Implementing quantum dimensionality reduction for non-Markovian stochastic simulation

Abstract

Complex systems are embedded in our everyday experience. Stochastic modelling enables us to understand and predict the behaviour of such systems, cementing its utility across the quantitative sciences. Accurate models of highly non-Markovian processes -- where the future behaviour depends on events that happened far in the past -- must track copious amounts of information about past observations, requiring high-dimensional memories. Quantum technologies can ameliorate this cost, allowing models of the same processes with lower memory dimension than corresponding classical models. Here we implement such memory-efficient quantum models for a family of non-Markovian processes using a photonic setup. We show that with a single qubit of memory our implemented quantum models can attain higher precision than possible with any classical model of the same memory dimension. This heralds a key step towards applying quantum technologies in complex systems modelling.

11+2 pages, 5 figures

References in corpus (6)

• Interfering trajectories in experimental quantum-enhanced stochastic simulation
• Implementation of generalized measurements on a qudit via quantum walks
• Memory compression and thermal efficiency of quantum implementations of non-deterministic hidden Markov models
• Quantum coarse-graining for extreme dimension reduction in modelling stochastic temporal dynamics
• Ultimate limit on time signal generation
• Provable superior accuracy in machine learned quantum models

Cited by in corpus (6)

• Embedding memory-efficient stochastic simulators as quantum trajectories
• Hamiltonian characterisation of multi-time processes with classical memory
• Quantum Advantage: A Single Qubit's Experimental Edge in Classical Data Storage
• Entanglement-breaking channels are a quantum memory resource
• Energetic advantages for quantum agents in online execution of complex strategies
• Quantum Dimension Reduction of Hidden Markov Models