Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Scientific Reports

Extreme Quantum Advantage when Simulating Classical Systems with Long-Range Interaction

Cina Aghamohammadi, John R. Mahoney, James P. Crutchfield

Published Jul 21, 2017• 26 citations
Publisher

Abstract

Classical stochastic processes can be generated by quantum simulators instead of the more standard classical ones, such as hidden Markov models. One reason for using quantum simulators has recently come to the fore: they generally require less memory than their classical counterparts. Here, we examine this quantum advantage for strongly coupled spin systems-in particular, the Dyson one-dimensional Ising spin chain with variable interaction length. We find that the advantage scales with both interaction range and temperature, growing without bound as interaction range increases. In particular, simulating Dyson's original spin chain with the most memory-efficient classical algorithm known requires infinite memory, while a quantum simulator requires only finite memory. Thus, quantum systems can very efficiently simulate strongly coupled one-dimensional classical spin systems.

DOI
10.1038/s41598-017-04928-7

Related papers

Extreme Quantum Advantage when Simulating Strongly Coupled Classical Systems

Cina Aghamohammadi, John R. Mahoney, James P. Crutchfield

Classical stochastic processes can be generated by quantum simulators instead of the more standard classical ones, such as hidden Markov models. One reason for using quantum simulators is that they generally require less memory than their classical counterparts. Here, we examine this quantum advantage for strongly coupled spin systems---the Dyson-like one-dimensional Ising spin chain with variable interaction length. We find that the advantage scales with both interaction range and temperature, growing without bound as interaction increases. Thus, quantum systems can very efficiently simulate strongly coupled classical systems.

arXiv:1609.03650•Bulletin of the American Physical Society•Sep 13, 2016•3 citations

Dimensional Quantum Memory Advantage in the Simulation of Stochastic Processes

Farzad Ghafari, Nora Tischler, Jayne Thompson +7 more

Stochastic processes underlie a vast range of natural and social phenomena.Some processes such as atomic decay feature intrinsic randomness, whereas other complex processes, e.g., traffic congestion, are effectively probabilistic because we cannot track all relevant variables.To simulate a stochastic system's future behavior, information about its past must be stored, and thus memory is a key resource.Quantum information processing promises a memory advantage for stochastic simulation.Here, we report the first experimental demonstration that a quantum stochastic simulator can encode the required information in fewer dimensions than any classical simulator, thereby achieving a quantum advantage in minimal memory requirements using an individual simulator.This advantage is in contrast to recent proof-of-concept experiments, where the memory saving would only become accessible in the limit of a large number of parallel simulations.In those examples, the minimal memory registers of individual quantum simulators had the same dimensionality as their classical counterparts.Our photonic experiment thus establishes the potential of new, practical resource savings in the simulation of complex systems.

arXiv:1812.04251•Physical Review X•Oct 17, 2019•28 citations

Thermodynamically-efficient local computation and the inefficiency of quantum memory compression

Samuel P. Loomis, James P. Crutchfield

The authors show that quantum simulations of stochastic processes require less memory than classical simulations---a key quantum advantage over classical computers. However, this compression comes at the cost of increased thermodynamic dissipation. That is, quantum supremacy is incompatible with thermodynamic efficiency.

arXiv:2001.02258•Physical Review Research•Apr 14, 2020•5 citations

Provably unbounded memory advantage in stochastic simulation using quantum mechanics

Andrew J. P. Garner, Qing Liu, Jayne Thompson +2 more

Simulating the stochastic evolution of real quantities on a digital computer requires a trade-off between the precision to which these quantities are approximated, and the memory required to store them. The statistical accuracy of the simulation is thus generally limited by the internal memory available to the simulator. Here, using tools from computational mechanics, we show that quantum processors with a fixed finite memory can simulate stochastic processes of real variables to arbitrarily high precision. This demonstrates a provable, unbounded memory advantage that a quantum simulator can exhibit over its best possible classical counterpart.

arXiv:1609.04408•New Journal of Physics•Oct 12, 2017•28 citations

The classical-quantum divergence of complexity in modelling spin chains

Whei Yeap Suen, Jayne E. Thompson, Andrew J. P. Garner +2 more

The minimal memory required to model a given stochastic process - known as the statistical complexity - is a widely adopted quantifier of structure in complexity science. Here, we ask if quantum mechanics can fundamentally change the qualitative behaviour of this measure. We study this question in the context of the classical Ising spin chain. In this system, the statistical complexity is known to grow monotonically with temperature. We evaluate the spin chain's quantum mechanical statistical complexity by explicitly constructing its provably simplest quantum model, and demonstrate that this measure exhibits drastically different behaviour: it rises to a maximum at some finite temperature then tends back towards zero for higher temperatures. This demonstrates how complexity, as captured by the amount of memory required to model a process, can exhibit radically different behaviour when quantum processing is allowed.

arXiv:1511.05738•Quantum•Aug 11, 2017•27 citations

Memory-efficient tracking of complex temporal and symbolic dynamics with quantum simulators

Thomas J. Elliott, Andrew J. P. Garner, Mile Gu

Tracking the behaviour of stochastic systems is a crucial task in the statistical sciences. It has recently been shown that quantum models can faithfully simulate such processes whilst retaining less information about the past behaviour of the system than the optimal classical models. We extend these results to general temporal and symbolic dynamics. Our systematic protocol for quantum model construction relies only on an elementary description of the dynamics of the process. This circumvents restrictions on corresponding classical construction protocols, and allows for a broader range of processes to be modelled efficiently. We illustrate our method with an example exhibiting an apparent unbounded memory advantage of the quantum model compared to its optimal classical counterpart.

arXiv:1803.05426•New Journal of Physics•Dec 12, 2018•18 citations
Classical stochastic processes can be generated by quantum simulators instead of the more standard classical ones, such as hidden Markov models. One reason for using quantum simulators has recently come to the fore: they generally require less memory than their classical counterparts. Here, we examine this quantum advantage for strongly coupled spin systems-in particular, the Dyson one-dimensional Ising spin chain with variable interaction length. We find that the advantage scales with both interaction range and temperature, growing without bound as interaction range increases. In particular, simulating Dyson's original spin chain with the most memory-efficient classical algorithm known requires infinite memory, while a quantum simulator requires only finite memory. Thus, quantum systems can very efficiently simulate strongly coupled one-dimensional classical spin systems.
Classical stochastic processes can be generated by quantum simulators instead of the more standard classical ones, such as hidden Markov models. One reason for using quantum simulators is that they generally require less memory than their classical counterparts. Here, we examine this quantum advantage for strongly coupled spin systems---the Dyson-like one-dimensional Ising spin chain with variable interaction length. We find that the advantage scales with both interaction range and temperature, growing without bound as interaction increases. Thus, quantum systems can very efficiently simulate strongly coupled classical systems.
Stochastic processes underlie a vast range of natural and social phenomena.Some processes such as atomic decay feature intrinsic randomness, whereas other complex processes, e.g., traffic congestion, are effectively probabilistic because we cannot track all relevant variables.To simulate a stochastic system's future behavior, information about its past must be stored, and thus memory is a key resource.Quantum information processing promises a memory advantage for stochastic simulation.Here, we report the first experimental demonstration that a quantum stochastic simulator can encode the required information in fewer dimensions than any classical simulator, thereby achieving a quantum advantage in minimal memory requirements using an individual simulator.This advantage is in contrast to recent proof-of-concept experiments, where the memory saving would only become accessible in the limit of a large number of parallel simulations.In those examples, the minimal memory registers of individual quantum simulators had the same dimensionality as their classical counterparts.Our photonic experiment thus establishes the potential of new, practical resource savings in the simulation of complex systems.
Simulating the stochastic evolution of real quantities on a digital computer requires a trade-off between the precision to which these quantities are approximated, and the memory required to store them. The statistical accuracy of the simulation is thus generally limited by the internal memory available to the simulator. Here, using tools from computational mechanics, we show that quantum processors with a fixed finite memory can simulate stochastic processes of real variables to arbitrarily high precision. This demonstrates a provable, unbounded memory advantage that a quantum simulator can exhibit over its best possible classical counterpart.
The minimal memory required to model a given stochastic process - known as the statistical complexity - is a widely adopted quantifier of structure in complexity science. Here, we ask if quantum mechanics can fundamentally change the qualitative behaviour of this measure. We study this question in the context of the classical Ising spin chain. In this system, the statistical complexity is known to grow monotonically with temperature. We evaluate the spin chain's quantum mechanical statistical complexity by explicitly constructing its provably simplest quantum model, and demonstrate that this measure exhibits drastically different behaviour: it rises to a maximum at some finite temperature then tends back towards zero for higher temperatures. This demonstrates how complexity, as captured by the amount of memory required to model a process, can exhibit radically different behaviour when quantum processing is allowed.
Tracking the behaviour of stochastic systems is a crucial task in the statistical sciences. It has recently been shown that quantum models can faithfully simulate such processes whilst retaining less information about the past behaviour of the system than the optimal classical models. We extend these results to general temporal and symbolic dynamics. Our systematic protocol for quantum model construction relies only on an elementary description of the dynamics of the process. This circumvents restrictions on corresponding classical construction protocols, and allows for a broader range of processes to be modelled efficiently. We illustrate our method with an example exhibiting an apparent unbounded memory advantage of the quantum model compared to its optimal classical counterpart.