[Paper Review] Quantum estimation of parameter in circuit QED by continuous quantum measurement

Cheng Zhang, Kai Zhou+2 more|arXiv (Cornell University)|Oct 5, 2018

Quantum Information and Cryptography10 citations

TL;DR

This paper proposes a high-precision quantum estimation scheme for the Rabi frequency in superconducting circuit QED using continuous quantum measurement and Bayesian estimation. By leveraging temporal quantum correlations in measurement output and optimizing measurement strength, the method achieves precision beyond the standard quantum limit without additional quantum resources, with performance sensitive to measurement efficiency.

ABSTRACT

Designing high-precision and efficient schemes is of crucial importance for quantum parameter estimation in practice. The estimation scheme based on continuous quantum measurement is one possible type of this, which looks also the most natural choice in case such as continuous dynamical process. In this work we specify the study to the stat-of-the-art superconducting circuit quantum-electrodynamics (QED) system, where the high-quality continuous measurement has been extensively exploited in the past decade. Within the framework of Bayesian estimation and particularly using the quantum Bayesian rule in circuit QED, we numerically simulate the likelihood function as estimator for the Rabi frequency of qubit oscillation. We find that, by proper design of the interaction strength of measurement, the estimate precision can scale with the measurement time beyond the standard quantum limit, which is usually assumed for this type of continuous measurement since no more special quantum resource is involved. We understand this remarkable result by quantum correlation in time between the output signals, and simulate the effect of quantum efficiency of the measurement on the precision scaling behavior.

Motivation & Objective

• To develop a high-precision, efficient parameter estimation scheme for superconducting qubits in circuit QED.
• To investigate whether continuous quantum measurement can surpass the standard quantum limit in estimating the Rabi frequency.
• To analyze the role of measurement strength and quantum efficiency in determining estimation precision.
• To understand the origin of improved precision through temporal quantum correlations in measurement signals.

Proposed method

• The study employs the quantum Bayesian rule within the framework of continuous quantum measurement to update belief states about the Rabi frequency in real time.
• Numerical simulations are used to compute the likelihood function as the estimator for the Rabi frequency based on measured output signals.
• The measurement interaction strength is systematically varied to optimize estimation precision and explore scaling behavior with measurement time.
• Temporal quantum correlations between successive measurement outputs are analyzed to explain the observed precision enhancement.
• The effect of measurement efficiency on the precision scaling is simulated to assess practical limitations.

Experimental results

Research questions

• RQ1 Can continuous quantum measurement in circuit QED achieve estimation precision beyond the standard quantum limit without additional quantum resources?
• RQ2 How does the measurement interaction strength influence the scaling of estimation precision with measurement time?
• RQ3 What role do temporal quantum correlations in measurement output play in enhancing estimation precision?
• RQ4 How does finite measurement efficiency affect the precision scaling behavior in the proposed scheme?

Key findings

• The estimation precision scales with measurement time beyond the standard quantum limit, even without additional quantum resources.
• Optimal measurement strength is identified as a key factor enabling the precision to surpass the standard quantum limit.
• Temporal quantum correlations in the measurement output signals are identified as the physical origin of the enhanced precision.
• Measurement efficiency significantly impacts the precision scaling, with lower efficiency degrading performance.