Protocols for optimal readout of qubits using a continuous quantum nondemolition measurement

TL;DR

This paper compares different measurement protocols for qubits under relaxation, showing that a non-linear filter yields higher fidelity estimates in shorter times compared to linear filters, optimizing quantum readout accuracy.

Contribution

It introduces a full non-linear filtering approach for qubit readout that outperforms linear filters, especially under relaxation effects, providing a theoretical basis for optimal quantum measurement strategies.

Findings

Non-linear filter achieves higher fidelity than linear filters.

Measurement time decreases linearly with desired fidelity.

Non-linear filter requires lower signal-to-noise ratio for high fidelity.

Abstract

We study how the spontaneous relaxation of a qubit affects a continuous quantum non-demolition measurement of the initial state of the qubit. Given some noisy measurement record $\Psi$, we seek an estimate of whether the qubit was initially in the ground or excited state. We investigate four different measurement protocols, three of which use a linear filter (with different weighting factors) and a fourth which uses a full non-linear filter that gives the theoretically optimal estimate of the initial state of the qubit. We find that relaxation of the qubit at rate $1/T_1$ strongly influences the fidelity of any measurement protocol. To avoid errors due to this decay, the measurement must be completed in a time that decrease linearly with the desired fidelity while maintaining an adequate signal to noise ratio. We find that for the non-linear filter the predicted fidelity, as expected, is always better than the linear filters and that the fidelity is a monotone increasing function of the measurement time. For example, to achieve a fidelity of 90%, the box car linear filter requires a signal to noise ratio of $\sim 30$ in a time $T_1$ whereas the non-linear filter only requires a signal to noise ratio of $\sim 18$.