Showing papers by "Matthias Troyer published in 2017"
TL;DR: This code works in the tight-binding framework, which can be generated by another software package Wannier90 Mostofi et al. (2008), and can help to classify the topological phase of a given materials by calculating the Wilson loop, and get the surface state spectrum.
1,566 citations
TL;DR: In this paper, a variational representation of quantum states based on artificial neural networks with a variable number of hidden neurons is introduced. But this model is not suitable for the many-body problem in quantum physics.
Abstract: The challenge posed by the many-body problem in quantum physics originates from the difficulty of describing the nontrivial correlations encoded in the exponential complexity of the many-body wave function. Here we demonstrate that systematic machine learning of the wave function can reduce this complexity to a tractable computational form for some notable cases of physical interest. We introduce a variational representation of quantum states based on artificial neural networks with a variable number of hidden neurons. A reinforcement-learning scheme we demonstrate is capable of both finding the ground state and describing the unitary time evolution of complex interacting quantum systems. Our approach achieves high accuracy in describing prototypical interacting spins models in one and two dimensions.
1,375 citations
TL;DR: In this article, the authors show that a quantum computer can be used to elucidate reaction mechanisms in complex chemical systems, using the open problem of biological nitrogen fixation in nitrogenase as an example.
Abstract: With rapid recent advances in quantum technology, we are close to the threshold of quantum devices whose computational powers can exceed those of classical supercomputers. Here, we show that a quantum computer can be used to elucidate reaction mechanisms in complex chemical systems, using the open problem of biological nitrogen fixation in nitrogenase as an example. We discuss how quantum computers can augment classical computer simulations used to probe these reaction mechanisms, to significantly increase their accuracy and enable hitherto intractable simulations. Our resource estimates show that, even when taking into account the substantial overhead of quantum error correction, and the need to compile into discrete gate sets, the necessary computations can be performed in reasonable time on small quantum computers. Our results demonstrate that quantum computers will be able to tackle important problems in chemistry without requiring exorbitant resources.
603 citations
TL;DR: In this paper, machine learning techniques are used for quantum state tomography (QST) of highly entangled states, in both one and two dimensions, and the resulting approach allows one to reconstruct traditionally challenging many-body quantities - such as the entanglement entropy - from simple, experimentally accessible measurements.
Abstract: 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 both one and two dimensions. 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.
434 citations
TL;DR: The Z2Pack software package as mentioned in this paper is suitable for high-throughput screening of materials databases for compounds with nontrivial topologies, which can be used to identify topological materials optimal for experimental probes.
Abstract: The intense theoretical and experimental interest in topological insulators and semimetals has established band structure topology as a fundamental material property Consequently, identifying band topologies has become an important, but often challenging, problem, with no exhaustive solution at the present time In this work we compile a series of techniques, some previously known, that allow for a solution to this problem for a large set of the possible band topologies The method is based on tracking hybrid Wannier charge centers computed for relevant Bloch states, and it works at all levels of materials modeling: continuous $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ models, tight-binding models, and ab initio calculations We apply the method to compute and identify Chern, ${\mathbb{Z}}_{2}$, and crystalline topological insulators, as well as topological semimetal phases, using real material examples Moreover, we provide a numerical implementation of this technique (the Z2Pack software package) that is ideally suited for high-throughput screening of materials databases for compounds with nontrivial topologies We expect that our work will allow researchers to (a) identify topological materials optimal for experimental probes, (b) classify existing compounds, and (c) reveal materials that host novel, not yet described, topological states
311 citations
TL;DR: In this paper, the authors proposed a system for the detection of anomalous anomalies in a set of synthetic data points in the U.S. Intelligence Advanced Research Projects Activity (Lincoln Laboratory).
Abstract: United States. Intelligence Advanced Research Projects Activity (Lincoln Laboratory. Air Force Contract FA8721-05-C-0002)
102 citations
TL;DR: In this article, the authors review and analyze alternative fermion-to-qubit mappings, including the two approaches by Bravyi and Kitaev and the auxiliary fermions transformation.
Abstract: Simulating fermionic lattice models with qubits requires mapping fermionic degrees of freedom to qubits. The simplest method for this task, the Jordan-Wigner transformation, yields strings of Pauli operators acting on an extensive number of qubits. This overhead can be a hindrance to implementation of qubit-based quantum simulators, especially in the analog context. Here we thus review and analyze alternative fermion-to-qubit mappings, including the two approaches by Bravyi and Kitaev and the auxiliary fermion transformation. The Bravyi-Kitaev transform is reformulated in terms of a classical data structure and generalized to achieve a further locality improvement for local fermionic models on a rectangular lattice. We conclude that the most compact encoding of the fermionic operators can be done using ancilla qubits with the auxiliary fermion scheme. Without introducing ancillas, a variant of the Bravyi-Kitaev transform provides the most compact fermion-to-qubit mapping for Hubbard-like models.
101 citations
TL;DR: This paper presents an updated and refactored version of the core ALPS libraries geared at the computational physics software development community, rewritten with focus on documentation, ease of installation, and software maintainability.
96 citations
TL;DR: It is shown that an L·S coupling in higher subbands leads to an enhancement of the g factor of an order of magnitude or more for small effective mass semiconductors and this finding is validated with simulations of InAs and InSb.
Abstract: Recent experiments on Majorana fermions in semiconductor nanowires [S. M. Albrecht, A. P. Higginbotham, M. Madsen, F. Kuemmeth, T. S. Jespersen, J. Nyg\aa{}rd, P. Krogstrup, and C. M. Marcus, Nature (London) 531, 206 (2016)] revealed a surprisingly large electronic Land\'e $g$ factor, several times larger than the bulk value---contrary to the expectation that confinement reduces the $g$ factor. Here we assess the role of orbital contributions to the electron $g$ factor in nanowires and quantum dots. We show that an $\mathbf{L}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{S}$ coupling in higher subbands leads to an enhancement of the $g$ factor of an order of magnitude or more for small effective mass semiconductors. We validate our theoretical finding with simulations of InAs and InSb, showing that the effect persists even if cylindrical symmetry is broken. A huge anisotropy of the enhanced $g$ factors under magnetic field rotation allows for a straightforward experimental test of this theory.
56 citations
TL;DR: The utility of the second Renyi entropy in predicting a topological phase transition and in extracting the localization length in a many-body localized system is illustrated and the tradeoffs between time and number of qubits are exposed.
Abstract: The efficient simulation of many-body quantum systems is an important application of quantum computers. However, extracting useful information from a system of qubits is not straightforward. The quantum computing equivalent of the vast array of diagnostic tools that extract information from classical numerical simulation are still being developed. This paper addresses the efficient calculation of quantities that characterize entanglement between different parts of a quantum state using a quantum computer. Illustrative examples of applications as diverse as many-body localization and fractional quantum Hall effect are discussed.
53 citations
TL;DR: In this article, an instantonic calculus was developed to derive an analytical expression for the thermally assisted tunneling decay rate of a metastable state in a fully connected quantum spin model.
Abstract: We develop an instantonic calculus to derive an analytical expression for the thermally assisted tunneling decay rate of a metastable state in a fully connected quantum spin model. The tunneling decay problem can be mapped onto the Kramers escape problem of a classical random dynamical field. This dynamical field is simulated efficiently by path-integral quantum Monte Carlo (QMC). We show analytically that the exponential scaling with the number of spins of the thermally assisted quantum tunneling rate and the escape rate of the QMC process are identical. We relate this effect to the existence of a dominant instantonic tunneling path. The instanton trajectory is described by nonlinear dynamical mean-field theory equations for a single-site magnetization vector, which we solve exactly. Finally, we derive scaling relations for the ``spiky'' barrier shape when the spin tunneling and QMC rates scale polynomially with the number of spins $N$ while a purely classical over-the-barrier activation rate scales exponentially with $N$.
TL;DR: In this paper, the authors extend the results obtained for quantum spin models and study continuous-variable models for proton transfer reactions, and demonstrate that QMC simulations efficiently recover the scaling of ground-state tunneling rates due to the existence of an instanton path, which always connects the reactant state with the product.
Abstract: 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, which aim to simulate quantum statistics with resources growing only polynomially with the system size. Here we extend the recent results obtained for quantum spin models [Phys. Rev. Lett. 117, 180402 (2016)], and we study continuous-variable models for proton transfer reactions. We demonstrate that QMC simulations efficiently recover the scaling of 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.
Posted Content•
TL;DR: In this paper, the authors illustrate the aspects and challenges to consider when implementing optimization problems on quantum annealing hardware based on the example of the traveling salesman problem (TSP) and demonstrate that tunneling between local minima can be exponentially suppressed if the quantum dynamics are not carefully tailored to the problem.
Abstract: With progress in quantum technology more sophisticated quantum annealing devices are becoming available. While they offer new possibilities for solving optimization problems, their true potential is still an open question. As the optimal design of adiabatic algorithms plays an important role in their assessment, we illustrate the aspects and challenges to consider when implementing optimization problems on quantum annealing hardware based on the example of the traveling salesman problem (TSP). We demonstrate that tunneling between local minima can be exponentially suppressed if the quantum dynamics are not carefully tailored to the problem. Furthermore we show that inequality constraints, in particular, present a major hurdle for the implementation on analog quantum annealers. We finally argue that programmable digital quantum annealers can overcome many of these obstacles and can - once large enough quantum computers exist - provide an interesting route to using quantum annealing on a large class of problems.
TL;DR: A high-temperature series expansion code for spin-1/2 Heisenberg models on arbitrary lattices using a linked-cluster expansion to obtain a high-order series in the inverse temperature for thermodynamic quantities in the thermodynamic limit.
TL;DR: In this paper, the relative performance of infinite matrix product states and infinite projected entangled-pair states on cylindrical geometries was evaluated by considering the Heisenberg and half-filled Hubbard models on the square lattice.
Abstract: In spite of their intrinsic one-dimensional nature, matrix product states have been systematically used to obtain remarkably accurate results for two-dimensional systems. Motivated by basic entropic arguments favoring projected entangled-pair states as the method of choice, we assess the relative performance of infinite matrix product states and infinite projected entangled-pair states on cylindrical geometries. By considering the Heisenberg and half-filled Hubbard models on the square lattice as our benchmark cases, we evaluate their variational energies as a function of both bond dimension and cylinder width. In both examples, we find crossovers at moderate cylinder widths, i.e., for the largest bond dimensions considered, we find an improvement on the variational energies for the Heisenberg model by using projected entangled-pair states at a width of about eleven sites, whereas for the half-filled Hubbard model, this crossover occurs at about seven sites.
TL;DR: In this paper, a novel simulated quantum annealing (SQA) algorithm which employs a multispin quantum fluctuation operator was introduced, at variance with the usual transverse field, short-range two-spin flip interactions are included in the driver Hamiltonian.
Abstract: We introduce a novel simulated quantum annealing (SQA) algorithm which employs a multispin quantum fluctuation operator. At variance with the usual transverse field, short-range two-spin flip interactions are included in the driver Hamiltonian. A Quantum Monte Carlo algorithm, capable of efficiently simulating large disordered systems, is described and tested. A first application to SQA, on a random square lattice Ising spin glass, reveals that the multi-spin driver Hamiltonian improves upon the usual transverse field. This work paves the way for more systematic investigations using multi-spin quantum fluctuations on a broader range of problems.
07 Apr 2017
TL;DR: In this paper, the authors compared simulated annealing, simulated quantum anealing and walkSAT, an open-source SAT solver, in terms of their ability to find disparate solutions to hard random $k$-SAT problems.
Abstract: Satisfiability filters, introduced by S. A. Weaver et al. in 2014, are a new and promising type of filters to address set membership testing. In order to construct satisfiability filters, it is necessary to find disparate solutions to hard random $k$-SAT problems. This paper compares simulated annealing, simulated quantum annealing and walkSAT, an open-source SAT solver, in terms of their ability to find such solutions. The results indicate that solutions found by simulated quantum annealing are generally less disparate than solutions found by the other solvers and therefore less useful for the construction of satisfiability filters.
Posted Content•
TL;DR: In this paper, a heuristic approach for the optimization of annealing schedules for QA was presented and applied to 3D Ising spin glass problems. But, the results showed that the classical and QA schedules are similarly optimized.
Abstract: Classical and quantum annealing are two heuristic optimization methods that search for an optimal solution by slowly decreasing thermal or quantum fluctuations. Optimizing annealing schedules is important both for performance and fair comparisons between classical annealing, quantum annealing, and other algorithms. Here we present a heuristic approach for the optimization of annealing schedules for quantum annealing and apply it to 3D Ising spin glass problems. We find that if both classical and quantum annealing schedules are similarly optimized, classical annealing outperforms quantum annealing for these problems when considering the residual energy obtained in slow annealing. However, when performing many repetitions of fast annealing, simulated quantum annealing is seen to outperform classical annealing for our benchmark problems.
TL;DR: In this article, the authors have exposed InAs/GaSb samples to variable compressive and tensile strain through piezo-electric elements and observed that the system's electrical properties are very susceptible to even small values of such mechanical deformation.
Abstract: Topological phenomena in two-dimensional materials are characterized by an electrical conductivity that is restricted to the edges of a sample A heterostructure of the semiconductors indium arsenide and gallium antimonide, InAs/GaSb, can be a quantum spin Hall insulator (QSHI), which exhibits spin-resolved channels at the edges but has an insulating bulk The QSHI is linked to a nontrivial inverted band structure that emerges only for certain thicknesses of the InAs and GaSb layers Here, the authors have exposed InAs/GaSb samples to variable compressive and tensile strain through piezo-electric elements It is observed that the system's electrical properties are very susceptible to even small values of such mechanical deformation Band structure calculations reveal the impact of strain on the nontrivial electronic band structure and highlight the potential of strain-engineering for the observation of the quantum spin Hall insulating phase in this material system
TL;DR: In this paper, a novel Simulated Quantum Annealing (SQA) algorithm which employs a multispin quantum fluctuation operator was introduced, at variance with the usual transverse field, short-range two-spin flip interactions are included in the driver Hamiltonian.
Abstract: We introduce a novel Simulated Quantum Annealing (SQA) algorithm which employs a multispin quantum fluctuation operator. At variance with the usual transverse field, short-range two-spin flip interactions are included in the driver Hamiltonian. A Quantum Monte Carlo algorithm, capable of efficiently simulating large disordered systems, is described and tested. A first application to SQA, on a random square lattice Ising spin glass reveals that the multi-spin driver Hamiltonian improves upon the usual transverse field. This work paves the way for more systematic investigations using multi-spin quantum fluctuations on a broader range of problems.
Posted Content•
TL;DR: In this paper, an optimization scheme that unfolds the k-local terms into a linear combination of 2-local term was proposed to ensure the conservation of all relevant physical properties of the original Hamiltonian, with several orders of magnitude smaller variation of coupling constants.
Abstract: Many-body fermionic quantum calculations performed on analog quantum computers are restricted by the presence of k-local terms, which represent interactions among more than two qubits. These originate from the fermion-to-qubit mapping applied to the electronic Hamiltonians. Current solutions to this problem rely on perturbation theory in an enlarged Hilbert space. The main challenge associated with this technique is that it relies on coupling constants with very different magnitudes. This prevents its implementation in currently available architectures. In order to resolve this issue, we present an optimization scheme that unfolds the k-local terms into a linear combination of 2-local terms, while ensuring the conservation of all relevant physical properties of the original Hamiltonian, with several orders of magnitude smaller variation of the coupling constants.
Patent•
15 Jun 2017
TL;DR: In some examples, techniques and architectures for solving combinatorial optimization or statistical sampling problems use a recursive hierarchical approach that involves reinitializing various subsets of a set of variables.
Abstract: In some examples, techniques and architectures for solving combinatorial optimization or statistical sampling problems use a recursive hierarchical approach that involves reinitializing various subsets of a set of variables The entire set of variables may correspond to a first level of a hierarchy In individual steps of the recursive process of solving an optimization problem, the set of variables may be partitioned into subsets corresponding to higher-order levels of the hierarchy, such as a second level, a third level, and so on Variables of individual subsets may be randomly initialized Based on the objective function, a combinatorial optimization operation may be performed on the individual subsets to modify variables of the individual subsets Reinitializing subsets of variables instead of reinitializing the entire set of variables may allow for preservation of information gained in previous combinatorial optimization operations