Thermalization, Freeze-out, and Noise: Deciphering Experimental Quantum Annealers

Marshall, Jeffrey; Rieffel, Eleanor; Hen, Itay

doi:10.1103/physrevapplied.8.064025

Cited by 41 publications

(63 citation statements)

References 31 publications

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“…The specific spin system we study, namely spin glasses, is very relevant as current experimental quantum annealers attempt to solve precisely this type of problem. With questions still lingering about which distribution these devices sample from [30], it is important to have an accurate tool to estimate the DOS (for instance to understand thermalization [30]). For this problem we specifically consider instances with vastly different hardnesses, confirming that the accuracy of the technique proposed degrades significantly less for harder samples that previous approaches.…”

Section: Summary and Discussionmentioning

confidence: 99%

“…It follows then that the planted solution is also a ground state of the total Hamiltonian. This class of instances has two attractive properties: (i) the ground-state energies of the generated problems are known in advance, and (ii) the exact degeneracies of the ground and first excited states are computable [27,30]. These in turn allow us to check how close entropic samplers come to these exact values.…”

Section: Verifiable Benchmarking Of Entropic Samplersmentioning

confidence: 99%

“…While this approach in principle works for arbitrary graphs, we focus here on Chimera lattices, i.e. twodimensional arrays of unit cells of eight spins with a K 4,4 bipartite connectivity [43,44], see for example [30]. Our choice is motivated by the attention these graphs have gained in recent years in the context of optimization as well as sampling via quantum annealing as the quantum annealers currently commercially available feature qubits connected with this topology [45][46][47].…”

Section: Verifiable Benchmarking Of Entropic Samplersmentioning

confidence: 99%

“…The currently available commercial realization of this paradigm [20] effectively samples low-lying energy configurations of spin-glass samples that are coded into the couplers connecting an array of superconducting flux qubits. The properties of the resulting samples and the question of whether such devices indeed provide superior performance as compared to classical algorithms for some problem classes has been the subject of much recent debate [21][22][23][24][25][26][27][28][29][30]. The questions of reliable Boltzmann sampling aided by quantum annealers for machine learning applications [24][25][26] as well as the advantages that quantum annealing devices potentially hold when tasked with fairly sampling the ground-state manifolds of spin glasses with multiple minimizing configurations [27][28][29] are now a topic of considerable interest.…”

Section: Introductionmentioning

confidence: 99%

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Estimating the density of states of frustrated spin systems

et al. 2019

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Estimating the density of states (DOS) of systems with rugged free energy landscapes is a notoriously difficult task of the utmost importance in many areas of physics ranging from spin glasses to biopolymers. DOS estimation has also recently become an indispensable tool for the benchmarking of quantum annealers when these function as samplers. Some of the standard approaches suffer from a spurious convergence of the estimates to metastable minima, and these cases are particularly hard to detect. Here, we introduce a sampling technique based on population annealing enhanced with a multi-histogram analysis and report on its performance for spin glasses. We demonstrate its ability to overcome the pitfalls of other entropic samplers, resulting in some cases in large scaling advantages that can lead to the uncovering of new physics. The new technique avoids some inherent difficulties in established approaches and can be applied to a wide range of systems without relevant tailoring requirements. Benchmarking of the studied techniques is facilitated by the introduction of several schemes that allow us to achieve exact counts of the degeneracies of the tested instances.

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Section: Summary and Discussionmentioning

confidence: 99%

Section: Verifiable Benchmarking Of Entropic Samplersmentioning

confidence: 99%

Section: Verifiable Benchmarking Of Entropic Samplersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Estimating the density of states of frustrated spin systems

et al. 2019

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“…To make matters worse, Ref. [13] found that effective sampling temperatures on an experimental quantum annealer tend to increase with problem size. Embedding therefore inevitably leads to the observation of states which are not in the logical subspace, and since the probability of this occurring nominally scales exponentially in N (Eq.…”

Section: Discussionmentioning

confidence: 99%

Perils of embedding for sampling problems

Marshall

Gioacchino

Rieffel

2020

Phys. Rev. Research

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Sampling from certain distributions is a prohibitively challenging task. Special-purpose hardware such as quantum annealers may be able to more efficiently sample from such distributions, which could find application in optimization, sampling tasks, and machine learning. Current quantum annealers impose certain constraints on the structure of the cost Hamiltonian due to the connectivity of the individual processing units. This means that in order to solve many problems of interest, one is required to embed the native graph into the hardware graph. The effect of embedding for sampling is more pronounced than for optimization; for optimization one is just concerned with mapping ground states to ground states, whereas for sampling one needs to consider states at all energies. We argue that as the problem size grows, or the embedding size grows, the chance of a sample being in the logical subspace is exponentially suppressed. It is therefore necessary to construct post-processing techniques to evade this exponential sampling overhead, techniques that project from the embedded distribution one is physically sampling from, back to the logical space of the native problem. We show that the most naive (and most common) projection technique, known as majority vote, can fail quite spectacularly at preserving distribution properties. We show that, even with care, one cannot avoid bias in the general case. Specifically we prove through a simple and generic (counter) example that no post-processing technique, under reasonable assumptions, can avoid biasing the statistics in the general case. On the positive side, we demonstrate a new resampling technique for performing this projection which substantially out-performs majority vote and may allow one to much more effectively sample from graphs of interest.

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