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arXiv:1907.12678 · npj Quantum Information

Analog errors in quantum annealing: doom and hope

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

Published Nov 28, 2019• 70 citations
arXivHTMLPDF

Abstract

Abstract Quantum annealing has the potential to provide a speedup over classical algorithms in solving optimization problems. Just as for any other quantum device, suppressing Hamiltonian control errors will be necessary before quantum annealers can achieve speedups. Such analog control errors are known to lead to $$J$$ J -chaos, wherein the probability of obtaining the optimal solution, encoded as the ground state of the intended Hamiltonian, varies widely depending on the control error. Here, we show that $$J$$ J -chaos causes a catastrophic failure of quantum annealing, in that the scaling of the time-to-solution metric becomes worse than that of a deterministic (exhaustive) classical solver. We demonstrate this empirically using random Ising spin glass problems run on the two latest generations of the D-Wave quantum annealers. We then proceed to show that this doomsday scenario can be mitigated using a simple error suppression and correction scheme known as quantum annealing correction (QAC). By using QAC, the time-to-solution scaling of the same D-Wave devices is improved to below that of the classical upper bound, thus restoring hope in the speedup prospects of quantum annealing.

DOI
10.1038/s41534-019-0210-7

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Abstract Quantum annealing has the potential to provide a speedup over classical algorithms in solving optimization problems. Just as for any other quantum device, suppressing Hamiltonian control errors will be necessary before quantum annealers can achieve speedups. Such analog control errors are known to lead to JJJ J -chaos, wherein the probability of obtaining the optimal solution, encoded as the ground state of the intended Hamiltonian, varies widely depending on the control error. Here, we show that JJJ J -chaos causes a catastrophic failure of quantum annealing, in that the scaling of the time-to-solution metric becomes worse than that of a deterministic (exhaustive) classical solver. We demonstrate this empirically using random Ising spin glass problems run on the two latest generations of the D-Wave quantum annealers. We then proceed to show that this doomsday scenario can be mitigated using a simple error suppression and correction scheme known as quantum annealing correction (QAC). By using QAC, the time-to-solution scaling of the same D-Wave devices is improved to below that of the classical upper bound, thus restoring hope in the speedup prospects of quantum annealing.
We demonstrate that the performance of a quantum annealer on hard random Ising optimization problems can be substantially improved using quantum annealing correction (QAC). Our error correction strategy is tailored to the D-Wave Two device. We find that QAC provides a statistically significant enhancement in the performance of the device over a classical repetition code, improving as a function of problem size as well as hardness. Moreover, QAC provides a mechanism for overcoming the precision limit of the device, in addition to correcting calibration errors. Performance is robust even to missing qubits. We present evidence for a constructive role played by quantum effects in our experiments by contrasting the experimental results with the predictions of a classical model of the device. Our work demonstrates the importance of error correction in appropriately determining the performance of quantum annealers.
Quantum annealing is a heuristic optimization algorithm that exploits quantum evolution to find low-energy states. Quantum annealers have scaled up in recent years to tackle increasingly larger and more highly connected discrete optimization and quantum simulation problems. Nevertheless, a computational quantum advantage in exact optimization using quantum annealing hardware has so far remained elusive. Here, we present evidence for a quantum annealing scaling advantage in approximate optimization. The advantage is relative to the top classical heuristic algorithm: parallel tempering with isoenergetic cluster moves (PT-ICM). The setting is a family of 2D spin-glass problems with high-precision spin-spin interactions. To achieve this advantage, we implement quantum annealing correction (QAC): an embedding of a bit-flip error-correcting code with energy penalties that leverages the properties of the D-Wave Advantage quantum annealer to yield over 1,300 error-suppressed logical qubits on a degree-5 interaction graph. We generate random spin-glass instances on this graph and benchmark their time-to-epsilon, a generalization of the time-to-solution metric for low-energy states. We demonstrate that, with QAC, quantum annealing exhibits a scaling advantage over PT-ICM at sampling low-energy states with an optimality gap of at least 1.0%. This amounts to the first demonstration of an algorithmic quantum speedup in approximate optimization.
Quantum annealing correction (QAC) models provide a promising approach for mitigating errors in quantum annealers. Previous studies have established that QAC models are crucial for ensuring the robustness of the ground state of the Ising model on hardware. In this work, the effects of QAC models incorporating replicas with additional interactions, specifically, the and the , are investigated for problems characterized by a small energy gap between the ground and first excited states during quantum annealing, a well-known bottleneck to reaching the ground state. The results demonstrate that these QAC models can obtain the optimal solution within short annealing times by exploiting diabatic transitions, even for problems with a small energy gap. These findings highlight the potential of QAC models as practical near-term algorithms for hardware subject to runtime limitations and control noise.
Abstract Quantum annealing is a heuristic optimization algorithm that exploits quantum evolution to approximately find lowest energy states [1, 2]. Quantum annealers have scaled up in recent years to tackle increasingly larger and more highly connected discrete optimization and quantum simulation problems [3–7]. Nevertheless, despite numerous attempts, a computational quantum advantage in exact optimization using quantum annealing hardware has so far remained elusive [8– 16]. Here, we present evidence for a quantum annealing scaling advantage in approximate optimization. The advantage is relative to the top classical heuristic algorithm: parallel tempering with isoenergetic cluster moves (PT-ICM) [17]. The setting is a family of 2D spin-glass problems with high-precision spin-spin interactions. To achieve this advantage, we implement quantum annealing correction (QAC) [18]: an embedding of a bit-flip error-correcting code with energy penalties that leverages the properties of the D-Wave Advantage quantum annealer to yield over 1,300 error-suppressed logical qubits on a degree-5 interaction graph. We generate random spin-glass instances on this graph and benchmark their time-to-epsilon, a generalization of the time-to-solution metric [8] for low-energy states. We demonstrate that with QAC, quantum annealing exhibits a scaling advantage over PT-ICM at sampling low energy states with an optimality gap [19] of at least 1.0%. This amounts to the first demonstration of an algorithmic quantum speedup in approximate optimization.
Recent tests performed on the D-Wave Two quantum annealer have revealed no clear evidence of speedup over conventional silicon-based technologies. Here we present results from classical parallel-tempering Monte Carlo simulations combined with isoenergetic cluster moves of the archetypal benchmark problem---an Ising spin glass---on the native chip topology. Using realistic uncorrelated noise models for the D-Wave Two quantum annealer, we study the best-case resilience, i.e., the probability that the ground-state configuration is not affected by random fields and random-bond fluctuations found on the chip. We thus compute classical upper-bound success probabilities for different types of disorder used in the benchmarks and predict that an increase in the number of qubits will require either error correction schemes or a drastic reduction of the intrinsic noise found in these devices. We restrict this study to the exact ground state, however, the approach can be trivially extended to the inclusion of excited states if the success metric is relaxed. We outline strategies to develop robust, as well as hard benchmarks for quantum annealing devices, as well as any other (black box) computing paradigm affected by noise.
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.