Analog errors in quantum annealing: doom and hope

Pearson, Adam; Mishra, Anurag; Hen, Itay; Lidar, Daniel A.

doi:10.1038/s41534-019-0210-7

Cited by 70 publications

(53 citation statements)

References 84 publications

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“…Such may include (i) finite temperature effects not considered in Refs. [73][74][75]; (ii) transient phenomena due to the finite annealing time; and (iii) control errors, i.e., imprecision in the parameter setting in the devices [15].…”

Section: Average Kink Densitymentioning

confidence: 99%

“…Quantum simulations are emerging to be one of the important applications of quantum annealing [1][2][3][4], quite different, and arguably more natural, than the original intent of using such devices for optimization, the subject of many recent studies [5][6][7][8][9][10][11][12][13][14][15]. Prominent examples include the simulation of the Kosterlitz-Thouless topological phase transition [16,17] and three-dimensional spin glasses [18] using the D-Wave quantum annealing devices, that have successfully reproduced the behavior of various physical quantities and the structure of the phase diagram, as predicted by classical simulations.…”

Section: Introductionmentioning

confidence: 99%

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Probing the universality of topological defect formation in a quantum annealer: Kibble-Zurek mechanism and beyond

Bando

Susa

Oshiyama

et al. 2020

Phys. Rev. Research

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120

112

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The number of topological defects created in a system driven through a quantum phase transition exhibits a power-law scaling with the driving time. This universal scaling law is the key prediction of the Kibble-Zurek mechanism (KZM), and testing it using a hardware-based quantum simulator is a coveted goal of quantum information science. Here we provide such a test using quantum annealing. Specifically, we report on extensive experimental tests of topological defect formation via the one-dimensional transverse-field Ising model on two different D-Wave quantum annealing devices. We find that the quantum simulator results can indeed be explained by the KZM for open-system quantum dynamics with phase-flip errors, with certain quantitative deviations from the theory likely caused by factors such as random control errors and transient effects. In addition, we probe physics beyond the KZM by identifying signatures of universality in the distribution and cumulants of the number of kinks and their decay, and again find agreement with the quantum simulator results. This implies that the theoretical predictions of the generalized KZM theory, which assumes isolation from the environment, applies beyond its original scope to an open system. We support this result by extensive numerical computations. To check whether an alternative, classical interpretation of these results is possible, we used the spin-vector Monte Carlo model, a candidate classical description of the D-Wave device. We find that the degree of agreement with the experimental data from the D-Wave annealing devices is better for the KZM, a quantum theory, than for the classical spin-vector Monte Carlo model, thus favoring a quantum description of the device. Our work provides an experimental test of quantum critical dynamics in an open quantum system, and paves the way to new directions in quantum simulation experiments.

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Section: Average Kink Densitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Probing the universality of topological defect formation in a quantum annealer: Kibble-Zurek mechanism and beyond

Bando

Susa

Oshiyama

et al. 2020

Phys. Rev. Research

Self Cite

120

112

View full text Add to dashboard Cite

show abstract

“…Implementing the exact Ising model with all cross terms on the scale of the Higgs optimization problem would require hundreds of fully connected qubits; therefore, we prune the cross terms in the Ising Hamiltonian, retaining only the largest 5% of weights. This reduces the sensitivity to analog errors associated with small weights [67] and also allows a minor embedding operation [45][46][47][48] in combination with the classical polynomial-time fix_variables procedure in the D-Wave API to program the problem on the quantum annealer. Each logical qubit is mapped to a chain of physical ferromagnetically coupled qubits on the D-Wave device, where the internal coupling of each chain may be set to prevent thermal excitations and other noise from breaking the chain while still ensuring that the Hamiltonian drives the system dynamics [68].…”

Section: A Quantum Annealing On D-wavementioning

confidence: 99%

Quantum adiabatic machine learning by zooming into a region of the energy surface

et al. 2020

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Recent work has shown that quantum annealing for machine learning, referred to as QAML, can perform comparably to state-of-the-art machine learning methods with a specific application to Higgs boson classification. We propose QAML-Z, an algorithm that iteratively zooms in on a region of the energy surface by mapping the problem to a continuous space and sequentially applying quantum annealing to an augmented set of weak classifiers. Results on a programmable quantum annealer show that QAML-Z matches classical deep neural network performance at small training set sizes and reduces the performance margin between QAML and classical deep neural networks by almost 50% at large training set sizes, as measured by area under the receiver operating characteristic curve. The significant improvement of quantum annealing algorithms for machine learning and the use of a discrete quantum algorithm on a continuous optimization problem both opens a class of problems that can be solved by quantum annealers and suggests the approach in performance of near-term quantum machine learning towards classical benchmarks.

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“…The numerical range of the physical Ising model can be equivalent to the numerical range of the logical Ising model since the physical Ising model's coefficients are normalized from the logical Ising model's coefficients. However, the actual machines using quantum effect are susceptible to errors due to decoherence, control errors, diabatic transitions, and thermal noises [24], [37], [38], [39], [40], [41]. As pointed out in Refs.…”

Section: Motivationmentioning

confidence: 99%

“…In Refs. [41], [43], the control noise is assumed to be the Gaussian distribution with zero mean and standard deviation η = 0.015. Thus, the magnitude relationship of small interactions can be broken by the influence of noises.…”

Section: Motivationmentioning

confidence: 99%