Hardware-aware quantum process tomography via Bayesian inference

The Pauli transfer matrix can be experimentally determined by quantum process tomography, where measurements of an exponentially large number of observables subject to an exponentially large number of initial conditions completely characterize the quantum process. When the goal is to characterize a small number of quasi-static parameters in a known (hardware-dependent) Hamiltonian, this problem can often be simplified. This is the case, for example, in a common model of electron spin qubits in quantum dots. For this system, it is possible to exploit an analytic description of the Pauli transfer matrix given a two-spin Heisenberg exchange and a magnetic field gradient. By exploiting this analytic description, we show that Bayesian inference techniques can be used to adaptively optimize preparations and measurements to rapidly learn the relevant parameters of this two-qubit system.