Model for monitoring of a charge qubit using a radio-frequency quantum point contact including experimental imperfections

TL;DR

This paper extends quantum trajectory theory to include realistic imperfections in rf measurements of solid-state charge qubits, providing analytical and numerical tools for improved quantum state monitoring and error correction.

Contribution

It introduces a new realistic quantum trajectory model for rf+dc measurements of charge qubits, accounting for experimental imperfections and providing analytical solutions in certain limits.

Findings

rf+dc QPC is a low-efficiency charge-qubit detector

Analytical solution for large oscillator dissipation limit

rf+dc mode can outperform pure dc measurement in noise resilience

Abstract

The extension of quantum trajectory theory to incorporate realistic imperfections in the measurement of solid-state qubits is important for quantum computation, particularly for the purposes of state preparation and error-correction as well as for readout of computations. Previously this has been achieved for low-frequency (dc) weak measurements. In this paper we extend realistic quantum trajectory theory to include radio frequency (rf) weak measurements where a low-transparency quantum point contact (QPC), coupled to a charge qubit, is used to damp a classical oscillator circuit. The resulting realistic quantum trajectory equation must be solved numerically. We present an analytical result for the limit of large dissipation within the oscillator (relative to the QPC), where the oscillator slaves to the qubit. The rf+dc mode of operation is considered. Here the QPC is biased (dc) as well as subjected to a small-amplitude sinusoidal carrier signal (rf). The rf+dc QPC is shown to be a low-efficiency charge-qubit detector, that may nevertheless be higher than the dc-QPC (which is subject to 1/f noise).