Optimal signal processing for continuous qubit readout

TL;DR

This paper introduces an optimal signal processing protocol for continuous qubit measurement, improving the accuracy of initial state inference amid noise and qubit dynamics using stochastic detection theory.

Contribution

It develops an analytic, optimal signal processing method for qubit readout under continuous measurement with noise and qubit transitions, applicable to various quantum systems.

Findings

Derived analytic solutions for the protocol using Itô calculus

Applicable to multi-hypothesis testing in qubit readout

Relevant to experiments in superconducting circuits, ions, NV centers, quantum dots, and donors

Abstract

The measurement of a quantum two-level system, or a qubit in modern terminology, often involves an electromagnetic field that interacts with the qubit, before the field is measured continuously and the qubit state is inferred from the noisy field measurement. During the measurement, the qubit may undergo spontaneous transitions, further obscuring the initial qubit state from the observer. Taking advantage of some well known techniques in stochastic detection theory, here we propose a novel signal processing protocol that can infer the initial qubit state optimally from the measurement in the presence of noise and qubit dynamics. Assuming continuous quantum-nondemolition measurements with Gaussian or Poissonian noise and a classical Markov model for the qubit, we derive analytic solutions to the protocol in some special cases of interest using It\={o} calculus. Our method is applicable to multi-hypothesis testing for robust qubit readout and relevant to experiments on qubits in superconducting microwave circuits, trapped ions, nitrogen-vacancy centers in diamond, semiconductor quantum dots, or phosphorus donors in silicon.