Fast and differentiable simulation of driven quantum systems

TL;DR

This paper introduces Dysolve, a semi-analytic Dyson expansion-based method for fast, accurate, and differentiable simulation of driven quantum systems, enabling efficient quantum control optimization beyond traditional approximations.

Contribution

The paper presents Dysolve, a novel semi-analytic solver that accelerates quantum system simulations and provides exact derivatives for optimal control, surpassing existing numerical methods.

Findings

Dysolve significantly reduces simulation run-time.

It accurately captures oscillatory dynamics in driven quantum systems.

It enables gradient-based quantum control optimization.

Abstract

The controls enacting logical operations on quantum systems are described by time-dependent Hamiltonians that often include rapid oscillations. In order to accurately capture the resulting time dynamics in numerical simulations, a very small integration time step is required, which can severely impact the simulation run-time. Here, we introduce a semi-analytic method based on the Dyson expansion that allows us to time-evolve driven quantum systems much faster than standard numerical integrators. This solver, which we name Dysolve, efficiently captures the effect of the highly oscillatory terms in the system Hamiltonian, significantly reducing the simulation's run time as well as its sensitivity to the time-step size. Furthermore, this solver provides the exact derivative of the time-evolution operator with respect to the drive amplitudes. This key feature allows for optimal control in the limit of strong drives and goes beyond common pulse-optimization approaches that rely on rotating-wave approximations. As an illustration of our method, we show results of the optimization of a two-qubit gate using transmon qubits in the circuit QED architecture.