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arXiv:1711.06172 · Physical Review A

Quantum metrology with a transmon qutrit

A. R. Shlyakhov, V. V. Zemlyanov, M. V. Suslov, A. V. Lebedev, Gheorghe Sorin Paraoanu, Gordey B. Lesovik, G. Blatter

Published Feb 27, 2018• 62 citations
arXivHTMLPDF

Abstract

Making use of coherence and entanglement as metrological quantum resources allows us 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 two 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 semiquantum Fourier transformation and enhances the quantum theoretical performance of the sensor by a factor of 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 the factor $ln(2)/ln(3)\ensuremath{\approx}0.63$ compared to the qubit mode. We show that a two-tone capacitively coupled radio-frequency signal is sufficient for implementation of the algorithm.

DOI
10.1103/physreva.97.022115

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Making use of coherence and entanglement as metrological quantum resources allows us 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 ddd rather than two 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 semiquantum Fourier transformation and enhances the quantum theoretical performance of the sensor by a factor of 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 the factor ln(2)/ln(3)\ensuremath≈0.63ln(2)/ln(3)\ensuremath{\approx}0.63ln(2)/ln(3)\ensuremath≈0.63 compared to the qubit mode. We show that a two-tone capacitively coupled radio-frequency signal is sufficient for implementation of the algorithm.
Quantum metrology based on superconducting qubits offers unprecedented precision in measuring fundamental physical quantities, particularly magnetic fields. In this study, we develop a modified quantum phase estimation algorithm utilizing superconducting qubits, enhanced by optimized initial state preparation, significantly improving measurement sensitivity and reducing estimation times compared to conventional techniques. To ensure practical applicability and robustness, we incorporate advanced noise modeling, including intrinsic decoherence effects such as flux-induced noise and Purcell losses. Through detailed analytical modeling and numerical simulations, we systematically evaluate sensitivity and practical implementation constraints across various superconducting qubit architectures—transmon, fluxonium, conventional flux, and C-shunt flux qubits. Our approach quantifies the critical trade-offs between coherence, measurement dynamics, and sensitivity, identifying optimal operational regimes for high-performance quantum sensing. We introduce custom circuit simulation methods enabling the analysis and optimization of arbitrary superconducting quantum devices. Our findings provide a framework for advancing quantum-enhanced magnetometry and promise to facilitate next-generation quantum sensors for fundamental physics research, gravitational field measurements, and quantum-assisted searches for dark matter candidates.
Phase estimation algorithms are key protocols in quantum information processing. Besides applications in quantum computing, they can also be employed in metrology as they allow for fast extraction of information stored in the quantum state of a system. Here, we implement two suitably modified phase estimation procedures, the Kitaev and the semiclassical Fourier-transform algorithms, using an artificial atom realized with a superconducting transmon circuit. We demonstrate that both algorithms yield a flux sensitivity exceeding the classical shot-noise limit of the device, allowing one to approach the Heisenberg limit. Our experiment paves the way for the use of superconducting qubits as metrological devices which are potentially able to outperform the best existing flux sensors with a sensitivity enhanced by few orders of magnitude.
Abstract Phase estimation algorithms are key protocols in quantum information processing. Besides applications in quantum computing, they can also be employed in metrology as they allow for fast extraction of information stored in the quantum state of a system. Here, we implement two suitably modified phase estimation procedures, the Kitaev and the semiclassical Fourier-transform algorithms, using an artificial atom realized with a superconducting transmon circuit. We demonstrate that both algorithms yield a flux sensitivity exceeding the classical shot-noise limit of the device, allowing one to approach the Heisenberg limit. Our experiment paves the way for the use of superconducting qubits as metrological devices which are potentially able to outperform the best existing flux sensors with a sensitivity enhanced by few orders of magnitude.
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The ubiquitous presence of shot noise sets a fundamental limit to the measurement precision in classical metrology. Recent advances in quantum devices and novel quantum algorithms utilizing interference effects are opening new routes for overcoming the detrimental noise tyranny. However, further progress is limited by the restricted capability of existing algorithms to account for the decoherence pervading experimental implementations. Here, adopting a systematic approach to the evaluation of effectiveness of metrological procedures, we devise the Linear Ascending Metrological Algorithm (LAMA), which offers a remarkable increase in precision in the demanding situation where a decohering quantum system is used to measure a continuously distributed variable. We introduce our protocol in the context of magnetic field measurements, assuming superconducting transmon devices as sensors operated in a qudit mode. Our findings demonstrate a quantum-metrological procedure capable of mitigating detrimental dephasing and relaxation effects.
Quantum metrology promises enhanced precision by harnessing entanglement and quantum algorithms. Yet, realizing such gains on current noisy quantum hardware remains a significant challenge. Here, we investigate quantum-enhanced magnetometry using phase estimation algorithms on superconducting quantum processors the IQM Garnet and Rigetti Ankaa-3. We experimentally compare the performance of different entangled, parallel and combined sensing strategies. While the entangled states should provide improvements in sensitivity in ideal conditions, we find that their advantage is less in practice on currently available systems. Instead, partitioning qubits into smaller entangled subsets and operating them in parallel achieves near-optimal sensitivity. We derive a general expression for magnetometric precision as a function of total qubit number and subset entanglement size, based on the attenuation of the system, identifying optimal configurations under realistic noise constraints.