrete groups in the framework of (1+1)-dimensional multiscale entanglement renormalization ansatz states on the lattice. Using matrix product operators, general topological restrictions on conformal data are derived. An ansatz class allowing for optimization of MERA with an anomalous symmetry is introduced. We utilize this class to numerically study a family of Hamiltonians with a symmetric critical line. Conformal data is obtained for all irreducible projective representations of each anomalous symmetry twist, corresponding to definite topological sectors. It is numerically demonstrated that this line is a protected gapless phase. Finally, we implement a duality transformation between a pair of critical lines using our subclass of MERA.
- Mar 30 2017 quant-ph arXiv:1703.09835v1Previous analysis of randomized benchmarking assumed that experimental noise "weakly" depends on the target gate. We show that this condition is more restrictive than it initially appears, so much so that it is practically unverifiable. We then resolve this limitation by proving that the exact impact of gate-dependent noise can be described by a single perturbation term that decays exponentially with the sequence length. That is, the exact behavior of randomized benchmarking under general gate-dependent noise converges exponentially to a true exponential decay of exactly the same form as that predicted by previous analysis for gate-independent noise. Moreover, we show that the operational meaning of the decay rate for gate-dependent noise is essentially unchanged, that is, we show that it quantifies the average fidelity of the noise between ideal gates. We numerically demonstrate that our analysis is valid for realistic gate-dependent noise models.
- Scrambling is a process by which the state of a quantum system is effectively randomized. Scrambling exhibits different complexities depending on the degree of randomness it produces. For example, the complete randomization of a pure quantum state (Haar scrambling) implies the inability to retrieve information of the initial state by measuring only parts of the system (Page/information scrambling), but the converse is not necessarily the case. Here, we formally relate scrambling complexities to the degree of randomness, by studying the behaviors of generalized entanglement entropies -- in particular Rényi entropies -- and their relationship to designs, ensembles of states or unitaries that match the completely random states or unitaries (drawn from the Haar measure) up to certain moments. The main result is that the Rényi-$\alpha$ entanglement entropies, averaged over $\alpha$-designs, are almost maximal. The result generalizes Page's theorem for the von Neumann entropies of small subsystems of random states. For designs of low orders, the average Rényi entanglement entropies can be non-maximal: we exhibit a projective 2-design such that all higher order Rényi entanglement entropies are bounded away from the maximum. However, we show that the Rényi entanglement entropies of all orders are almost maximal for state or unitary designs of order logarithmic in the dimension of the system. That is, such designs are indistinguishable from Haar-random by the entanglement spectrum. Our results establish a formal correspondence between generalized entropies and designs of the same order.
- Mar 30 2017 quant-ph arXiv:1703.10133v1We investigate the relationship between the energy spectrum of a local Hamiltonian and the geometric properties of its ground state. By generalizing a standard framework from the analysis of Markov chains to arbitrary (non-stoquastic) Hamiltonians we are naturally led to see that the spectral gap can always be upper bounded by an isoperimetric ratio that depends only on the ground state probability distribution and the range of the terms in the Hamiltonian, but not on any other details of the interaction couplings. This means that for a given probability distribution the inequality constrains the spectral gap of any local Hamiltonian with this distribution as its ground state probability distribution in some basis (Eldar and Harrow derived a similar result [1] in order to characterize the output of low-depth quantum circuits). Going further, we relate the Hilbert space localization properties of the ground state to higher energy eigenvalues by showing that the presence of k strongly localized ground state modes (i.e. clusters of probability, or subsets with small expansion) in Hilbert space implies the presence of k energy eigenvalues that are close to the ground state energy. Our results suggest that quantum adiabatic optimization using local Hamiltonians will inevitably encounter small spectral gaps when attempting to prepare ground states corresponding to multi-modal probability distributions with strongly localized modes, and this problem cannot necessarily be alleviated with the inclusion of non-stoquastic couplings.
- In this thesis we study properties of open quantum dissipative evolutions of spin systems on lattices described by Lindblad generators, in a particular regime that we denote rapid mixing. We consider dissipative evolutions with a unique fixed point, and which compress the whole space of input states into increasingly small neighborhoods of the fixed point. The time scale at which this compression takes place, or in other words the time we have to wait for any input state to become almost indistinguishable from the fixed point, is called the mixing time of the process. Rapid mixing is a condition on the scaling of this mixing time with the system size: if it is logarithmic, then we have rapid mixing. The main contribution of this thesis is to show that rapid mixing has profound implications for the corresponding system: it is stable against external perturbations and its fixed point satisfies an area law for mutual information.
- Mar 27 2017 quant-ph arXiv:1703.08508v1We give an arguably simpler and more direct proof of a recent result by Miller, Jain and Shi, who proved device-independent security of a protocol for quantum key distribution in which the devices can be used in parallel. Our proof combines existing results on immunization (Kempe et al., SICOMP 2011) and parallel repetition (Bavarian et al., STOC 2017) of entangled games.
- Mar 29 2017 quant-ph arXiv:1703.09656v1We quantify the usefulness of a bipartite quantum state in the ancilla-assisted channel discrimination of arbitrary quantum channels, formally defining a worst-case-scenario channel discrimination power for bipartite quantum states. We show that such a quantifier is deeply connected with the operator Schmidt decomposition of the state. We compute the channel discrimination power exactly for pure states, and provide upper and lower bounds for general mixed states. We show that highly entangled states can outperform any state that passes the realignment criterion for separability. Furthermore, while also unentangled states can be used in ancilla-assisted channel discrimination, we show that the channel discrimination power of a state is bounded by its quantum discord.
- Mar 30 2017 quant-ph arXiv:1703.09747v1We compute the expected randomized benchmarking sequence fidelity for a system subject to Gaussian time-correlated noise. For single qubit benchmarking we show that the expected sequence fidelity is given by the partition function of a long-range coupled spin-one Ising model, with each site in the Ising model corresponding to a free evolution interval. For d-state systems, the expected sequence fidelity is given by an Ising-like model partition function whose site variables are given by the weights of the adjoint representation of SU(d). A high effective temperature expansion for the partition function in the single qubit case shows decay of sequence fidelity varying from exponential for uncorrelated noise to a power law for quasistatic noise. Fitting an exponential to the sequence fidelity decay under correlated noise gives unreliable estimates of the average gate error rate.
- In this work we consider a quantum generalization of the task considered by Slepian and Wolf [1973] regarding distributed source compression. In our task Alice, Bob, Charlie and Referee share a joint pure state. Alice and Bob wish to send a part of their respective systems to Charlie without collaborating with each other. We give achievability bounds for this task in the one-shot setting and provide asymptotic analysis in the case when there is no side information with Charlie. Our result implies the result of Abeyesinghe, Devetak, Hayden and Winter [2009] who studied a special case of this problem. As another special case wherein Bob holds trivial registers, we recover the result of Devetak and Yard [2008] regarding quantum state redistribution.
- Mar 24 2017 quant-ph arXiv:1703.07901v1Recent years have seen significant advances in the study of symmetric informationally complete (SIC) quantum measurements, also known as maximal sets of complex equiangular lines. Previously, the published record contained solutions up to dimension 67, and was with high confidence complete up through dimension 50. Computer calculations have now furnished solutions in all dimensions up to 151, and in several cases beyond that, as large as dimension 323. These new solutions exhibit an additional type of symmetry beyond the basic definition of a SIC, and so verify a conjecture of Zauner in many new cases. The solutions in dimensions 68 through 121 were obtained by Andrew Scott, and his catalogue of distinct solutions is, with high confidence, complete up to dimension 90. Additional results in dimensions 122 through 151 were calculated by the authors using Scott's code. We recap the history of the problem, outline how the numerical searches were done, and pose some conjectures on how the search technique could be improved. In order to facilitate communication across disciplinary boundaries, we also present a comprehensive bibliography of SIC research.
- Mar 29 2017 quant-ph arXiv:1703.09277v1Recent theoretical and experimental studies have suggested that quantum Monte Carlo (QMC) simulation can behave similarly to quantum annealing (QA). The theoretical analysis was based on calculating transition rates between local minima, in the large spin limit using WentzelKramers-Brillouin (WKB) approximation, for highly symmetric systems of ferromagnetically coupled qubits. The rate of transition was observed to scale the same in QMC and incoherent quantum tunneling, implying that there might be no quantum advantage of QA compared to QMC other than a prefactor. Quantum annealing is believed to provide quantum advantage through large scale superposition and entanglement and not just incoherent tunneling. Even for incoherent tunneling, the scaling similarity with QMC observed above does not hold in general. Here, we compare incoherent tunneling and QMC escape using perturbation theory, which has much wider validity than WKB approximation. We show that the two do not scale the same way when there are multiple homotopy-inequivalent paths for tunneling. We demonstrate through examples that frustration can generate an exponential number of tunneling paths, which under certain conditions can lead to an exponential advantage for incoherent tunneling over classical QMC escape. We provide analytical and numerical evidence for such an advantage and show that it holds beyond perturbation theory.
- Mar 27 2017 quant-ph arXiv:1703.08272v1The appearance of negative terms in quasiprobability representations of quantum theory is known to be inevitable, and, due to its equivalence with the onset of contextuality, of central interest in quantum computation and information. Until recently, however, nothing has been known about how much negativity is necessary in a quasiprobability representation. Zhu proved that the upper and lower bounds with respect to one type of negativity measure are saturated by quasiprobability representations which are in one-to-one correspondence with the elusive symmetric informationally complete quantum measurements (SICs). We define a family of negativity measures which includes Zhu's as a special case and consider another member of the family which we call "sum negativity." We prove a sufficient condition for local maxima in sum negativity and find exact global maxima in dimensions $3$ and $4$. Notably, we find that Zhu's result on the SICs does not generally extend to sum negativity, although the analogous result does hold in dimension $4$. Finally, the Hoggar lines in dimension $8$ make an appearance in a conjecture on sum negativity.
- Mar 27 2017 cond-mat.mes-hall quant-ph arXiv:1703.08224v1We analyse the control of Majorana zero-energy states by mapping the fermionic system onto a chain of Ising spins. Although the topological protection is lost for the Ising chain, the properties of this system provide added insight into the nature of the quantum states. By controlling the local magnetic field, the Ising chain can be separated into topological and non-topological parts. In this paper we propose (topologically non-protected) schemes which allow performing the braiding operation, and in fact also more general rotations. We consider a T-junction geometry, but we also propose a protocol for a strictly one-dimensional setup. Both setups rely on an extra spin-1/2 coupler included either in the T-junction, or as part of the chain such that it controls one of the Ising links. Depending on the quantum state of the coupler, this link can be either ferromagnetic or antiferromagnetic. The coupler can be manipulated once the topological parts of the chain hosting the Majorana fermions are moved far away. Our scheme overcomes limitations which are a consequence of the 1D character of the Jordan-Wigner transformation. We also propose an experimental implementation of our scheme based on a chain of flux qubits with a design providing the needed control fields.
- Mar 30 2017 quant-ph arXiv:1703.10134v1We define a discrete-time, coined quantum walk on weighted graphs that is inspired by Szegedy's quantum walk. Using this, we prove that many lackadaisical quantum walks, where each vertex has $l$ integer self-loops, can be generalized to a quantum walk where each vertex has a single self-loop of real-valued weight $l$. We apply this real-valued lackadaisical quantum walk to two problems. First, we analyze it on the line or one-dimensional lattice, showing that it is exactly equivalent to a continuous deformation of the three-state Grover walk with faster ballistic dispersion. Second, we generalize Grover's algorithm, or search on the complete graph, to have a weighted self-loop at each vertex, yielding an improved success probability when $l < 3 + 2\sqrt{2} \approx 5.828$.
- Quantum Tunneling is ubiquitous across different fields, from quantum chemical reactions, and magnetic materials to quantum simulators and quantum computers. While simulating the real-time quantum dynamics of tunneling is infeasible for high-dimensional systems, quantum tunneling also shows up in quantum Monte Carlo (QMC) simulations that scale polynomially with system size. Here we extend a recent results obtained for quantum spin models [Phys. Rev. Lett. \bf 117, 180402 (2016)], and study high-dimensional continuos variable models for proton transfer reactions. We demonstrate that QMC simulations efficiently recover ground state tunneling rates due to the existence of an instanton path, which always connects the reactant state with the product. We discuss the implications of our results in the context of quantum chemical reactions and quantum annealing, where quantum tunneling is expected to be a valuable resource for solving combinatorial optimization problems.
- Mar 28 2017 quant-ph arXiv:1703.09123v1We develop a general theory to estimate magnetic field gradients in quantum metrology. We consider a system of $N$ particles distributed on a line whose internal degrees of freedom interact with a magnetic field. Classically, gradient estimation is based on precise measurements of the magnetic field at two different locations, performed with two independent groups of particles. This approach, however, is sensitive to fluctuations of the off-set field determining the level-splitting of the ions and therefore suffers from collective dephasing, so we concentrate on states which are insensitive to these fluctuations. States from the decoherence-free subspace (DFS) allow to measure the gradient directly, without estimating the magnetic field. We use the framework of quantum metrology to assess the maximal accuracy of the precision of gradient estimation. We find that states from the DFS achieve the highest measurement sensitivity, as quantified by the quantum Fisher information and find measurements saturating the quantum Cramér-Rao bound.
- We consider sequences of random quantum channels defined using the Stinespring formula with Haar-distributed random orthogonal matrices. For any fixed sequence of input states, we study the asymptotic eigenvalue distribution of the outputs through tensor powers of random channels. We show that the input states achieving minimum output entropy are tensor products of maximally entangled states (Bell states) when the tensor power is even. This phenomenon is completely different from the one for random quantum channels constructed from Haar-distributed random unitary matrices, which leads us to formulate some conjectures about the regularized minimum output entropy.
- Mar 30 2017 quant-ph cond-mat.supr-con arXiv:1703.09762v1One of the largest obstacles to building a quantum computer is gate error, where the physical evolution of the state of a qubit or group of qubits during a gate operation does not match the intended unitary transformation. Gate error stems from a combination of control errors and random single qubit errors from interaction with the environment. While great strides have been made in mitigating control errors, intrinsic qubit error remains a serious problem that sets the primary limit for gate fidelity in modern superconducting qubit architectures. Simultaneously, recent developments of small error-corrected logical qubit devices promise significant increases in logical state lifetime, but translating those improvements into increases in gate fidelity is a complex challenge. In this Letter, we propose a new formalism for implementing gates on and between small logical qubit devices which inherit the parent device's tolerance to single qubit errors which occur at any time before or during the gate. Using a standard phenomenological noise model for superconducting qubits, we demonstrate a universal one- and two-qubit gate set with error rates an order of magnitude lower than those for equivalent operations on single qubits or pairs of qubits, running for the same total duration. The effective logical gate error rate in these models displays superlinear error reduction with linear increases in single qubit lifetime, proving that passive error correction is capable of increasing gate fidelity. These developments further suggest that incorporating small logical qubits into a measurement based code could substantially improve code performance.
- Mar 28 2017 cond-mat.stat-mech arXiv:1703.09195v1The existence or absence of non-analytic cusps in the Loschmidt-echo return rate is traditionally employed to distinguish between a regular dynamical phase (regular cusps) and a trivial phase (no cusps) in quantum spin chains after a global quench. However, numerical evidence in a recent study [J. C. Halimeh and V. Zauner-Stauber, arXiv:1610.02019] suggests that instead of the trivial phase a distinct anomalous dynamical phase characterized by a novel type of non-analytic cusps occurs in the one-dimensional transverse-field Ising model when interactions are sufficiently long-range. Using an analytic semiclassical approach and exact diagonalization, we show that this anomalous phase also arises in the fully-connected case of infinite-range interactions, and we discuss its defining signature. Our results show that the transition from the regular to the anomalous dynamical phase coincides with Z2-symmetry breaking in the infinite-time limit, thereby showing a connection between two different concepts of dynamical criticality. Our work further expands the dynamical phase diagram of long-range interacting quantum spin chains, and can be tested experimentally in ion-trap setups and ultracold atoms in optical cavities, where interactions are inherently long-range.
- Mar 28 2017 quant-ph arXiv:1703.09056v1We study gradient magnetometry with an ensemble of atoms with arbitrary spin. We consider the case of a very general spatial probability distribution function. We calculate precision bounds for estimating the gradient of the magnetic field based on the quantum Fisher information. For quantum states that are invariant under homogeneous magnetic fields, we need to measure a single observable to estimate the gradient. On the other hand, for states that are sensitive to homogeneous fields, the measurement of two observables are needed, as the homogeneous field must also be estimated. This leads to a two-parameter estimation problem. We present a method to calculate precision bounds for gradient estimation with a chain of atoms or with two spatially separated atomic ensembles feeling different magnetic fields. We also consider a single atomic ensemble with an arbitrary density profile, in which the atoms cannot be addressed individually, and which is a very relevant case for experiments. Our model can take into account even correlations between particle positions.
- Mar 27 2017 cond-mat.str-el arXiv:1703.08421v1We review two important non-perturbative approaches for extracting the physics of low-dimensional strongly correlated quantum systems. Firstly, we start by providing a comprehensive review of non-Abelian bosonization. This includes an introduction to the basic elements of conformal field theory as applied to systems with a current algebra, and we orient the reader by presenting a number of applications of non-Abelian bosonization to models with large symmetries. We then tie this technique into recent advances in the ability of cold atomic systems to realize complex symmetries. Secondly, we discuss truncated spectrum methods for the numerical study of systems in one and two dimensions. For one-dimensional systems we provide the reader with considerable insight into the methodology by reviewing canonical applications of the technique to the Ising model (and its variants) and the sine-Gordon model. Following this we review recent work on the development of renormalization groups, both numerical and analytical, that alleviate the effects of truncating the spectrum. Using these technologies, we consider a number of applications to one-dimensional systems: properties of carbon nanotubes, quenches in the Lieb-Liniger model, 1+1D quantum chromodynamics, as well as Landau-Ginzburg theories. In the final part we move our attention to consider truncated spectrum methods applied to two-dimensional systems. This involves combining truncated spectrum methods with matrix product state algorithms. We describe applications of this method to two-dimensional systems of free fermions and the quantum Ising model, including their non-equilibrium dynamics.
- Mar 24 2017 cond-mat.str-el arXiv:1703.08172v1Non-Fermi liquids arise when metals are subject to singular interactions mediated by soft collective modes. In the absence of well-defined quasiparticle, universal physics of non-Fermi liquids is captured by interacting field theories which replace Landau Fermi liquid theory. In this review, we discuss two approaches that have been recently developed for non-Fermi liquid theory with emphasis on two space dimensions. The first is a perturbative scheme based on a dimensional regularization, which achieves a controlled access to the low-energy physics by tuning the number of co-dimensions of Fermi surface. The second is a non-perturbative approach which treats the interaction ahead of the kinetic term through a non-Gaussian scaling called interaction-driven scaling. Examples of strongly coupled non-Fermi liquids amenable to exact treatments through the interaction-driven scaling are discussed.
- Models of quantum systems on curved space-times lack sufficient experimental verification. Some speculative theories suggest that quantum properties, such as entanglement, may exhibit entirely different behavior to purely classical systems. By measuring this effect or lack thereof, we can test the hypotheses behind several such models. For instance, as predicted by Ralph and coworkers [T C Ralph, G J Milburn, and T Downes, Phys. Rev. A, 79(2):22121, 2009; T C Ralph and J Pienaar, New Journal of Physics, 16(8):85008, 2014], a bipartite entangled system could decohere if each particle traversed through a different gravitational field gradient. We propose to study this effect in a ground to space uplink scenario. We extend the above theoretical predictions of Ralph and coworkers and discuss the scientific consequences of detecting/failing to detect the predicted gravitational decoherence. We present a detailed mission design of the European Space Agency's (ESA) Space QUEST (Space - Quantum Entanglement Space Test) mission, and study the feasibility of the mission schema.
- Mar 24 2017 cond-mat.stat-mech hep-th arXiv:1703.08054v1The flow of the low energy eigenstates of a $U_q[sl(2|1)]$ superspin chain with alternating fundamental ($3$) and dual ($\bar{3}$) representations is studied as function of a twist angle determining the boundary conditions. The finite size spectrum is characterized in terms of scaling dimensions and quasi momenta representing the two families of commuting transfer matrices for the model which are even and odd under the interchange $3\leftrightarrow \bar{3}$, respectively. Varying boundary conditions from periodic to antiperiodic for the fermionic degrees of freedom levels from the continuous part of the finite size spectrum are found to flow into discrete levels and vice versa.
- Mar 29 2017 quant-ph arXiv:1703.09576v1In the task of assisted coherence distillation via the set of operations X, where X is either local incoherent operations and classical communication (LICC), local quantum-incoherent operations and classical communication (LQICC), separable incoherent operations (SI), or separable quantum incoherent operations (SQI), two parties, namely Alice and Bob, share many copies of a bipartite joint state. The aim of the process is to generate the maximal possible coherence on the subsystem of Bob. In this paper, we investigate the assisted coherence distillation of some special mixed states, the states with vanished basis-dependent discord and Werner states. We show that all the four sets of operations are equivalent for assisted coherence distillation, whenever Alice and Bob share one of those mixed quantum states. Moreover, we prove that the assisted coherence distillation of the former can reach the upper bound, namely QI relative entropy, while that of the latter can not. Meanwhile, we also present a sufficient condition such that the assistance of Alice via the set of operations X can not help Bob improve his distillable coherence, and this condition is that the state shared by Alice and Bob has vanished basis-dependent discord.
- Mar 29 2017 quant-ph arXiv:1703.09568v1Quantum samplers are believed capable of sampling efficiently from distributions that are classically hard to sample from. We consider a sampler inspired by the Ising model. It is nonadaptive and therefore experimentally amenable. Under a plausible average-case hardness conjecture, classical sampling upto additive errors from this model is known to be hard. We present a trap-based verification scheme for quantum supremacy that only requires the verifier to prepare single-qubit states. The verification is done on the same model as the original sampler, a square lattice, with only a constant factor overhead. We next revamp our verification scheme to operate in the presence of noise by emulating a fault-tolerant procedure without correcting on-line for the errors, thus keeping the model non-adaptive, but verifying supremacy fault-tolerantly. We show that classically sampling upto additive errors is likely hard in our revamped scheme. Our results are applicable to more general sampling problems such as the Instantaneous Quantum Polynomial-time (IQP) computation model. It should also assist near-term attempts at experimentally demonstrating quantum supremacy and guide long-term ones.
- Mar 29 2017 quant-ph arXiv:1703.09236v1We address the dynamics of a bosonic system coupled to either a bosonic or a magnetic environment, and derive a set of sufficient conditions that allow one to describe the dynamics in terms of the effective interaction with a classical fluctuating field. We find that for short interaction times the dynamics of the open system is described by a Gaussian noise map for several different interaction models and independently on the temperature of the environment. More generally, our results indicate that quantum environments may be described by classical fields whenever global symmetries lead to the definition of environmental operators that remain well defined when increasing the size of the environment.
- Mar 30 2017 cond-mat.str-el cond-mat.quant-gas arXiv:1703.10141v1It is commonly believed that in quantum Monte Carlo approaches to fermionic many- body problems, the infamous sign problem generically implies prohibitively large computational times for obtaining thermodynamic-limit quantities. We point out that for convergent Feynman diagrammatic series evaluated with the Monte Carlo algorithm of [Rossi, arXiv:1612.05184], the computational time increases only polynomially with the inverse error on thermodynamic-limit quantities.
- A text-to-speech synthesis system typically consists of multiple stages, such as a text analysis frontend, an acoustic model and an audio synthesis module. Building these components often requires extensive domain expertise and may contain brittle design choices. In this paper, we present Tacotron, an end-to-end generative text-to-speech model that synthesizes speech directly from characters. Given <text, audio> pairs, the model can be trained completely from scratch with random initialization. We present several key techniques to make the sequence-to-sequence framework perform well for this challenging task. Tacotron achieves a 3.82 subjective 5-scale mean opinion score on US English, outperforming a production parametric system in terms of naturalness. In addition, since Tacotron generates speech at the frame level, it's substantially faster than sample-level autoregressive methods.
- Mar 30 2017 quant-ph arXiv:1703.10118v1Amplitude amplification is one of primary tools in building algorithms for quantum computers. This technique develops key ideas of the Grover search algorithm. The original formulation by Grover has been reformulated in order to to make building blocks of the algorithm as generally as possible. Potentially useful modifications are connected with changing phases in the rotation operations and replacing the intermediate Hadamard transform with arbitrary unitary one. In addition, arbitrary initial distribution of the amplitudes may be prepared. There are practical problems, in which we may have \it a priori information about the database. We examine trade-off relations between measures of quantum coherence and the success probability in amplitude amplification processes. We try to understand how prior knowledge and other modifications of algorithm blocks should be exploited properly. As measures of coherence, the geometric coherence and the relative entropy of coherence are mainly considered. In terms of the relative entropy of coherence, complementarity relations with the success probability seem to be the most expository. The general relations presented are illustrated within several model scenarios of amplitude amplification process.
- Mar 30 2017 cs.CV arXiv:1703.10106v1We address human action recognition from multi-modal video data involving articulated pose and RGB frames and propose a two-stream approach. The pose stream is processed with a convolutional model taking as input a 3D tensor holding data from a sub-sequence. A specific joint ordering, which respects the topology of the human body, ensures that different convolutional layers correspond to meaningful levels of abstraction. The raw RGB stream is handled by a spatio-temporal soft-attention mechanism conditioned on features from the pose network. An LSTM network receives input from a set of image locations at each instant. A trainable glimpse sensor extracts features on a set of predefined locations specified by the pose stream, namely the 4 hands of the two people involved in the activity. Appearance features give important cues on hand motion and on objects held in each hand. We show that it is of high interest to shift the attention to different hands at different time steps depending on the activity itself. Finally a temporal attention mechanism learns how to fuse LSTM features over time. We evaluate the method on 3 datasets. State-of-the-art results are achieved on the largest dataset for human activity recognition, namely NTU-RGB+D, as well as on the SBU Kinect Interaction dataset. Performance close to state-of-the-art is achieved on the smaller MSR Daily Activity 3D dataset.
- Mar 30 2017 math.RT arXiv:1703.10093v1This article surveys recent advances and future challenges in the $2$-representation theory of finitary $2$-categories with a particular emphasis on problems related to classification of various classes of $2$-representations.
- The recognition of actions from video sequences has many applications in health monitoring, assisted living, surveillance, and smart homes. Despite advances in sensing, in particular related to 3D video, the methodologies to process the data are still subject to research. We demonstrate superior results by a system which combines recurrent neural networks with convolutional neural networks in a voting approach. The gated-recurrent-unit-based neural networks are particularly well-suited to distinguish actions based on long-term information from optical tracking data; the 3D-CNNs focus more on detailed, recent information from video data. The resulting features are merged in an SVM which then classifies the movement. In this architecture, our method improves recognition rates of state-of-the-art methods by 14% on standard data sets.
- Mar 29 2017 cs.SE arXiv:1703.09603v1Committing to a version control system means submitting a software change to the system. Each commit can have a message to describe the submission. Several approaches have been proposed to automatically generate the content of such messages. However, the quality of the automatically generated messages falls far short of what humans write. In studying the differences between auto-generated and human-written messages, we found that 82% of the human-written messages have only one sentence, while the automatically generated messages often have multiple lines. Furthermore, we found that the commit messages often begin with a verb followed by an direct object. This finding inspired us to use a "verb+object" format in this paper to generate short commit summaries. We split the approach into two parts: verb generation and object generation. As our first try, we trained a classifier to classify a diff to a verb. We are seeking feedback from the community before we continue to work on generating direct objects for the commits.
- I will briefly discuss three cosmological models built upon three distinct quantum gravity proposals. I will first highlight the cosmological role of a vector field in the framework of a string/brane cosmological model. I will then present the resolution of the big bang singularity and the occurrence of an early era of accelerated expansion of a geometric origin, in the framework of group field theory condensate cosmology. I will then summarise results from an extended gravitational model based on non-commutative spectral geometry, a model that offers a purely geometric explanation for the standard model of particle physics.
- Mar 29 2017 cs.CV arXiv:1703.09393v1This paper proposes a crowd counting method. Crowd counting is difficult because of large appearance changes of a target which caused by density and scale changes. Conventional crowd counting methods generally utilize one predictor (e,g., regression and multi-class classifier). However, such only one predictor can not count targets with large appearance changes well. In this paper, we propose to predict the number of targets using multiple CNNs specialized to a specific appearance, and those CNNs are adaptively selected according to the appearance of a test image. By integrating the selected CNNs, the proposed method has the robustness to large appearance changes. In experiments, we confirm that the proposed method can count crowd with lower counting error than a CNN and integration of CNNs with fixed weights. Moreover, we confirm that each predictor automatically specialized to a specific appearance.
- Recently, deep learning (DL) methods have been introduced very successfully into human activity recognition (HAR) scenarios in ubiquitous and wearable computing. Especially the prospect of overcoming the need for manual feature design combined with superior classification capabilities render deep neural networks very attractive for real-life HAR application. Even though DL-based approaches now outperform the state-of-the-art in a number of recognitions tasks of the field, yet substantial challenges remain. Most prominently, issues with real-life datasets, typically including imbalanced datasets and problematic data quality, still limit the effectiveness of activity recognition using wearables. In this paper we tackle such challenges through Ensembles of deep Long Short Term Memory (LSTM) networks. We have developed modified training procedures for LSTM networks and combine sets of diverse LSTM learners into classifier collectives. We demonstrate, both formally and empirically, that Ensembles of deep LSTM learners outperform the individual LSTM networks. Through an extensive experimental evaluation on three standard benchmarks (Opportunity, PAMAP2, Skoda) we demonstrate the excellent recognition capabilities of our approach and its potential for real-life applications of human activity recognition.
- In applications of Einstein gravity one replaces the quantum-mechanical energy-momentum tensor of sources such as the degenerate electrons in a white dwarf or the black-body photons in the microwave background by c-number matrix elements. And not only that, one ignores the zero-point fluctuations in these sources by only retaining the normal-ordered parts of those matrix elements. There is no apparent justification for this procedure, and we show that it is precisely this procedure that leads to the cosmological constant problem. We suggest that solving the problem requires that gravity be treated just as quantum-mechanically as the sources to which it couples, and show that one can then solve the cosmological constant problem if one replaces Einstein gravity by the fully quantum-mechanically consistent conformal gravity theory.
- Mar 29 2017 quant-ph arXiv:1703.09243v1Hyperpolarisation at room temperature is one of the most important research fields in order to improve liquid, gas or nanoparticle tracer for Magnetic Resonance Imaging (MRI) in medical applications. In this paper we utilize nuclear magnetic resonance (NMR) to investigate the hyperpolarisation effect of negatively charged nitrogen vacancy (NV) centres on carbon-13 nuclei and their spin diffusion in a diamond single crystal close to the excited state level anti crossing (ESLAC) around 50 mT. Whereas the electron spins of the NV centre can be easily polarized in its m = 0 ground state at room temperature just by irradiation with green light , the swop of the NV electron spin polarization to a carbon-13 nuclei is a complex task. We found that the coupling between the polarized NV electron spin, the electron spin of a substitutional nitrogen impurity (P1) as well as its nitrogen-14 nuclei and the carbon-13 nuclear spin has to be considered. Here we show that through an optimization of this procedure, in about two minutes a signal to noise ratio which corresponds to a 23 hour standard measurement without hyperpolarisation and an accumulation of 460 single scans can be obtained. Furthermore we were able to identify several polarisation peaks of different sign at different magnetic fields in a region of some tens of gauss. Most of the peaks can be attributed to a coupling of the NV centres to nearby P1 centres. We present a new theoretical model in a framework of cross polarisation of a four spin dynamic model in good agreement with our experimental data. The results demonstrate the opportunities and power as well as limitations of hyperpolarisation in diamond via NV centres. We expect that the current work may have a significant impact on future applications.
- This work presents a study on the extraction and analysis of a set of 101 categories of eye movement features from three types of eye movement events: fixations, saccades, and post-saccadic oscillations. The eye movements were recorded during a reading task. For the categories of features with multiple instances in a recording we extract corresponding feature subtypes by calculating descriptive statistics on the distributions of these instances. A unified framework of detailed descriptions and mathematical formulas are provided for the extraction of the feature set. The analysis of feature values is performed using a large database of eye movement recordings from a normative population of 298 subjects. We demonstrate the central tendency and overall variability of feature values over the experimental population, and more importantly, we quantify the test-retest reliability (repeatability) of each separate feature. The described methods and analysis can provide valuable tools in fields exploring the eye movements, such as in behavioral studies, attention and cognition research, medical research, biometric recognition, and human-computer interaction.
- Mar 28 2017 cs.CV arXiv:1703.08897v1Zero-shot learning (ZSL) endows the computer vision system with the inferential capability to recognize instances of a new category that has never seen before. Two fundamental challenges in it are visual-semantic embedding and domain adaptation in cross-modality learning and unseen class prediction steps, respectively. To address both challenges, this paper presents two corresponding methods named Adaptive STructural Embedding (ASTE) and Self-PAsed Selective Strategy (SPASS), respectively. Specifically, ASTE formulates the visualsemantic interactions in a latent structural SVM framework to adaptively adjust the slack variables to embody the different reliableness among training instances. In this way, the reliable instances are imposed with small punishments, wheras the less reliable instances are imposed with more severe punishments. Thus, it ensures a more discriminative embedding. On the other hand, SPASS offers a framework to alleviate the domain shift problem in ZSL, which exploits the unseen data in an easy to hard fashion. Particularly, SPASS borrows the idea from selfpaced learning by iteratively selecting the unseen instances from reliable to less reliable to gradually adapt the knowledge from the seen domain to the unseen domain. Subsequently, by combining SPASS and ASTE, we present a self-paced Transductive ASTE (TASTE) method to progressively reinforce the classification capacity. Extensive experiments on three benchmark datasets (i.e., AwA, CUB, and aPY) demonstrate the superiorities of ASTE and TASTE. Furthermore, we also propose a fast training (FT) strategy to improve the efficiency of most of existing ZSL methods. The FT strategy is surprisingly simple and general enough, which can speed up the training time of most existing methods by 4~300 times while holding the previous performance.
- Mar 28 2017 cs.CV arXiv:1703.08893v1As an important and challenging problem in computer vision, zero-shot learning (ZSL) aims at automatically recognizing the instances from unseen object classes without training data. To address this problem, ZSL is usually carried out in the following two aspects: 1) capturing the domain distribution connections between seen classes data and unseen classes data; and 2) modeling the semantic interactions between the image feature space and the label embedding space. Motivated by these observations, we propose a bidirectional mapping based semantic relationship modeling scheme that seeks for crossmodal knowledge transfer by simultaneously projecting the image features and label embeddings into a common latent space. Namely, we have a bidirectional connection relationship that takes place from the image feature space to the latent space as well as from the label embedding space to the latent space. To deal with the domain shift problem, we further present a transductive learning approach that formulates the class prediction problem in an iterative refining process, where the object classification capacity is progressively reinforced through bootstrapping-based model updating over highly reliable instances. Experimental results on three benchmark datasets (AwA, CUB and SUN) demonstrate the effectiveness of the proposed approach against the state-of-the-art approaches.
- Mar 28 2017 quant-ph arXiv:1703.08700v1We establish the equivalence between the loss of coherence due to mixing in a quantum system and the loss of information after performing a projective measurement. Subsequently, it is demonstrated that the quantum discord, a measure of correlation for the bipartite system $\rho_{Alice\leftarrow Bob}$, is identical to the minimum difference (over all projectors |i><i|) between local coherence (LQICC monotone) on Bob side and coherence of the reduced density matrix $\rho^B$.
- Mar 27 2017 cs.NE arXiv:1703.08535v1Grammatical Evolution (GE) is a population-based evolutionary algorithm, where a formal grammar is used in the genotype to phenotype mapping process. PonyGE2 is an open source implementation of GE in Python, developed at UCD's Natural Computing Research and Applications group. It is intended as an advertisement and a starting-point for those new to GE, a reference for students and researchers, a rapid-prototyping medium for our own experiments, and a Python workout. As well as providing the characteristic genotype to phenotype mapping of GE, a search algorithm engine is also provided. A number of sample problems and tutorials on how to use and adapt PonyGE2 have been developed.
- Mar 27 2017 math.CO arXiv:1703.08414v1Recently, Naruse presented a beautiful cancellation-free hook-length formula for skew shapes. The formula involves a sum over objects called \emphexcited diagrams, and the term corresponding to each excited diagram has hook lengths in the denominator, like the classical hook-length formula due to Frame, Robinson and Thrall.\{In this paper, we present a simple bijection that proves an equivalent recursive version of Naruse's result, in the same way that the celebrated hook-walk proof due to Green, Nijenhuis and Wilf gives a bijective (or probabilistic) proof of the hook-length formula for ordinary shapes.\{In particular, we also give a new bijective proof of the classical hook-length formula, quite different from the known proofs.