Qubit assignment on NISQ hardware using Simulated Annealing and a Loschmidt Echo heuristic

As the number of qubits available on noisy quantum computers grows, it becomes difficult to efficiently map logical qubits to a subset of physical qubits for use in a quantum computation. Evaluating the device performance using fidelity estimation introduces significant experimental overhead and may be infeasible for many applications. Furthermore, the number of possible mappings grows combinatorially in the number of qubits, motivating the use of heuristic optimization techniques. Here, we study this problem using simulated annealing with a cost function based on the Loschmidt Echo. We provide theoretical justification for this choice of cost function by demonstrating that the optimal qubit assignment coincides with the optimal mapping based on the fidelity function in the weak error limit, and we provide experimental justification using diagnostics performed on Google's superconducting qubit devices. We then establish the performance of simulated annealing for qubit assignment using classical simulations of noisy devices and optimization experiments performed on a quantum processor. Our technique provides a scalable and flexible approach to optimizing the performance of quantum programs executed on near-term hardware.