Robust Quantum Gate Preparation in Open Environments

TL;DR

This work tackles robust quantum gate synthesis for open quantum systems described by the Lindblad master equation, addressing parameter uncertainty in both the Hamiltonian and dissipator terms. It introduces a robust optimal-control framework that uses adaptive linearization and iterative quadratic programming to shape control signals while projecting the uncertain dynamics onto a finite Legendre polynomial basis, enabling tractable synthesis with a small polynomial order. The proposed method reduces to the conventional GRAPE algorithm when robustness and signal restrictions are removed, and it is demonstrated by designing robust CNOT and SWAP gates with extreme uncertainty in the interaction strength and significant amplitude fluctuations. The approach promises more resilient quantum gate implementations in harsh environments and under hardware limitations, with potential impact on scalable quantum computing and error-robust circuit design.

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.