Optimal signal processing for continuous qubit readout

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 Itō 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.

8 pages, 8 figures; v2: improved the introduction; v3: updated and accepted by PRA

References in corpus (20)

• Single-shot read-out of an individual electron spin in a quantum dot
• Magnetometry with nitrogen-vacancy defects in diamond
• Single-shot readout of an electron spin in silicon
• High-fidelity projective readout of a solid-state spin quantum register
• Approaching Unit Visibility for Control of a Superconducting Qubit with Dispersive Readout
• High-fidelity readout and control of a nuclear spin qubit in silicon
• High-fidelity readout of trapped-ion qubits
• Quantum non-demolition measurement of a superconducting two-level system
• Heralded state preparation in a superconducting qubit
• Protocols for optimal readout of qubits using a continuous quantum nondemolition measurement
• Evading quantum mechanics
• State and dynamical parameter estimation for open quantum systems
• Quantum Hamiltonian Learning Using Imperfect Quantum Resources
• Single shot parameter estimation via continuous quantum measurement
• Continuous Quantum Hypothesis Testing
• Entanglement verification with finite data
• Programmable Logic Devices in Experimental Quantum Optics
• Fundamental quantum limits to waveform detection
• Optimal post-processing for a generic single-shot qubit readout
• Testing quantum mechanics: a statistical approach

Cited by in corpus (9)

• Low-Latency Digital Signal Processing for Feedback and Feedforward in Quantum Computing and Communication
• Repetitive quantum non-demolition measurement and soft decoding of a silicon spin qubit
• Maximal adaptive-decision speedups in quantum-state readout
• Robust readout of bosonic qubits in the dispersive coupling regime
• Single-shot number-resolved detection of microwave photons with error mitigation
• Enhancing qubit readout through dissipative sub-Poissonian dynamics
• Generalized figure of merit for qubit readout
• Volterra filters for quantum estimation and detection
• Spin-qubit readout analysis based on a hidden Markov model