Optimal signal processing for continuous qubit readout

Shilin Ng and Mankei Tsang
Phys. Rev. A 90, 022325 – Published 22 August 2014

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 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 Itō calculus. Our method is applicable to multihypothesis 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.

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  • Received 3 June 2014

DOI:https://doi.org/10.1103/PhysRevA.90.022325

©2014 American Physical Society

Authors & Affiliations

Shilin Ng1 and Mankei Tsang1,2,*

  • 1Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117551
  • 2Department of Electrical and Computer Engineering, National University of Singapore, 4 Engineering Drive 3, Singapore 117583

  • *eletmk@nus.edu.sg

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Vol. 90, Iss. 2 — August 2014

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