  As the number of qubits available on noisy quantum computers grows, it will
become necessary to efficiently select a subset of physical qubits to use in a
quantum computation. For any given quantum program and device there are many
ways to assign physical qubits for execution of the program, and assignments
will differ in performance due to the variability in quality across qubits and
entangling operations on a single device. Evaluating the performance of each
assignment using fidelity estimation introduces significant experimental
overhead and will be infeasible for many applications, while relying on
standard device benchmarks provides incomplete information about the
performance of any specific program. Furthermore, the number of possible
assignments grows combinatorially in the number of qubits on the device and in
the program, motivating the use of heuristic optimization techniques. We
approach this problem using simulated annealing with a cost function based on
the Loschmidt Echo, a diagnostic that measures the reversibility of a quantum
process. We provide theoretical justification for this choice of cost function
by demonstrating that the optimal qubit assignment coincides with the optimal
qubit assignment based on state fidelity 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 as
well as optimization experiments performed on a quantum processor. Our results
demonstrate that the use of Loschmidt Echoes and simulated annealing provides a
scalable and flexible approach to optimizing qubit assignment on near-term
hardware.
