Robust Quantum Gate Preparation in Open Environments

TL;DR

This paper introduces an optimal control algorithm for preparing robust quantum gates in open environments, achieving high precision and resilience against uncertainties in quantum systems.

Contribution

The paper presents a novel adaptive control algorithm that enhances robustness of quantum gate preparation, extending GRAPE to uncertain open quantum systems using Legendre polynomial expansions.

Findings

Achieves exponential convergence in robustness against parameter uncertainties.

Successfully prepares CNOT and SWAP gates with high precision.

Demonstrates robustness to 100% uncertainty in interaction strength.

Abstract

We develop an optimal control algorithm for robust quantum gate preparation in open environments with the state of the quantum system represented using the Lindblad master equation. The algorithm is based on adaptive linearization and iterative quadratic programming to progressively shape the control signal into an optimal form. Robustness is achieved with exponential rates of convergence by introducing uncertain parameters into the master equation and expanding the parameterized state over the basis of Legendre polynomials. We prove that the proposed control algorithm reduces to GRadient Ascent Pulse Engineering (GRAPE) when the robustness portion of the algorithm is bypassed and signal restrictions are relaxed. The control algorithm is applied to prepare Controlled NOT and SWAP gates with high precision. Using only second order Legendre polynomials, the examples showcase unprecedented robustness to 100% parameter uncertainty in the interaction strength between the qubits, while simultaneously compensating for 20% uncertainty in signal intensity. The results could enable new capabilities for robust implementation of quantum gates and circuits subject to harsh environments and hardware limitations.