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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Enhancing quantum annealing accuracy through replication-based error mitigation *

Abstract Quantum annealers like those manufactured by D-Wave Systems are designed to find high quality solutions to optimization problems that are typically hard for classical computers. They utilize quantum effects like tunneling to evolve toward low-energy states representing solutions to optimization problems. However, their analog nature and limited control functionalities present challenges to correcting or mitigating hardware errors. As quantum computing advances towards applications, effective error suppression is an important research goal. We propose a new approach called replication based mitigation (RBM) based on parallel quantum annealing (QA). In RBM, physical qubits representing the same logical qubit are dispersed across different copies of the problem embedded in the hardware. This mitigates hardware biases, is compatible with limited qubit connectivity in current annealers, and is well-suited for currently available noisy intermediate-scale quantum annealers. Our experimental analysis shows that RBM provides solution quality on par with previous methods while being more flexible and compatible with a wider range of hardware connectivity patterns. In comparisons against standard QA without error mitigation on larger problem instances that could not be handled by previous methods, RBM consistently gets better energies and ground state probabilities across parameterized problem sets.

Djidjev, Hristo N. (ORCID:0000000192868824)↗
DOE OSTI2021

Charged particle tracking with quantum annealing optimization

Abstract At the High Luminosity Large Hadron Collider (HL-LHC), traditional track reconstruction techniques that are critical for physics analysis will need to be upgraded to scale with track density. Quantum annealing has shown promise in its ability to solve combinatorial optimization problems amidst an ongoing effort to establish evidence of a quantum speedup. As a step towards exploiting such potential speedup, we investigate a track reconstruction approach by adapting the existing geometric Denby-Peterson (Hopfield) network method to the quantum annealing framework for HL-LHC conditions. We develop additional techniques to embed the problem onto existing and near-term quantum annealing hardware. Results using simulated annealing and quantum annealing with the D-Wave 2X system on the TrackML open dataset are presented, demonstrating the successful application of a quantum annealing algorithm to the track reconstruction challenge. We find that combinatorial optimization problems can effectively reconstruct tracks, suggesting possible applications for fast hardware-specific implementations at the HL-LHC while leaving open the possibility of a quantum speedup for tracking.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Quantum Annealing with Inequality Constraints: The Set Cover Problem

Abstract Quantum annealing is a promising method for solving hard optimization problems by transforming them into quadratic unconstrained binary optimization (QUBO) problems. However, when constraints are involved, particularly multiple inequality constraints, incorporating them into the objective function poses challenges. In this paper, the authors present two novel approaches for solving problems with multiple inequality constraints on a quantum annealer and apply them to the set cover problem (SCP). The first approach uses the augmented Lagrangian method to represent the constraints, while the second approach employs a higher‐order binary optimization (HUBO) formulation. The experiments show that both approaches outperform the standard approach for solving the SCP on the D‐Wave Advantage quantum annealer. The HUBO formulation performs slightly better than the augmented Lagrangian method in solving the SCP, but its scalability in terms of embeddability in the quantum chip is worse. The results demonstrate that the proposed augmented Lagrangian and HUBO methods can successfully implement a large number of inequality constraints, making them applicable to a broad range of constrained problems beyond the SCP.

Djidjev, Hristo N.↗
DOE OSTI2024

On the emerging potential of quantum annealing hardware for combinatorial optimization

Abstract Over the past decade, the usefulness of quantum annealing hardware for combinatorial optimization has been the subject of much debate. Thus far, experimental benchmarking studies have indicated that quantum annealing hardware does not provide an irrefutable performance gain over state-of-the-art optimization methods. However, as this hardware continues to evolve, each new iteration brings improved performance and warrants further benchmarking. To that end, this work conducts an optimization performance assessment of D-Wave Systems’ Advantage Performance Update computer, which can natively solve sparse unconstrained quadratic optimization problems with over 5,000 binary decision variables and 40,000 quadratic terms. We demonstrate that classes of contrived problems exist where this quantum annealer can provide run time benefits over a collection of established classical solution methods that represent the current state-of-the-art for benchmarking quantum annealing hardware. Although this work does not present strong evidence of an irrefutable performance benefit for this emerging optimization technology, it does exhibit encouraging progress, signaling the potential impacts on practical optimization tasks in the future.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗
NASA NTRS2020

A Path Towards Quantum Advantage in Training Deep Generative Models with Quantum Annealing

A class of quantum-classical hybrid machine-learning algorithms can be obtained by integrating classical deep generative models with quantum probability distributions as 'priors' over their latent variables. We introduce a hybrid implementation of variational autoencoders (QVAE) and also present a technique to hybridize flow-based invertible generative models. We demonstrate the use of D-Wave quantum annealers as physical simulators of quantum Boltzmann machines (QBM) to perform quantum-assisted training of QVAE. Latent-space QBM develop slowly mixing modes, opening a path to obtain quantum advantage in generative modeling with available quantum devices.

Vinci, Walter↗
DOE OSTI2024

Quantum Annealing for Real-World Machine Learning Applications

Optimizing the training of a machine learning pipeline is important for reducing training costs and improving model performance. One such optimizing strategy is quantum annealing, which is an emerging computing paradigm that has shown potential in optimizing the training of a machine learning model. The implementation of a physical quantum annealer has been realized by D-Wave systems and is available to the research community for experiments. Recent experimental results on a variety of machine learning applications have shown interesting results especially under the conditions where the performance of classical machine learning techniques are limited such as limited training data and high dimensional features. This chapter explores the application of D-Wave’s quantum annealer for optimizing machine learning pipelines for real-world classification problems. We review the application domains on which a physical quantum annealer has been used to train machine learning classifiers. We discuss and analyze the experiments performed on the D-Wave quantum annealer for applications such as image recognition, remote sensing imagery, security, computational biology, biomedical sciences, and physics. We discuss the possible advantages and the problems for which quantum annealing is likely to be advantageous over classical computation.

Kumar nath, Rajdeep↗
DOE OSTI2025

Quantum annealing for combinatorial optimization: a benchmarking study

Quantum annealing (QA) has the potential to significantly improve solution quality and reduce time complexity in solving combinatorial optimization problems compared to classical optimization methods. However, due to the limited number of qubits and their connectivity, the QA hardware did not show such an advantage over classical methods in past benchmarking studies. Recent advancements in QA with more than 5000 qubits, enhanced qubit connectivity, and the hybrid architecture promise to realize the quantum advantage. Here, we use a quantum annealer with state-of-the-art techniques and benchmark its performance against classical solvers. To compare their performance, we solve over 50 optimization problem instances represented by large and dense Hamiltonian matrices using quantum and classical solvers. The results demonstrate that a state-of-the-art quantum solver has higher accuracy (~0.013%) and a significantly faster problem-solving time (~6561×) than the best classical solver. Our results highlight the advantages of leveraging QA over classical counterparts, particularly in hybrid configurations, for achieving high accuracy and substantially reduced problem solving time in large-scale real-world optimization problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Short-depth QAOA circuits and quantum annealing on higher-order ising models

Abstract We present a direct comparison between QAOA (Quantum Alternating Operator Ansatz), and QA (Quantum Annealing) on 127 qubit problem instances. QAOA with p = 1, 2 rounds is executed on the 127 qubit heavy-hex graph gate-model quantum computer ibm_washington, using on-device grid-searches for angle finding, and QA is executed on two Pegasus-chip D-Wave quantum annealers. The problems are random Ising models whose connectivity matches heavy-hex graphs and the Pegasus graph connectivity, and optionally include hardware-compatible cubic terms ( Z Z Z terms). The QAOA circuits are heavily optimized and of extremely short depth, with a CNOT depth of 6 per round, which allows whole chip usage of the heavy-hex lattice. QAOA and QA are both compared against simulated annealing and the optimal solutions are computed exactly using CPLEX. The noiseless mean QAOA expectation values for p = 1, 2 are computed using classical light-cone based simulations. We find QA outperforms QAOA on the evaluated devices.

127 qubits↗
NASA NTRS2017

Exponentially-Biased Ground-State Sampling of Quantum Annealing Machines with Transverse-Field Driving Hamiltonians

We study the performance of the D-Wave 2X quantum annealing machine on systems with well-controlled ground-state degeneracy. While obtaining the ground state of a spin-glass benchmark instance represents a difficult task, the gold standard for any optimization algorithm or machine is to sample all solutions that minimize the Hamiltonian with more or less equal probability. Our results show that while naive transverse-field quantum annealing on the D-Wave 2X device can find the ground-state energy of the problems, it is not well suited in identifying all degenerate ground-state configurations associated to a particular instance. Even worse, some states are exponentially suppressed, in agreement with previous studies on toy model problems [New J. Phys. 11, 073021 (2009)]. These results suggest that more complex driving Hamiltonians are needed in future quantum annealing machines to ensure a fair sampling of the ground-state manifold.

Quantum Annealing↗
DOE OSTI2023

Diabatic quantum annealing for the frustrated ring model

Abstract Quantum annealing (QA) is a continuous-time heuristic quantum algorithm for solving or approximately solving classical optimization problems. The algorithm uses a schedule to interpolate between a driver Hamiltonian with an easy-to-prepare ground state and a problem Hamiltonian whose ground state encodes solutions to an optimization problem. The standard implementation relies on the evolution being adiabatic: keeping the system in the instantaneous ground state with high probability and requiring a time scale inversely related to the minimum energy gap between the instantaneous ground and excited states. However, adiabatic evolution can lead to evolution times that scale exponentially with the system size, even for computationally simple problems. Here, we study whether non-adiabatic evolutions with optimized annealing schedules can bypass this exponential slowdown for one such class of problems called the frustrated ring model. For sufficiently optimized annealing schedules and system sizes of up to 39 qubits, we provide numerical evidence that we can avoid the exponential slowdown. Our work highlights the potential of highly-controllable QA to circumvent bottlenecks associated with the standard implementation of QA.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2023

Quantum Image Denoising: A Framework via Boltzmann Machines, QUBO, and Quantum Annealing

We investigate a framework for binary image denoising via restricted Boltzmann machines (RBMs) that introduces a denoising objective in quadratic unconstrained binary optimization (QUBO) form and is well-suited for quantum annealing. The denoising objective is attained by balancing the distribution learned by a trained RBM with a penalty term for derivations from the noisy image. We derive the statistically optimal choice of the penalty parameter assuming the target distribution has been well-approximated, and further suggest an empirically supported modification to make the method robust to that idealistic assumption. We also show under additional assumptions that the denoised images attained by our method are, in expectation, strictly closer to the noise-free images than the noisy images are. While we frame the model as an image denoising model, it can be applied to any binary data. As the QUBO formulation is well-suited for implementation on quantum annealers, we test the model on a D-Wave Advantage machine, and also test on data too large for current quantum annealers by approximating QUBO solutions through classical heuristics.

restricted Boltzmann machine↗
DOE OSTI2024

Solving the homogeneous Bethe-Salpeter equation with a quantum annealer

The homogeneous Bethe-Salpeter equation (hBSE), describing a bound system in a genuinely relativistic quantum-field theory framework, was solved for the first time by using a D-Wave quantum annealer. After applying standard techniques of discretization, the hBSE, in ladder approximation, can be formally transformed in a generalized eigenvalue problem (GEVP), with two square matrices: one symmetric and the other nonsymmetric. The latter matrix poses the challenge of obtaining a suitable formal approach for investigating the GEVP by means of a quantum annealer, i.e., to recast it as a quadratic unconstrained binary optimization problem. A broad numerical analysis of the proposed algorithms, applied to matrices of dimension up to 64, was carried out by using both the simulated-annealing package and the D-Wave . The numerical results very nicely compare with those obtained with standard classical algorithms, and also show interesting scalability features. Published by the American Physical Society 2024

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Prediction and compression of lattice QCD data using machine learning algorithms on quantum annealer

We present regression and compression algorithms for lattice QCD data utilizing the efficient binary optimization ability of quantum annealers. In the regression algorithm, we encode the correlation between the input and output variables into a sparse coding machine learning algorithm. The trained correlation pattern is used to predict lattice QCD observables of unseen lattice configurations from other observables measured on the lattice. In the compression algorithm, we define a mapping from lattice QCD data of floating-point numbers to the binary coefficients that closely reconstruct the input data from a set of basis vectors. Since the reconstruction is not exact, the mapping defines a lossy compression, but, a reasonably small number of binary coefficients are able to reconstruct the input vector of lattice QCD data with the reconstruction error much smaller than the statistical fluctuation. In both applications, we use D-Wave quantum annealers to solve the NP-hard binary optimization problems of the machine learning algorithms.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Lower Bounds on Quantum Annealing Times

The adiabatic theorem provides sufficient conditions for the time needed to prepare a target ground state. While it is possible to prepare a target state much faster with more general quantum annealing protocols, rigorous results beyond the adiabatic regime are rare. Here, we provide such a result, deriving lower bounds on the time needed to successfully perform quantum annealing. The bounds are asymptotically saturated by three toy models where fast annealing schedules are known: the Roland and Cerf unstructured search model, the Hamming spike problem, and the ferromagnetic p-spin model. Our bounds demonstrate that these schedules have optimal scaling. Herein, our results also show that rapid annealing requires coherent superpositions of energy eigenstates, singling out quantum coherence as a computational resource.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2019

The Power of Pausing: Advancing Understanding of Thermalization in Experimental Quantum Annealers

We investigate alternative annealing schedules on the current generation of quantum annealing hardware (the D-Wave 2000Q), which includes the use of forward and reverse annealing with an- intermediate pause. This work provides new insights into the inner workings of these devices (and quantum devices in general), particular into how thermal effects govern the system dynamics. We show that a pause mid-way through the anneal can cause a dramatic change in the output distribution, and we provide evidence suggesting thermalization is indeed occurring during such a pause. We demonstrate that upon pausing the system in a narrow region shortly after the minimum gap, the probability of successfully finding the ground state of the problem Hamiltonian can be increased by several orders of magnitude. We relate this effect to relaxation (i.e. thermalization) after diabatic and thermal excitations that occur in the region near to the minimum gap. For a set of large-scale problems of up to 500 qubits, we demonstrate that the distribution returned from the annealer very closely matches a (classical) Boltzmann distribution of the problem Hamiltonian, albeit one with a temperature at least 1.5 times higher than the (effective) temperature of the device. Moreover, we show that larger problems are more likely to thermalize to a classical Boltzmann distribution.

Marshall, Jeffrey↗
DOE OSTI2025

Comparing quantum annealing and spiking neuromorphic computing for sampling binary sparse coding QUBO problems

We consider the problem of computing a sparse binary representation of an image. Given an image and an overcomplete, non-orthonormal basis, we aim to find a sparse binary vector indicating the minimal set of basis vectors that when added together best reconstruct the given input. We formulate this problem with an L 2 loss on the reconstruction error, and an L 0 loss on the binary vector enforcing sparsity. First, we solve the sparse representation QUBOs by solving them both on a D-Wave quantum annealer with Pegasus chip connectivity, as well as on the Intel Loihi 2 spiking neuromorphic processor using a stochastic Non-equilibrium Boltzmann Machine (NEBM). Second, using Quantum Evolution Monte Carlo with Reverse Annealing and iterated warm starting on Loihi 2 to evolve the solution quality from the respective machines. We demonstrate that both quantum annealing and neuromorphic computing are suitable for solving binary sparse coding QUBOs.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Increasing the hardness of posiform planting using random QUBOs for programmable quantum annealer benchmarking

Posiform planting is a method for constructing QUBO instances with a unique planted solution that can be tailored to arbitrary connectivity graphs. In this study we investigate making posiform planted QUBOs computationally harder by fusing many smaller random Ising models, whose global minimum is computed classically, with posiform planted QUBOs. The unique ground state of the resulting QUBO is the concatenation of (exactly one of) the ground states of each smaller problem. Our method generates QUBO instances that have a unique solution, are native to the hardware graph, and have tunable computational hardness. We use our QUBOs to benchmark three D-Wave quantum annealing processors (with 563–5627 qubits), and compare them against simulated annealing and Gurobi. Surprisingly, we find that the D-Wave ground state sampling success rate is not dependent on the glued random QUBO size, and that some QUBO classes are solved at high success rates at short annealing times on the Zephyr processors.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗