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

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.

Quantum jump metrology

“…Similarly, quantum neural networks have also been shown to offer an enhancement versus their classical counterpart [56]. The dynamics of these quantum versions exhibit a higher degree of complexity which can result in an extreme advantage for a wide range of computational tasks, like the simulation of complex systems [57].…”

Matrix Product States for Quantum Stochastic Modeling

“…The classically minimal models, ε-machines, have been used in diverse contexts from neuroscience to nonequilibrium contextuality [6][7][8][9][10][11][12][13][14][15]. Recently, it was shown that quantum extensions of ε-machines can further reduce their memory [16], leading recent studies to find memoryefficient quantum means of predictive modeling [17][18][19][20][21][22][23][24][25][26][27].In condensed matter, on the other hand, simplicity is sought after for the description of quantum many-body systems. Tensor networks, such as matrix product states (MPS), for instance, provide an efficient and useful description of one-dimensional quantum systems-i.e., spin chains [28][29][30].…”

Practical Unitary Simulator for Non-Markovian Complex Processes

“…In general, C q ≤ C µ , C 0 q ≤ C 0 µ , and the ratios C µ /C q and C 0 µ /C 0 q can become arbitrarily large (see Supplementary Information B for an example of C µ /C q → ∞). Moreover, there are processes for which C q (ζ) (or C 0 q (ζ)) attains a finite asymptotic value while lim C µ (ζ) → ∞ (or lim C 0 µ (ζ) → ∞) as a function of some system parameter ζ [15,[28][29][30].…”