Quantum metrology with a transmon qutrit

TL;DR

This paper demonstrates that using a superconducting transmon device in a qutrit mode enhances quantum metrological performance and efficiency compared to qubit mode, by employing a base-3 Fourier transform for magnetometry.

Contribution

The study introduces a novel qutrit-based quantum metrology algorithm that improves sensitivity and reduces operational steps over traditional qubit-based methods.

Findings

Qutrit mode enhances sensor performance by a factor of 2.

Reduction of quantum Fourier transform steps by approximately 37%.

Implementation with a two-tone rf-signal is feasible.

Abstract

Making use of coherence and entanglement as metrological quantum resources allows to improve the measurement precision from the shot-noise- or quantum limit to the Heisenberg limit. Quantum metrology then relies on the availability of quantum engineered systems that involve controllable quantum degrees of freedom which are sensitive to the measured quantity. Sensors operating in the qubit mode and exploiting their coherence in a phase-sensitive measurement have been shown to approach the Heisenberg scaling in precision. Here, we show that this result can be further improved by operating the quantum sensor in the qudit mode, i.e., by exploiting $d$ rather than 2 levels. Specifically, we describe the metrological algorithm for using a superconducting transmon device operating in a qutrit mode as a magnetometer. The algorithm is based on the base-3 semi-quantum Fourier transformation and enhances the quantum theoretical performance of the sensor by a factor 2. Even more, the practical gain of our qutrit-implementation is found in a reduction of the number of iteration steps of the quantum Fourier transformation by a factor $\log 2/\log 3 \approx 0.63$ as compared to the qubit mode. We show, that a two-tone capacitively coupled rf-signal is sufficient for the implementation of the algorithm.