Optimized trajectory unraveling for classical simulation of noisy quantum dynamics

TL;DR

This paper develops optimized unraveling schemes for classical simulation of noisy quantum dynamics, reducing the entanglement threshold and extending the simulatable regime for open quantum systems with decoherence.

Contribution

It introduces an analytical method to find the optimal unraveling basis and a heuristic algorithm for adaptive optimization, enhancing classical simulation efficiency of noisy quantum systems.

Findings

Optimized unraveling lowers the entanglement phase transition threshold.

Heuristic algorithm extends the simulation regime for noisy Hamiltonian dynamics.

Quasi-local unraveling enables efficient simulation at small decoherence rates.

Abstract

The dynamics of open quantum systems can be simulated by unraveling it into an ensemble of pure state trajectories undergoing non-unitary monitored evolution, which has recently been shown to undergo measurement-induced entanglement phase transition. Here, we show that, for an arbitrary decoherence channel, one can optimize the unraveling scheme to lower the threshold for entanglement phase transition, thereby enabling efficient classical simulation of the open dynamics for a broader range of decoherence rates. Taking noisy random unitary circuits as a paradigmatic example, we analytically derive the optimum unraveling basis that on average minimizes the threshold. Moreover, we present a heuristic algorithm that adaptively optimizes the unraveling basis for given noise channels, also significantly extending the simulatable regime. When applied to noisy Hamiltonian dynamics, the heuristic approach indeed extends the regime of efficient classical simulation based on matrix product states beyond conventional quantum trajectory methods. Finally, we assess the possibility of using a quasi-local unraveling, which involves multiple qubits and time steps, to efficiently simulate open systems with an arbitrarily small but finite decoherence rate.