Dimensional Quantum Memory Advantage in the Simulation of Stochastic Processes

Abstract

Stochastic processes underlie a vast range of natural and social phenomena [1,2]. 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 behaviour, information about its past must be stored [3,4]and thus memory is a key resource. Quantum information processing promises a memory advantage for stochastic simulation [5][6][7][8][9][10][11][12][13][14][15] that has been validated in recent proof-of-concept experiments [16,17]. Yet, in all past works, the memory saving would only become accessible in the limit of a large number of parallel simulations [6,18], because the memory registers of individual quantum simulators had the same dimensionality as their classical counterparts. Here, we report the first experimental demonstration that a quantum stochastic simulator can encode the relevant information in fewer dimensions than any classical simulator, thereby achieving a quantum memory advantage even for an individual simulator. Our photonic experiment thus establishes the potential of a new, practical resource saving in the simulation of complex systems.

Memory compression and thermal efficiency of quantum implementations of non-deterministic hidden Markov models

“…As with quantum implementations of predictive generators, proof-of-principle demonstrations of these advantages are within reach of current experiments [67][68][69]. In taking quantum memory and thermodynamical advantages in stochastic modelling to a more general medium, we open up a number of future research avenues, some paralleling developments in quantum implementations of predictive generators, some unique to the wider spectrum.…”

Quantum adaptive agents with efficient long-term memories

“…( 3). Proof-ofprinciple demonstrations are feasible with current setups, by, for example, adapting prior implementations of quantum models of passive stochastic processes in photonic setups [45,46] to undergo different evolutions at each timestep conditional on the input.…”

Quantum-enhanced analysis of discrete stochastic processes

“…Simulation of physical processes on quantum computers [1,2] has many facets, with recent developments improving the usage of this technology [3][4][5][6][7][8][9][10][11][12][13][14]. While one obvious task for a quantum computer is to simulate quantum mechanical behaviors of nature [1], quantum simulation of probability distributions and stochastic processes has gained attention recently [15][16][17][18][19][20]. Since quantum mechanics can be viewed as a mathematical generalization of probability theory, where non-negative real-valued probabilities are replaced by complex-valued probability amplitudes, quantum computing appears to be a natural tool for simulating classical probabilistic processes.…”