Noisy Simulation of Quantum Beats in Radical Pairs on a Quantum Computer

Abstract

Current and near term quantum computers (i.e. NISQ devices) are limited in their computational power in part due to imperfect gate operations and imperfect qubits. This naturally constrains the computations run on these devices to be low-depth and short lived, lest the output turn to random noise. Here we seek to take advantage of the imperfect qubit as a means of simulating thermal relaxation in physical systems with no additional computational overhead. As a first step toward this goal we simulate the thermal relaxation of quantum beats in radical pairs on a quantum computer. Our approach is to classically compute a dynamic quantity of interest, construct a parameterized quantum circuit which returns this quantity as a function of the parameters (e.g. magnetic field, time), then simulate the system undergoing thermal relaxation. We simulate the thermal relaxation by 1) explicitly constructing an ancillary circuit to implement Kraus operators associated with the thermal decay channels. 2) Adding wait cycles into the quantum circuit to allow the natural thermal decay of the qubits to effectively simulate the thermal decay of the system of interest. Time dependence of radical pairs in a magnetic field as the dynamical quantity of interest was chosen because it is amenable to analytic solutions classically and also has readily available experimental data, allowing for easy and robust comparison of the results. We find the Kraus operator method gives very accurate results, agreeing with the experiment across its entire range of validity and having a mean squared error of 0.015% compared to the theoretical calculations. We also demonstrate a proof of concept for using the thermal relaxation of the qubits to model the thermal relaxation of the physical system.