A time-parallel multiple-shooting method for large-scale quantum optimal control

TL;DR

This paper introduces a parallelized multiple-shooting method for quantum optimal control that significantly accelerates computations, enabling efficient optimization of multi-qubit gates by dividing the time domain and using convex infidelity measures.

Contribution

It proposes a novel time-parallel multiple-shooting approach with convex infidelity measures and an efficient gradient computation technique for large-scale quantum control problems.

Findings

Achieved up to 80x speedup in gradient evaluation for 4-qubit systems.

Demonstrated effective control pulse optimization for quantum Fourier transform gates.

Validated the method's scalability across 2 to 4 qubits.

Abstract

Quantum optimal control plays a crucial role in quantum computing by providing the interface between compiler and hardware. Solving the optimal control problem is particularly challenging for multi-qubit gates, due to the exponential growth in computational complexity with the system's dimensionality and the deterioration of optimization convergence. To ameliorate the computational complexity of time-integration, this paper introduces a multiple-shooting approach in which the time domain is divided into multiple windows and the intermediate states at window boundaries are treated as additional optimization variables. This enables parallel computation of state evolution across time-windows, significantly accelerating objective function and gradient evaluations. Since the initial state matrix in each window is only guaranteed to be unitary upon convergence of the optimization algorithm, the conventional gate trace infidelity is replaced by a generalized infidelity that is convex for non-unitary state matrices. Continuity of the state across window boundaries is enforced by equality constraints. A quadratic penalty optimization method is used to solve the constrained optimal control problem, and an efficient adjoint technique is employed to calculate the gradients in each iteration. We demonstrate the effectiveness of the proposed method through numerical experiments on quantum Fourier transform gates in systems with 2, 3, and 4 qubits, noting a speedup of 80x for evaluating the gradient in the 4-qubit case, highlighting the method's potential for optimizing control pulses in multi-qubit quantum systems.