Quantum algorithm for dephasing of coupled systems: decoupling and IQP duality

TL;DR

This paper introduces a quantum algorithm for simulating Lindbladian dynamics, including a decoupling scheme for dephasing systems, enabling efficient sampling of complex quantum evolutions and linking to IQP circuit sampling complexity.

Contribution

The authors develop a novel quantum algorithm for simulating unital Lindbladian dynamics without ancillas and propose a decoupling scheme to reduce circuit complexity in dephasing systems.

Findings

Algorithm efficiently simulates Lindbladian dynamics

Decoupling reduces circuit complexity in dephasing models

Sampling from IQP circuits relates to classical computational hardness

Abstract

Noise and decoherence are ubiquitous in the dynamics of quantum systems coupled to an external environment. In the regime where environmental correlations decay rapidly, the evolution of a subsytem is well described by a Lindblad quantum master equation. In this work, we introduce a quantum algorithm for simulating unital Lindbladian dynamics by sampling unitary quantum channels without extra ancillas. Using ancillary qubits we show that this algorithm allows approximating general Lindbladians as well. For interacting dephasing Lindbladians coupling two subsystems, we develop a decoupling scheme that reduces the circuit complexity of the simulation. This is achieved by sampling from a time-correlated probability distribution - determined by the evolution of one subsystem, which specifies the stochastic circuit implemented on the complementary subsystem. We demonstrate our approach by studying a model of bosons coupled to fermions via dephasing, which naturally arises from anharmonic effects in an electron-phonon system coupled to a bath. Our method enables tracing out the bosonic degrees of freedom, reducing part of the dynamics to sampling an instantaneous quantum polynomial (IQP) circuit. The sampled bitstrings then define a corresponding fermionic problem, which in the non-interacting case can be solved efficiently classically. We comment on the computational complexity of this class of dissipative problems, using the known fact that sampling from IQP circuits is believed to be difficult classically.