Optimal Readout of Spin Qubits with Correlated Noise

As estimated fidelities for quantum control, state preparation, and readout of semiconductor spin qubits begin to approach or exceed thresholds for fault-tolerant quantum computing, it is essential to develop rigorous measurement protocols that account for the known sources of noise in spin-qubit devices.  Here, we develop a theory of optimal spin readout in the presence of time-correlated noise processes.  For white noise, the spin readout fidelity from the optimal Bayesian inference strategy can be obtained from a time-local transfer matrix analysis of the measured current signal, analogous to the calculation of the partition function of a local one-dimensional statistical mechanics model.  However, in the presence of noise correlations, the optimal readout strategy becomes non-local in time, requiring one to keep track of an exponentially growing number of trajectories in the analysis.  We develop efficient algorithms for this problem and use our readout method to benchmark other commonly employed sub-optimal strategies.  Our work unifies the theory of several recently proposed methodologies for spin-readout.  Moreover, these results represent a first step towards a rigorous theory of spin-qubit quantum process tomography in the presence of correlated noise.