Bipartite Control of Coherent Noise Using Quantum Approximate Optimization Algorithm

We employ bipartite control with a Quantum Approximate Optimization Algorithm (QAOA) control ansatz to mitigate coherent quantum noise. We illustrate the approach with application to protection of quantum gates performed on i) a central spin qubit coupling to bath qubits through isotropic Heisenberg interactions and ii) a superconducting transmon qubit coupling to environmental two-level-systems (TLS) through dipole-dipole interactions. The control field is classical and only acts on the system qubit. We use policy gradient (PG) and sequential convex programming (SCP) as classical optimization methods to optimize the QAOA control protocols with a fidelity objective defined with respect to specific target quantum gates, to find the optimal protocol for implementation of the target gate with high fidelity. We demonstrate effective suppression of coherent noise, with numerical studies achieving target gate implementation having fidelities over 0.999999 in the majority of our test cases. We analyze how will the control depth, total evolution time, number of bath systems and choice of optimization method affect the fidelity achieved by the optimal protocols and reveal some critical behaviors of bipartite QAOA control.