Classical Simulation of Noiseless Quantum Dynamics without Randomness

TL;DR

This paper introduces the Low-weight Pauli Dynamics (LPD) algorithm for efficiently simulating noiseless quantum dynamics classically, leveraging entanglement to improve accuracy without relying on randomness or noise.

Contribution

The authors develop a novel classical simulation method that bounds truncation error without randomness, exploiting entanglement to simulate short-time quantum dynamics more effectively.

Findings

LPD algorithm provides average-case error bounds for entangled states.

Entanglement reduces classical simulation error, contrary to common assumptions.

Method extends the regime of accessible quantum dynamics for classical simulation.

Abstract

Simulating noiseless quantum dynamics classically faces a fundamental dilemma: tensor-network methods become inefficient as entanglement saturates, while Pauli-truncation approaches typically rely on noise or randomness. To close the gap, we propose the Low-weight Pauli Dynamics (LPD) algorithm that efficiently approximates local observables for short-time dynamics in the absence of noise. We prove that the truncation error admits an average-case bound without assuming randomness, provided that the state is sufficiently entangled. Counterintuitively, entanglement--usually an obstacle for classical simulation--alleviates classical simulation error. We further show that such entangled states can be generated either by tensor-network classical simulation or near-term quantum devices. Our results establish a rigorous synergy between existing classical simulation methods and provide a complementary route to quantum simulation that reduces circuit depth for long-time dynamics, thereby extending the accessible regime of quantum dynamics.