arXiv subjects

Travis S. Humble

Publications and source records attributed to Travis S. Humble.

At least 91 records · Page 5Linked to original sources

arXiv2020

Training and Classification using a Restricted Boltzmann Machine on the D-Wave 2000Q

Restricted Boltzmann Machine (RBM) is an energy based, undirected graphical model. It is commonly used for unsupervised and supervised machine learning. Typically, RBM is trained using contrastive divergence (CD). However, training with CD is slow and does not estimate exact gradient of log-likelihood cost function. In this work, the model expectation of gradient learning for RBM has been calculated using a quantum annealer (D-Wave 2000Q), which is much faster than Markov chain Monte Carlo (MCMC) used in CD. Training and classification results are compared with CD. The classification accuracy results indicate similar performance of both methods. Image reconstruction as well as log-likelihood calculations are used to compare the performance of quantum and classical algorithms for RBM training. It is shown that the samples obtained from quantum annealer can be used to train a RBM on a 64-bit `bars and stripes' data set with classification performance similar to a RBM trained with CD. Though training based on CD showed improved learning performance, training using a quantum annealer eliminates computationally expensive MCMC steps of CD.

cs.LG↗

arXiv2020

Simulating the Shastry-Sutherland Ising Model using Quantum Annealing

Frustration represents an essential feature in the behavior of magnetic materials when constraints on the microscopic Hamiltonian cannot be satisfied simultaneously. This gives rise to exotic phases of matter including spin liquids, spin ices, and stripe phases. Here we demonstrate an approach to understanding the microscopic effects of frustration by computing the phases of a 468-spin Shastry-Sutherland Ising Hamiltonian using a quantum annealer. Our approach uses mean-field boundary conditions to mitigate effects of finite size and defects alongside an iterative quantum annealing protocol to simulate statistical physics. We recover all phases of the Shastry-Sutherland Ising model -- including the well-known fractional magnetization plateau -- and the static structure factor characterizing the critical behavior at these transitions. These results establish quantum annealing as an emerging method in understanding the effects of frustration on the emergence of novel phases of matter and pave the way for future comparisons with real experiments.

quant-ph↗

arXiv2019

Supplementary information for "Quantum supremacy using a programmable superconducting processor"

This is an updated version of supplementary information to accompany "Quantum supremacy using a programmable superconducting processor", an article published in the October 24, 2019 issue of Nature. The main article is freely available at https://www.nature.com/articles/s41586-019-1666-5. Summary of changes since arXiv:1910.11333v1 (submitted 23 Oct 2019): added URL for qFlex source code; added Erratum section; added Figure S41 comparing statistical and total uncertainty for log and linear XEB; new References [1,65]; miscellaneous updates for clarity and style consistency; miscellaneous typographical and formatting corrections.

quant-ph↗

arXiv2019

XACC: A System-Level Software Infrastructure for Heterogeneous Quantum-Classical Computing

Quantum programming techniques and software have advanced significantly over the past five years, with a majority focusing on high-level language frameworks targeting remote REST library APIs. As quantum computing architectures advance and become more widely available, lower-level, system software infrastructures will be needed to enable tighter, co-processor programming and access models. Here we present XACC, a system-level software infrastructure for quantum-classical computing that promotes a service-oriented architecture to expose interfaces for core quantum programming, compilation, and execution tasks. We detail XACC's interfaces, their interactions, and its implementation as a hardware-agnostic framework for both near-term and future quantum-classical architectures. We provide concrete examples demonstrating the utility of this framework with paradigmatic tasks. Our approach lays the foundation for the development of compilers, associated runtimes, and low-level system tools tightly integrating quantum and classical workflows.

quant-ph↗

arXiv2019

Quantum annealing for systems of polynomial equations

Numerous scientific and engineering applications require numerically solving systems of equations. Classically solving a general set of polynomial equations requires iterative solvers, while linear equations may be solved either by direct matrix inversion or iteratively with judicious preconditioning. However, the convergence of iterative algorithms is highly variable and depends, in part, on the condition number. We present a direct method for solving general systems of polynomial equations based on quantum annealing, and we validate this method using a system of second-order polynomial equations solved on a commercially available quantum annealer. We then demonstrate applications for linear regression, and discuss in more detail the scaling behavior for general systems of linear equations with respect to problem size, condition number, and search precision. Finally, we define an iterative annealing process and demonstrate its efficacy in solving a linear system to a tolerance of $10^{-8}$.

quant-ph↗

arXiv2019

Application of Quantum Annealing to Nurse Scheduling Problem

Quantum annealing is a promising heuristic method to solve combinatorial optimization problems, and efforts to quantify performance on real-world problems provide insights into how this approach may be best used in practice. We investigate the empirical performance of quantum annealing to solve the Nurse Scheduling Problem (NSP) with hard constraints using the D-Wave 2000Q quantum annealing device. NSP seeks the optimal assignment for a set of nurses to shifts under an accompanying set of constraints on schedule and personnel. After reducing NSP to a novel Ising-type Hamiltonian, we evaluate the solution quality obtained from the D-Wave 2000Q against the constraint requirements as well as the diversity of solutions. For the test problems explored here, our results indicate that quantum annealing recovers satisfying solutions for NSP and suggests the heuristic method is sufficient for practical use. Moreover, we observe that solution quality can be greatly improved through the use of reverse annealing, in which it is possible to refine a returned results by using the annealing process a second time. We compare the performance NSP using both forward and reverse annealing methods and describe how these approach might be used in practice.

quant-ph↗

arXiv2019

Quantum Chemistry as a Benchmark for Near-Term Quantum Computers

We present a quantum chemistry benchmark for noisy intermediate-scale quantum computers that leverages the variational quantum eigensolver, active space reduction, a reduced unitary coupled cluster ansatz, and reduced density purification as error mitigation. We demonstrate this benchmark on the 20 qubit IBM Tokyo and 16 qubit Rigetti Aspen processors via the simulation of alkali metal hydrides (NaH, KH, RbH),with accuracy of the computed ground state energy serving as the primary benchmark metric. We further parameterize this benchmark suite on the trial circuit type, the level of symmetry reduction, and error mitigation strategies. Our results demonstrate the characteristically high noise level present in near-term superconducting hardware, but provide a relevant baseline for future improvement of the underlying hardware, and a means for comparison across near-term hardware types. We also demonstrate how to reduce the noise in post processing with specific error mitigation techniques. Particularly, the adaptation of McWeeny purification of noisy density matrices dramatically improves accuracy of quantum computations, which, along with adjustable active space, significantly extends the range of accessible molecular systems. We demonstrate that for specific benchmark settings, the accuracy metric can reach chemical accuracy when computing over the cloud on certain quantum computers.

quant-ph↗

arXiv2019

Function Maximization with Dynamic Quantum Search

Finding the maximum value of a function in a dynamic model plays an important role in many application settings, including discrete optimization in the presence of hard constraints. We present an iterative quantum algorithm for finding the maximum value of a function in which prior search results update the acceptable response. Our approach is based on quantum search and utilizes a dynamic oracle function to mark items in a specified input set. As a realization of function optimization, we verify the correctness of the algorithm using numerical simulations of quantum circuits for the Knapsack problem. Our simulations make use of an explicit oracle function based on arithmetic operations and a comparator subroutine, and we verify these implementations using numerical simulations up to 30 qubits.

quant-ph↗

arXiv2018

Spiking label propagation for community detection

In this paper we present results from a method of community detection using label propagation in undirected, unweighted graphs which incorporates elements of neural computing and spike-based data. Using a fully connected, edge-weighted system of spiking neurons driven by external currents, we generate spike responses that are decoded into a binary signal. The similarity between pairs of signals is quantified using a Hamming-distance based metric and is used to classify vertices into communities. We test our approach on a set of graph instances, each with 128 vertices and either homogeneous or heterogeneous community size distributions. We present our method as a candidate for a split-computing workflow that incorporates neuromorphic hardware and does not require extensive pre-training of network parameters.

cond-mat.dis-nn↗

arXiv2018

Quantum Circuit Designs of Integer Division Optimizing T-count and T-depth

Quantum circuits for mathematical functions such as division are necessary to use quantum computers for scientific computing. Quantum circuits based on Clifford+T gates can easily be made fault-tolerant but the T gate is very costly to implement. The small number of qubits available in existing quantum computers adds another constraint on quantum circuits. As a result, reducing T-count and qubit cost have become important optimization goals. The design of quantum circuits for integer division has caught the attention of researchers and designs have been proposed in the literature. However, these designs suffer from excessive T gate and qubit costs. Many of these designs also produce significant garbage output resulting in additional qubit and T gate costs to eliminate these outputs. In this work, we propose two quantum integer division circuits. The first proposed quantum integer division circuit is based on the restoring division algorithm and the second proposed design implements the non-restoring division algorithm. Both proposed designs are optimized in terms of T-count, T-depth and qubits. Both proposed quantum circuit designs are based on (i) a quantum subtractor, (ii) a quantum adder-subtractor circuit, and (iii) a novel quantum conditional addition circuit. Our proposed restoring division circuit achieves average T-count savings from $79.03 \%$ to $91.69 \%$ compared to the existing works. Our proposed non-restoring division circuit achieves average T-count savings from $49.75 \%$ to $90.37 \%$ compared to the existing works. Further, both our proposed designs have linear T-depth.

quant-ph↗

arXiv2018

Compiling Adiabatic Quantum Programs

We develop a non-cooperative game-theoretic model for the problem of graph minor-embedding to show that optimal compiling of adiabatic quantum programs in the sense of Nash equilibrium is possible.

cs.GT↗

arXiv2018

Nash embedding and equilibrium in pure quantum states

With respect to probabilistic mixtures of the strategies in non-cooperative games, quantum game theory provides guarantee of fixed-point stability, the so-called Nash equilibrium. This permits players to choose mixed quantum strategies that prepare mixed quantum states optimally under constraints. In this letter, we show that fixed-point stability of Nash equilibrium can also be guaranteed for pure quantum strategies via an application of the Nash embedding theorem, permitting players to prepare pure quantum states optimally under constraints.

quant-ph↗

arXiv2018

A Language and Hardware Independent Approach to Quantum-Classical Computing

Heterogeneous high-performance computing (HPC) systems offer novel architectures which accelerate specific workloads through judicious use of specialized coprocessors. A promising architectural approach for future scientific computations is provided by heterogeneous HPC systems integrating quantum processing units (QPUs). To this end, we present XACC (eXtreme-scale ACCelerator) --- a programming model and software framework that enables quantum acceleration within standard or HPC software workflows. XACC follows a coprocessor machine model that is independent of the underlying quantum computing hardware, thereby enabling quantum programs to be defined and executed on a variety of QPUs types through a unified application programming interface. Moreover, XACC defines a polymorphic low-level intermediate representation, and an extensible compiler frontend that enables language independent quantum programming, thus promoting integration and interoperability across the quantum programming landscape. In this work we define the software architecture enabling our hardware and language independent approach, and demonstrate its usefulness across a range of quantum computing models through illustrative examples involving the compilation and execution of gate and annealing-based quantum programs.

quant-ph↗

arXiv2018

Validating Quantum-Classical Programming Models with Tensor Network Simulations

The exploration of hybrid quantum-classical algorithms and programming models on noisy near-term quantum hardware has begun. As hybrid programs scale towards classical intractability, validation and benchmarking are critical to understanding the utility of the hybrid computational model. In this paper, we demonstrate a newly developed quantum circuit simulator based on tensor network theory that enables intermediate-scale verification and validation of hybrid quantum-classical computing frameworks and programming models. We present our tensor-network quantum virtual machine (TNQVM) simulator which stores a multi-qubit wavefunction in a compressed (factorized) form as a matrix product state, thus enabling single-node simulations of larger qubit registers, as compared to brute-force state-vector simulators. Our simulator is designed to be extensible in both the tensor network form and the classical hardware used to run the simulation (multicore, GPU, distributed). The extensibility of the TNQVM simulator with respect to the simulation hardware type is achieved via a pluggable interface for different numerical backends (e.g., ITensor and ExaTENSOR numerical libraries). We demonstrate the utility of our TNQVM quantum circuit simulator through the verification of randomized quantum circuits and the variational quantum eigensolver algorithm, both expressed within the eXtreme-scale ACCelerator (XACC) programming model.

quant-ph↗

arXiv2018

Benchmarking treewidth as a practical component of tensor-network--based quantum simulation

Tensor networks are powerful factorization techniques which reduce resource requirements for numerically simulating principal quantum many-body systems and algorithms. The computational complexity of a tensor network simulation depends on the tensor ranks and the order in which they are contracted. Unfortunately, computing optimal contraction sequences (orderings) in general is known to be a computationally difficult (NP-complete) task. In 2005, Markov and Shi showed that optimal contraction sequences correspond to optimal (minimum width) tree decompositions of a tensor network's line graph, relating the contraction sequence problem to a rich literature in structural graph theory. While treewidth-based methods have largely been ignored in favor of dataset-specific algorithms in the prior tensor networks literature, we demonstrate their practical relevance for problems arising from two distinct methods used in quantum simulation: multi-scale entanglement renormalization ansatz (MERA) datasets and quantum circuits generated by the quantum approximate optimization algorithm (QAOA). We exhibit multiple regimes where treewidth-based algorithms outperform domain-specific algorithms, while demonstrating that the optimal choice of algorithm has a complex dependence on the network density, expected contraction complexity, and user run time requirements. We further provide an open source software framework designed with an emphasis on accessibility and extendability, enabling replicable experimental evaluations and future exploration of competing methods by practitioners.

cs.DS↗

arXiv2018

Quantum Annealing for Prime Factorization

We have developed a framework to convert an arbitrary integer factorization problem to an executable Ising model by first writing it as an optimization function and then transforming the k-bit coupling ($k\geq 3$) terms to quadratic terms using ancillary variables. The method is efficient and uses $\mathcal{O}(\text{log}^2(N))$ binary variables (qubits) for finding the factors of integer $N$. The method was tested using the D-Wave 2000Q for finding an embedding and determining the prime factors for a given composite number. As examples, we present quantum annealing results for factoring 15, 143, 59989, and 376289 using 4, 12, 59, and 94 logical qubits respectively. The method is general and could be used to factor larger numbers

quant-ph↗

arXiv2018

Quantum Computing Circuits and Devices

The development of quantum computing technologies builds on the unique features of quantum physics while borrowing familiar principles from the design of conventional devices. We introduce the fundamental concepts required for designing and operating quantum computing devices by reviewing state of the art efforts to fabricate and demonstrate quantum gates and qubits. We summarize the near-term challenges for devices based on semiconducting, superconducting, and trapped ion technologies with an emphasis on design tools as well as methods of verification and validation. We then discuss the generation and synthesis of quantum circuits for higher-order logic that can be carried out using quantum computing devices.

quant-ph↗

arXiv2017

No fixed-point guarantee of Nash equilibrium in quantum games

The theory of quantum games permits players to choose strategies that prepare and measure quantum states. Whereas conventional game theory provides guarantees for fixed-point stability in non-cooperative games, so-called Nash equilibria, we find this guarantee is not provided for quantum games. In particular, we show the conditions for Glickberg's fixed-point theorem do not apply to pure quantum games when the payoff is a physical observable. We further show that Nash equilibrium can be guaranteed when the payoff is defined with respect to state preparation.

quant-ph↗