Quantum-inspired classical simulation through randomized time evolution

TL;DR

This paper introduces a quantum-inspired classical simulation method that leverages randomized time evolution and tensor networks to enable highly parallelized and efficient simulation of quantum many-body dynamics.

Contribution

It adapts randomized quantum algorithms for classical simulation, achieving unbiased, parallelizable, and more robust time evolution of quantum systems with reduced computational costs.

Findings

Reduces per-sample gate count by up to 10^3 compared to Trotterized MPS.

Achieves orders of magnitude reduction in time-to-solution with parallelization.

More robust against bond-dimension truncation than product formulas.

Abstract

Tensor-network simulations of quantum many-body dynamics are fundamentally limited by entanglement build-up, which leads to exponentially growing computational costs. Furthermore, these classical simulation algorithms are inherently sequential as typically a tensor network representation of the quantum state is updated incrementally at each time step. We build on recently introduced randomized quantum algorithms for time evolution (TE-PAI), and adapt them to the classical simulation context with the purpose of enabling massive parallelisation. Our MPS TE-PAI approach achieves exact time evolution on average (unbiased estimator) and proceeds by representing an ensemble of randomized shallow Trotter-variant circuits as tensor networks. As each circuit instance yields a deterministic quantum state (or observable expecation value), the only source of randomness is the sampling of circuit variants; the absence of shot noise therefore yields a reduced estimator variance relative to quantum hardware implementations of TE-PAI. We simulate representative disordered one-dimensional spin-ring Hamiltonians, and numerically observe reductions in the per-sample gate-count by a factor of up to $10^3$ relative to Trotterized MPS evolution, yielding orders of magnitude reduction in the time-to-solution under realistic levels of parallelisation. Finally, we numerically observe that MPS TE-PAI is substantially more robust against severe bond-dimension truncation than product formulas, potentially making it useful for the simulation of strongly correlated systems where truncation is necessary in practice. We also demonstrate that the approach can be used naturally in combination with existing time evolution algorithms, effectively extending their time depth via parallelisation.