On Post-processing the Results of Quantum Optimizers

Borle, Ajinkya; McCarter, Josh

doi:10.1007/978-3-030-34500-6_16

Cited by 6 publications

(3 citation statements)

References 33 publications

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“…For the benchmarks, we draw the Hamiltonian coefficients of the QMIs from the standard normal distribution (a mean of 0 and a standard deviation of 1). This approach is a common practice used in prior works related to benchmarking QAs 7,27,31,49,50 . To avoid the impact of embedding on our evaluations, we directly use the connectivity graph of the D-Wave QA.…”

Section: Benchmarksmentioning

confidence: 99%

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EQUAL: Improving the Fidelity of Quantum Annealers by Injecting Controlled Perturbations

Ayanzadeh

Das²,

Tannu³

et al. 2022

Preprint

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Quantum Annealers (QAs) are single-instruction quantum machines that can only sample from the ground state of an energy function, called Hamiltonian. To execute a program, the problem is cast to a Hamiltonian, embedded on the hardware, and a single quantum machine instruction (QMI) is run. Noise and imperfections in hardware result in sub-optimal solutions on QAs even if the QMI is run for thousands of trials. Owing to the limited programmability of QAs, users execute the same QMI for all trials. This subjects all trials to a similar noise profile throughout the execution, resulting in a systematic bias. We observe that systematic bias leads to sub-optimal solutions and cannot be alleviated by executing more trials or using existing error-mitigation schemes. To address this challenge, we propose EQUAL (Ensemble QUantum AnneaLing). EQUAL generates an ensemble of QMIs by adding controlled perturbations to the program QMI. When executed on the QA, the ensemble of QMIs steers the program away from encountering the same bias during all trials and thus, improves the quality of solutions. Our evaluations using the D-Wave 2000Q machine show that EQUAL bridges the difference between the baseline and the ideal by an average of 14% (and up to 26%), without requiring any additional trials. EQUAL can be combined with existing error mitigation schemes to bridge further the difference between the baseline and ideal by an average of 55% (and up to 68%).

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Section: Benchmarksmentioning

confidence: 99%

“…Addressing these limitations requires device-level enhancements that may span generations of QAs. Therefore, leveraging software techniques to improve the reliability of QAs is an important area of research [28][29][30][31][32][33] .…”

Section: Introductionmentioning

confidence: 99%

EQUAL: Improving the Fidelity of Quantum Annealers by Injecting Controlled Perturbations

Ayanzadeh

Das²,

Tannu³

et al. 2022

Preprint

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“…Other approaches combining quantum annealing with classical simulated annealing have been considered [15]. In [8,3], an approach is discussed that starts off with a collection of samples from the D-Wave annealer. Using the pool of samples, a new sample is constructed for every pair of samples, with the property that its energy is never higher than the one of the two samples it was derived from.…”

Section: Literature Reviewmentioning

confidence: 99%

Advanced unembedding techniques for quantum annealers

Pelofske,

Hahn,

Djidjev

2020

Preprint

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The D-Wave quantum annealers make it possible to obtain high quality solutions of NP-hard problems by mapping a problem in a QUBO (quadratic unconstrained binary optimization) or Ising form to the physical qubit connectivity structure on the D-Wave chip. However, the latter is restricted in that only a fraction of all pairwise couplers between physical qubits exists. Modeling the connectivity structure of a given problem instance thus necessitates the computation of a minor embedding of the variables in the problem specification onto logical qubits, which consist of several physical qubits "chained" together to act as a logical one. After annealing, it is however not guaranteed that all chained qubits get the same value (-1 or +1 for an Ising model, and 0 or 1 for a QUBO), and several approaches exist to assign a final value to each logical qubit (a process called "unembedding"). In this work, we present tailored unembedding techniques for four important NP-hard problems: the Maximum Clique, Maximum Cut, Minimum Vertex Cover, and Graph Partitioning problems. Our techniques are simple and yet make use of structural properties of the problem being solved. Using Erdős-Rényi random graphs as inputs, we compare our unembedding techniques to three popular ones (majority vote, random weighting, and minimize energy). We demonstrate that our proposed algorithms outperform the currently available ones in that they yield solutions of better quality, while being computationally equally efficient.

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Multi-qubit correction for quantum annealers

Ayanzadeh

Dorband

Halem

et al. 2021

Sci Rep

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We present multi-qubit correction (MQC) as a novel postprocessing method for quantum annealers that views the evolution in an open-system as a Gibbs sampler and reduces a set of excited states to a new synthetic state with lower energy value. After sampling from the ground state of a given (Ising) Hamiltonian, MQC compares pairs of excited states to recognize virtual tunnels—i.e., a group of qubits that changing their states simultaneously can result in a new state with lower energy value—and successively converges to the ground state. Experimental results using D-Wave 2000Q quantum annealers demonstrate that MQC finds samples with notably lower energy values and improves the reproducibility of results when compared to recent hardware/software advances in the realm of quantum annealing, such as spin-reversal transforms, classical postprocessing techniques, and increased inter-sample delay between successive measurements.

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On Post-processing the Results of Quantum Optimizers

Cited by 6 publications

References 33 publications

EQUAL: Improving the Fidelity of Quantum Annealers by Injecting Controlled Perturbations

EQUAL: Improving the Fidelity of Quantum Annealers by Injecting Controlled Perturbations

Advanced unembedding techniques for quantum annealers

Multi-qubit correction for quantum annealers

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