Quantum trajectories for time-dependent adiabatic master equations

TL;DR

This paper introduces a quantum trajectories method for solving time-dependent adiabatic master equations more efficiently, enabling larger system simulations and providing detailed insights into quantum jump trajectories in open quantum systems.

Contribution

The paper presents a novel quantum trajectories approach that reduces computational complexity for adiabatic master equations and allows for parallel computation, improving scalability and insight.

Findings

Method agrees with direct solutions for 8-qubit systems.

Enables simulation of 16-qubit systems more efficiently.

Provides detailed analysis of quantum jump trajectories.

Abstract

We describe a quantum trajectories technique for the unraveling of the quantum adiabatic master equation in Lindblad form. By evolving a complex state vector of dimension $N$ instead of a complex density matrix of dimension $N^2$, simulations of larger system sizes become feasible. The cost of running many trajectories, which is required to recover the master equation evolution, can be minimized by running the trajectories in parallel, making this method suitable for high performance computing clusters. In general, the trajectories method can provide up to a factor $N$ advantage over directly solving the master equation. In special cases where only the expectation values of certain observables are desired, an advantage of up to a factor $N^2$ is possible. We test the method by demonstrating agreement with direct solution of the quantum adiabatic master equation for $8$-qubit quantum annealing examples. We also apply the quantum trajectories method to a $16$-qubit example originally introduced to demonstrate the role of tunneling in quantum annealing, which is significantly more time consuming to solve directly using the master equation. The quantum trajectories method provides insight into individual quantum jump trajectories and their statistics, thus shedding light on open system quantum adiabatic evolution beyond the master equation.