Fast and differentiable simulation of driven quantum systems

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.

arXiv comment14 pages, 8 figures

References in corpus (15)

• Charge insensitive qubit design derived from the Cooper pair box
• QuTiP 2: A Python framework for the dynamics of open quantum systems
• Simple pulses for elimination of leakage in weakly nonlinear qubits
• Procedure for systematically tuning up crosstalk in the cross resonance gate
• A simple all-microwave entangling gate for fixed-frequency superconducting qubits
• Complete universal quantum gate set approaching fault-tolerant thresholds with superconducting qubits
• Process verification of two-qubit quantum gates by randomized benchmarking
• Analytically solvable driven time-dependent two-level quantum systems
• First-principles analysis of cross-resonance gate operation
• Optimal control methods for fast time-varying Hamiltonians
• Gradient-based optimal control of open quantum systems using quantum trajectories and automatic differentiation
• Calibration of the cross-resonance two-qubit gate between directly-coupled transmons
• Optimized cross-resonance gate for coupled transmon systems
• Operational definition of a quantum speed limit
• Optimal control of two qubits via a single cavity drive in circuit quantum electrodynamics

Cited by in corpus (4)

• Accurate methods for the analysis of strong-drive effects in parametric gates
• Engineering, control and longitudinal readout of Floquet qubits
• Algorithms for perturbative analysis and simulation of quantum dynamics
• Time-dependent Schrieffer-Wolff-Lindblad Perturbation Theory: measurement-induced dephasing and second-order Stark shift in dispersive readout