Optimizing quantum control pulses with complex constraints and few variables through Tensorflow

TL;DR

This paper introduces a TensorFlow-based algorithm for optimizing quantum control pulses that efficiently incorporates complex physical constraints and minimizes variables, improving practical quantum system control.

Contribution

The novel algorithm integrates multiple constraints into gradient optimization over piece-wise pulses transformed via Fourier basis, utilizing auto-differentiation for complex quantum control tasks.

Findings

Successfully optimized control pulses for single- and two-qubit gates

Demonstrated effectiveness on superconducting transmon qubits

Enhanced control under complex physical constraints

Abstract

Applying optimal control algorithms on realistic quantum systems confronts two key challenges: to efficiently adopt physical constraints in the optimization and to minimize the variables for the convenience of experimental tune-ups. In order to resolve these issues, we propose a novel algorithm by incorporating multiple constraints into the gradient optimization over piece-wise pulse constant values, which are transformed to contained numbers of the finite Fourier basis for bandwidth control. Such complex constraints and variable transformation involved in the optimization introduce extreme difficulty in calculating gradients. We resolve this issue efficiently utilizing auto-differentiation on Tensorflow. We test our algorithm by finding smooth control pulses to implement single-qubit and two-qubit gates for superconducting transmon qubits with always-on interaction, which remains a challenge of quantum control in various qubit systems. Our algorithm provides a promising optimal quantum control approach that is friendly to complex and optional physical constraints.