Gradient-based optimal control of open quantum systems using quantum trajectories and automatic differentiation

Abstract

We present a gradient-based optimal-control technique for open quantum systems that utilizes quantum trajectories to simulate the quantum dynamics during optimization. Using trajectories allows for optimizing open systems with less computational cost than the regular density matrix approaches in most realistic optimization problems. We introduce an improved-sampling algorithm which minimizes the number of trajectories needed per optimization iteration. Together with employing stochastic gradient descent techniques, this reduces the complexity of optimizing many realistic open quantum systems to the complexity encountered with closed systems. Our optimizer harnesses automatic differentiation to provide flexibility in optimization and to suit the different constraints and diverse parameter regimes of real-life experiments. We utilize the optimizer in a variety of applications to demonstrate how the use of quantum trajectories significantly reduces the computation complexity while achieving a multitude of simultaneous optimization targets. Demonstrated targets include high state-transfer fidelities despite dissipation, faster gate times and maximization of qubit-readout fidelity while maintaining the quantum non-demolition nature of the measurement and allowing for subsequent fast resonator reset.

20 pages, 12 figures

References in corpus (11)

• Quantum trajectories and open many-body quantum systems
• Dispersive regime of circuit QED: photon-dependent qubit dephasing and relaxation rates
• Optimal Dynamical Decoherence Control of a Qubit
• Protocols for optimal readout of qubits using a continuous quantum nondemolition measurement
• Machine learning for discriminating quantum measurement trajectories and improving readout
• Non-linear dispersive regime of cavity QED: The dressed dephasing model
• Low-lying bifurcations in cavity quantum electrodynamics
• Montonic convergent optimal control theory to modulate bandwidth limited laser pulses in linear and non-linear optical processes
• Optimal control of fast and high-fidelity quantum gates with electron and nuclear spins of a nitrogen-vacancy center in diamond
• Implementation of Quantum Gates via Optimal Control
• Optimal control of quantum gates in an exactly solvable non-Markovian open quantum bit system