Correlators in continuous measurement of non-commuting qubit observables and their applications

Presenting Author: Juan Atalaya, University of California, Riverside
Contributing Author(s): Shay Hacohen-Gourgy, Leigh S. Martin, Leonid P. Pryadko, Irfan Siddiqi, and Alexander N. Korotkov

There has been a rapid experimental progress in continuous quantum measurement of superconducting qubits, including simultaneous measurement of non-commuting observables. In this talk, we focus on temporal correlations of the noisy measurement outputs and discuss the theory for the correlators, comparison with experiment, and applications in parameter estimation and quantum error correction. First, using the quantum Bayesian formalism, we derive analytics for the correlators in simultaneous measurement of two non-commuting observables of a qubit. The theory agrees with experiment very well. Moreover, the correlators can be used for an ultrasensitive estimation of residual Rabi oscillations. Next, we derive a general theoretical result for multi-time correlators in measurement of several non-commuting observables. Surprisingly, we find that for a unital evolution in the absence of phase backaction from measurement, the N-time correlators factorize into a product of two-time correlators for even N. For odd N, a similar factorization also includes the average signal at the earliest time. Experimental results for N=3 and N=4 with two non-commuting measurement channels show a good agreement with this prediction. Finally, we discuss application of the theoretical results for correlators in the error analysis for the 4-qubit Bacon-Shor code, operating with continuous measurement of non-commuting gauge operators.

Read this article online: https://arxiv.org/abs/1710.05249, https://arxiv.org/abs/1702.08077, https://journals.aps.org/pra/abstract/10.1103/PhysRevA.95.032317

(Session 6 : Friday from 9:15am-9:45am)


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