- Anyons exist as point like particles in two dimensions and carry braid statistics which enable interactions that are independent of the distance between the particles. Except for a relatively few number of models which are analytically tractable, much of the physics of anyons remain still unexplored. In this paper, we show how U(1)-symmetry can be combined with the previously proposed anyonic Matrix Product States to simulate ground states and dynamics of anyonic systems on a lattice at any rational particle number density. We provide proof of principle by studying itinerant anyons on a one dimensional chain where no natural notion of braiding arises and also on a two-leg ladder where the anyons hop between sites and possibly braid. We compare the result of the ground state energies of Fibonacci anyons against hardcore bosons and spinless fermions. In addition, we report the entanglement entropies of the ground states of interacting Fibonacci anyons on a fully filled two-leg ladder at different interaction strength, identifying gapped or gapless points in the parameter space. As an outlook, our approach can also prove useful in studying the time dynamics of a finite number of nonabelian anyons on a finite two-dimensional lattice.
- Sep 04 2015 quant-ph arXiv:1509.01062v1An essential element of classical computation is the "if-then" construct, that accepts a control bit and an arbitrary gate, and provides conditional execution of the gate depending on the value of the controlling bit. On the other hand, quantum theory prevents the existence of an analogous universal construct accepting a control qubit and an arbitrary quantum gate as its input. Nevertheless, there are controllable sets of quantum gates for which such a construct exists. Here we provide a necessary and sufficient condition for a set of unitary transformations to be controllable, and we give a complete characterization of controllable sets in the two dimensional case. This result reveals an interesting connection between the problem of controllability and the problem of extracting information from an unknown quantum gate while using it.
- Classical thermodynamics is unrivalled in its range of applications and relevance to everyday life. It enables a description of complex systems, made up of microscopic particles, in terms of a small number of macroscopic quantities, such as work and entropy. As systems get ever smaller, fluctuations of these quantities become increasingly relevant, prompting the development of stochastic thermodynamics. Recently we have seen a surge of interest in exploring the quantum regime, where the origin of fluctuations is quantum rather than thermal. Many questions, such as the role of entanglement and the emergence of thermalisation, lie wide open. Answering these questions may lead to the development of quantum heat engines and refrigerators, as well as to vitally needed simple descriptions of quantum many-body systems.
- Sep 04 2015 physics.optics quant-ph arXiv:1509.01227v1Entangled photons have the remarkable ability to be more sensitive to signal and less sensitive to noise than classical light. Joint photons can sample an object collectively, resulting in faster phase accumulation and higher spatial resolution, while common components of noise can be subtracted. Even more, they can accomplish this while physically separate, due to the nonlocal properties of quantum mechanics. Indeed, nearly all quantum optics experiments rely on this separation, using individual point detectors that are scanned to measure coincidence counts and correlations. Scanning, however, is tedious, time consuming, and ill-suited for imaging. Moreover, the separation of beam paths adds complexity to the system while reducing the number of photons available for sampling, and the multiplicity of detectors does not scale well for greater numbers of photons and higher orders of entanglement. We bypass all of these problems here by directly imaging collinear photon pairs with an electron-multiplying CCD camera. We show explicitly the benefits of quantum nonlocality by engineering the spatial entanglement of the illuminating photons and introduce a new method of correlation measurement by converting time-domain coincidence counting into spatial-domain detection of selected pixels. We show that classical transport-of-intensity methods are applicable in the quantum domain and experimentally demonstrate nearly optimal (Heisenberg-limited) phase measurement for the given quantum illumination. The methods show the power of direct imaging and hold much potential for more general types of quantum information processing and control.
- I propose that the information loss paradox can be resolved by considering the supertranslation of the horizon caused by the ingoing particles. Information can be recovered in principle, but it is lost for all practical purposes.
- The Temperley--Lieb algebra is a finite dimensional associative algebra that arose in the context of statistical mechanics and occurs naturally as a quotient of the Hecke algebra arising from a Coxeter group of type $A$. It is often realized in terms of a certain diagram algebra, where every diagram can be written as a product of "simple diagrams." These factorizations correspond precisely to factorizations of the so-called fully commutative elements of the Coxeter group that index a particular basis. Given a reduced factorization of a fully commutative element, it is straightforward to construct the corresponding diagram. On the other hand, it is generally difficult to reconstruct the factorization given an arbitrary diagram. In this paper, we present an efficient algorithm for obtaining a reduced factorization for a given diagram.
- Sep 04 2015 hep-th arXiv:1509.01195v1An introduction to and a partial review of supergravity theories is given, insisting on concepts and on some important technical aspects. Topics covered include elements of global supersymmetry, a derivation of the simplest N=1 supergravity theory, a discussion of N=1 matter-supergravity couplings, of the scalar sector and of some simple models. Space-time is four-dimensional.
- Entanglement is one of the most intriguing features of quantum mechanics. It describes non-local correlations between quantum objects, and is at the heart of quantum information sciences. Entanglement is rapidly gaining prominence in diverse fields ranging from condensed matter to quantum gravity. Despite this generality, measuring entanglement remains challenging. This is especially true in systems of interacting delocalized particles, for which a direct experimental measurement of spatial entanglement has been elusive. Here, we measure entanglement in such a system of itinerant particles using quantum interference of many-body twins. Leveraging our single-site resolved control of ultra-cold bosonic atoms in optical lattices, we prepare and interfere two identical copies of a many-body state. This enables us to directly measure quantum purity, Renyi entanglement entropy, and mutual information. These experiments pave the way for using entanglement to characterize quantum phases and dynamics of strongly-correlated many-body systems.
- Sep 04 2015 quant-ph cond-mat.supr-con arXiv:1509.01127v1As experimental quantum information processing (QIP) rapidly advances, an emerging challenge is to design a scalable architecture that combines various quantum elements into a complex device without compromising their performance. In particular, superconducting quantum circuits have successfully demonstrated many of the requirements for quantum computing, including coherence levels that approach the thresholds for scaling. However, it remains challenging to couple a large number of circuit components through controllable channels while suppressing any other interactions. We propose a hardware platform intended to address these challenges, which combines the advantages of integrated circuit fabrication and long coherence times achievable in three-dimensional circuit quantum electrodynamics (3D cQED). This multilayer microwave integrated quantum circuit (MMIQC) platform provides a path toward the realization of increasingly complex superconducting devices in pursuit of a scalable quantum computer.
- Sep 04 2015 quant-ph arXiv:1509.00914v1We determine the minimum energy required to control the evolution of any mesoscopic quantum system in the presence of arbitrary Markovian noise processes. This result provides the mesoscopic equivalent of the fundamental cost of refrigeration, sets the minimum power consumption of mesoscopic devices that operate out of equilibrium, and allows one to calculate the efficiency of any control protocol, whether it be open-loop or feedback control. As examples we calculate the energy cost of maintaining a qubit in the ground state, the efficiency of resolved-sideband cooling of nano-mechanical resonators, and discuss the energy cost of quantum information processing.
- We show that any model trained by a stochastic gradient method with few iterations has vanishing generalization error. We prove this by showing the method is algorithmically stable in the sense of Bousquet and Elisseeff. Our analysis only employs elementary tools from convex and continuous optimization. Our results apply to both convex and non-convex optimization under standard Lipschitz and smoothness assumptions. Applying our results to the convex case, we provide new explanations for why multiple epochs of stochastic gradient descent generalize well in practice. In the nonconvex case, we provide a new interpretation of common practices in neural networks, and provide a formal rationale for stability-promoting mechanisms in training large, deep models. Conceptually, our findings underscore the importance of reducing training time beyond its obvious benefit.
- We consider the problem of solving TAP mean field equations by iteration for Ising model with coupling matrices that are drawn at random from general invariant ensembles. We develop an analysis of iterative algorithms using a dynamical functional approach that in the thermodynamic limit yields an effective dynamics of a single variable trajectory. Our main novel contribution is the expression for the implicit memory term of the dynamics for general invariant ensembles. By subtracting these terms, that depend on magnetizations at previous time steps, the implicit memory terms cancel making the iteration dependent on a Gaussian distributed field only. The TAP magnetizations are stable fixed points if an AT stability criterion is fulfilled. We illustrate our method explicitly for coupling matrices drawn from the random orthogonal ensemble.
- Sep 04 2015 cond-mat.stat-mech physics.soc-ph arXiv:1509.01207v1We present a comprehensive and versatile theoretical framework to study site and bond percolation on clustered and correlated random graphs. Our contribution can be summarized in three main points. (i) We introduce a set of iterative equations that solve the exact distribution of the size and composition of components in finite size quenched or random multitype graphs. (ii) We define a very general random graph ensemble that encompasses most of the models published to this day, and also that permits to model structural properties not yet included in a theoretical framework. Site and bond percolation on this ensemble is solved exactly in the infinite size limit using probability generating functions [i.e., the percolation threshold, the size and the composition of the giant (extensive) and small components]. Several examples and applications are also provided. (iii) Our approach can be adapted to model interdependent graphs---whose most striking feature is the emergence of an extensive component via a discontinuous phase transition---in an equally general fashion. We show how a graph can successively undergo a continuous then a discontinuous phase transition, and preliminary results suggest that clustering increases the amplitude of the discontinuity at the transition.
- An extension of QED is considered in which the Dirac fermion has both Hermitian and anti-Hermitian mass terms, as well as both vector and axial-vector couplings to the gauge field. Gauge invariance is restored when the Hermitian and anti-Hermitian masses are of equal magnitude, and the theory reduces to that of a single massless Weyl fermion. An analogous non-Hermitian Yukawa theory is considered and it is shown that this model can explain the smallness of the light-neutrino masses and provide an additional source of leptonic CP violation.
- Sep 04 2015 cs.SY arXiv:1509.01186v1We present one of the first algorithms on model based reinforcement learning and trajectory optimization with free final time horizon. Grounded on the optimal control theory and Dynamic Programming, we derive a set of backward differential equations that propagate the value function and provide the optimal control policy and the optimal time horizon. The resulting policy generalizes previous results in model based trajectory optimization. Our analysis shows that the proposed algorithm recovers the theoretical optimal solution on linear low dimensional problem. Finally we provide application results on nonlinear systems.
- Sep 04 2015 quant-ph arXiv:1509.01100v1Besides achieving secure communication between two spatially-separated parties, another important issue in modern cryptography is related to secure communication in time, i.e., the possibility to confidentially store information on a memory for later retrieval. Here we explore this possibility in the setting of quantum reading, which exploits quantum entanglement to efficiently read data from a memory whereas classical strategies (e.g., based on coherent states or their mixtures) cannot retrieve any information. From this point of view, the technique of quantum reading can provide a new form of technological security for data storage.
- Sep 04 2015 cs.LG arXiv:1509.00913v1Despite the promise of brain-inspired machine learning, deep neural networks (DNN) have frustratingly failed to bridge the deceptively large gap between learning and memory. Here, we introduce a Perpetual Learning Machine; a new type of DNN that is capable of brain-like dynamic 'on the fly' learning because it exists in a self-supervised state of Perpetual Stochastic Gradient Descent. Thus, we provide the means to unify learning and memory within a machine learning framework.
- Sep 04 2015 quant-ph arXiv:1509.01239v1
- Sep 04 2015 gr-qc arXiv:1509.01235v1
- Sep 04 2015 astro-ph.IM arXiv:1509.01232v1
- Sep 04 2015 physics.flu-dyn arXiv:1509.01230v1
- Sep 04 2015 q-bio.NC arXiv:1509.01224v1
- Sep 04 2015 hep-ex physics.ins-det arXiv:1509.01223v1
- Sep 04 2015 hep-th cond-mat.stat-mech arXiv:1509.01222v1
- Sep 04 2015 cs.FL arXiv:1509.01221v1
- Sep 04 2015 math.FA arXiv:1509.01210v1
- Sep 04 2015 cond-mat.mtrl-sci cond-mat.mes-hall arXiv:1509.01209v1
- Sep 04 2015 q-bio.NC arXiv:1509.01206v1
- Sep 04 2015 cond-mat.mtrl-sci arXiv:1509.01204v1
- Sep 04 2015 astro-ph.SR arXiv:1509.01202v1
- Sep 04 2015 astro-ph.HE arXiv:1509.01201v1
- Sep 04 2015 math.CO arXiv:1509.01196v1
- Sep 04 2015 nucl-th arXiv:1509.01193v1
- Sep 04 2015 math.NT arXiv:1509.01192v1
- Sep 04 2015 math.LO arXiv:1509.01191v1
- Sep 04 2015 cs.DS arXiv:1509.01190v1
- Sep 04 2015 math.CO arXiv:1509.01185v1
- Sep 04 2015 cond-mat.mes-hall cond-mat.mtrl-sci arXiv:1509.01182v1
- Sep 04 2015 hep-ph arXiv:1509.01181v1