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arXiv:1906.00263

Quantum-inspired memory-enhanced stochastic algorithms

John Realpe-Gómez, Nathan Killoran

Published Jun 1, 2019• 0 citations
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Abstract

Stochastic models are highly relevant tools in science, engineering, and society. Recent work suggests emerging quantum computing technologies can substantially decrease the memory requirements for simulating stochastic models. Here we show that some of these recent quantum memory-enhanced algorithms can be either implemented or approximated classically. In other words, we show that it is possible to develop quantum-inspired classical algorithms that require much less memory than the best classical algorithms known to date. Being classical, such algorithms could be implemented in state-of-the-art high-performance computers, which could potentially enhance the study of large-scale complex systems. Furthermore, since memory is the main bottleneck limiting the performance of classical supercomputers in one of the most promising avenues to demonstrate quantum 'supremacy', we expect adaptations of these ideas may potentially further raise the bar for near-term quantum computers to reach such a milestone.

DOI
10.48550/arxiv.1906.00263

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Stochastic models are highly relevant tools in science, engineering, and society. Recent work suggests emerging quantum computing technologies can substantially decrease the memory requirements for simulating stochastic models. Here we show that some of these recent quantum memory-enhanced algorithms can be either implemented or approximated classically. In other words, we show that it is possible to develop quantum-inspired classical algorithms that require much less memory than the best classical algorithms known to date. Being classical, such algorithms could be implemented in state-of-the-art high-performance computers, which could potentially enhance the study of large-scale complex systems. Furthermore, since memory is the main bottleneck limiting the performance of classical supercomputers in one of the most promising avenues to demonstrate quantum 'supremacy', we expect adaptations of these ideas may potentially further raise the bar for near-term quantum computers to reach such a milestone.
Stochastic modeling of complex systems plays an essential, yet often computationally intensive, role across the quantitative sciences.Recent advances in quantum information processing have elucidated the potential for quantum simulators to exhibit memory advantages for such tasks.Heretofore, the focus has been on lossless memory compression, wherein the advantage is typically in terms of lessening the amount of information tracked by the model, while-arguably more practical-reductions in memory dimension are not always possible.Here, we address the case of lossy compression for quantum stochastic modeling of continuous-time processes, introducing a method for coarse graining in quantum state space that drastically reduces the requisite memory dimension for modeling temporal dynamics while retaining near-exact statistics.In contrast to classical coarse graining, this compression is not based on sacrificing temporal resolution and brings memory-efficient high-fidelity stochastic modeling within reach of present quantum technologies.
Error mitigation has been one of the recently sought after methods to reduce the effects of noise when computation is performed on a noisy near-term quantum computer. Interest in simulating stochastic processes with quantum models gained popularity after being proven to require less memory than their classical counterparts. With previous work on quantum models focusing primarily on further compressing memory, this work branches out into the experimental scene; we aim to bridge the gap between theoretical quantum models and practical use with the inclusion of error mitigation methods. It is observed that error mitigation is successful in improving the resultant expectation values. While our results indicate that error mitigation work, we show that its methodology is ultimately constrained by hardware limitations in these quantum computers.
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As we begin to reach the limits of classical computing, quantum computing has emerged as a technology that has captured the imagination of the scientific world. While for many years, the ability to execute quantum algorithms was only a theoretical possibility, recent advances in hardware mean that quantum computing devices now exist that can carry out quantum computation on a limited scale. Thus, it is now a real possibility, and of central importance at this time, to assess the potential impact of quantum computers on real problems of interest. One of the earliest and most compelling applications for quantum computers is Feynman's idea of simulating quantum systems with many degrees of freedom. Such systems are found across chemistry, physics, and materials science. The particular way in which quantum computing extends classical computing means that one cannot expect arbitrary simulations to be sped up by a quantum computer, thus one must carefully identify areas where quantum advantage may be achieved. In this review, we briefly describe central problems in chemistry and materials science, in areas of electronic structure, quantum statistical mechanics, and quantum dynamics that are of potential interest for solution on a quantum computer. We then take a detailed snapshot of current progress in quantum algorithms for ground-state, dynamics, and thermal-state simulation and analyze their strengths and weaknesses for future developments.
Isolating past information relevant for future prediction is central to quantitative science. Quantum models offer a promising approach, enabling statistically faithful modeling while using less past information than any classical counterpart. Here we introduce a class of phase-enhanced quantum models, representing the most general means of simulating a stochastic process unitarily in causal order. The resulting constructions surpass previous state-of-art methods---both in reducing the information they need to store about the past and in the minimal memory dimension they require to store this information. Moreover, these two features are generally competing factors in optimization---leading to an ambiguity in optimal modeling that is unique to the quantum regime. Our results simultaneously offer quantum advantages for stochastic simulation and illustrate further qualitative differences between classical and quantum notions of complexity.
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