Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2508.13405 · Physical Review A

Application of optimal control to the time-resolution protocol for quantum sensing

Chungwei Lin, Qi Ding, Yanting Ma

Published Nov 7, 2025• 1 citation
arXivHTMLPDF

Abstract

Time-resolution protocol of quantum sensing aims to measure the fast temporal variation of an external field and demands a high field sensitivity in a short interrogation time $\ensuremath{\tau}$. Since any operation that evolves the quantum state takes time and is counted as part of the interrogation, evaluating the performance of the time-resolution protocol requires a complete end-to-end description of the measurement process. In particular, the initial state has to be one of the quantum sensor's eigenstates in the absence of external fields, and the final projective measurements must be performed in the same eigenstate basis. Building upon prior works which proposed limits for time-resolved sensing using a quantum sensor, we apply optimal control theory to optimize the time-resolution protocol. Our analysis indicates that there exists a critical interrogation time ${T}^{*}$: When $\ensuremath{\tau}<{T}^{*}$ the optimal protocol is a purely bang-bang strategy; when $\ensuremath{\tau}>{T}^{*}$ the optimal protocol involves a singular control during the interrogation. In the short-$\ensuremath{\tau}$ regime, which is relevant to high time resolution, we propose a detune protocol that involves only smooth control during the entire interrogation. As the discontinuities of control pose the main obstacles to experimental realization, we expect the presented detune protocol to be practically useful. In the long-$\ensuremath{\tau}$ regime, the optimal protocol closely resembles the Ramsey sequence; protocols based on maximizing quantum Fisher information are constructed to highlight the difference between the theoretically optimal and practically implementable measurements. Effective use of the time-resolution protocol requires a setup where the unknown time-domain signal of interest can be identically and repeatedly generated. As a potentially relevant application, we outline the calibration of baseband flux pulse distortion in the control of superconducting qubits.

DOI
10.1103/1nsd-2574

Related papers

Quantum Speed Limit in Quantum Sensing

Konstantin Herb, Christian L. Degen

Quantum sensors capitalize on advanced control sequences for maximizing sensitivity and precision. However, protocols are not usually optimized for temporal resolution. Here, we establish the limits for time-resolved sensing of dynamical signals using qubit probes. We show that the best possible time resolution is closely related to the quantum speed limit (QSL), which describes the minimum time needed to transform between basis states. We further show that a composite control sequence consisting of two phase-shifted pulses reaches the QSL. Practical implementation is discussed based on the example of the spin-1 qutrit of a nitrogen-vacancy center in diamond.

arXiv:2406.18348•Physical Review Letters•Nov 19, 2024•20 citations

Time-optimal single-scalar control on a qubit of unitary dynamics

Chungwei Lin, Qi Ding, Petros T. Boufounos +4 more

Optimal control theory is applied to analyze the time-optimal solution with a single scalar control knob in a two-level quantum system without quantum decoherence. Emphasis is placed on the dependence on the maximum control strength ${u}_{\text{max}}$. General constraints on the optimal protocol are derived and used to rigorously parametrize the time-optimal solution. Two concrete problems are investigated. For generic state preparation problems, both multiple bang-bang and bang-singular-bang are legitimate and should be considered. Generally, the optimal is bang-bang for small ${u}_{\text{max}}$, and there exists a state-dependent critical amplitude above which singular control emerges. For the X-gate operation of a qubit, the optimal protocol is exclusively multiple bang-bang. The minimum gate time is about 80% of that based on the resonant Rabi $\ensuremath{\pi}$-pulse over a wide range of control strength; in the ${u}_{\text{max}}\ensuremath{\rightarrow}0$ limit, this ratio is derived to be $\ensuremath{\pi}/4$. To develop practically feasible protocols, we present methods to smooth the abrupt changes in the bang-bang control while preserving perfect gate fidelity. The presence of bang-bang segments in the time-optimal protocol indicates that the high-frequency components and a full calculation (instead of the commonly adopted rotating wave approximation) are essential for the ultimate quantum speed limit.

arXiv:2504.01785•Physical Review A•Apr 2, 2025•2 citations

Optimal Protocols for Quantum Metrology with Noisy Measurements

Sisi Zhou, Spyridon Michalakis, Tuvia Gefen

Measurement noise is a major source of noise in quantum metrology.Here, we explore preprocessing protocols that apply quantum controls to the quantum sensor state prior to the final noisy measurement (but after the unknown parameter has been imparted), aiming to maximize the estimation precision.We define the quantum preprocessing-optimized Fisher information, which determines the ultimate precision limit for quantum sensors under measurement noise, and conduct a thorough investigation into optimal preprocessing protocols.First, we formulate the preprocessing optimization problem as a biconvex optimization using the error observable formalism, based on which we prove that unitary controls are optimal for pure states and derive analytical solutions of the optimal controls in several practically relevant cases.Then we prove that for classically mixed states (whose eigenvalues encode the unknown parameter) under commuting-operator measurements, coarse-graining controls are optimal, while unitary controls are suboptimal in certain cases.Finally, we demonstrate that in multiprobe systems where noisy measurements act independently on each probe, the noiseless precision limit can be asymptotically recovered using global controls for a wide range of quantum states and measurements.Applications to noisy Ramsey interferometry and thermometry are presented, as well as explicit circuit constructions of optimal controls.

arXiv:2210.11393•PRX Quantum•Oct 9, 2023•18 citations

The temporal resolution limit in quantum sensing

Cong-Gang Song, Qing-yu Cai

Temporal resolution is a critical figure of merit in quantum sensing. This study combines the distinguishable condition of quantum states with quantum speed limits to establish a lower bound on interrogation time. When the interrogation time falls below this bound, the output state becomes statistically indistinguishable from the input state, and the information will inevitably be lost in noise. Without loss of generality, we extend these conclusions to time-dependent signal Hamiltonian. In theory, leveraging certain quantum control techniques allows us to calculate the minimum interrogation time for arbitrary signal Hamiltonian. Finally, we illustrate the impact of quantum speed limits on magnetic field measurements and temporal resolution.

arXiv:2507.09172•EPJ Quantum Technology•Jun 16, 2025•0 citations

Beating the Ramsey limit on sensing with deterministic qubit control

Malida Hecht, Kumar Saurav, Evangelos Vlachos +2 more

Abstract Quantum sensors promise revolutionary advances in medical imaging, energy production, mass detection, geodesy, foundational physics research, and a host of other fields. In many sensors, the signal takes the form of a changing qubit frequency, which is detected with a Ramsey interference measurement. Unfortunately, environmental noise decoheres the qubit state, reducing signal. Here we introduce a protocol for enhancing the sensitivity of a measurement of a qubit's frequency in the presence of decoherence. We use a continuous drive to stabilize one component of the qubit's Bloch vector, enhancing the effect of a small static frequency shift. We demonstrate our protocol on a superconducting qubit, enhancing sensitivity per measurement shot by 1.65x and sensitivity per qubit evolution time by 1.09x compared to standard Ramsey interferometry. We explore the protocol theoretically and numerically, finding maximum enhancements of 1.96x and 1.18x, respectively. We also show that the protocol is robust to parameter miscalibrations. Our protocol provides an unconditional enhancement in signal-to-noise ratio compared to standard Ramsey interferometry. It requires no feedback and no extra control or measurement resources, and can be immediately applied in a wide variety of quantum computing and quantum sensor technologies to enhance their sensitivities.

arXiv:2408.15926•Nature Communications•Apr 29, 2025•4 citations

Based on Quantum Sensors: High-Precision Time Measurement

Jincheng Zhang

This paper explores the potential of quantum sensors for achieving unprecedented levels of precision in time measurement. The core concept leverages the inherent sensitivity of quantum systems to external perturbations, particularly quantum entanglement and coherence, to directly measure the passage of time. Traditional timekeeping methods rely on periodic phenomena like atomic oscillations, which introduce systematic errors and limitations. Quantum sensors, however, offer a fundamentally different approach, promising a shift towards a measurement paradigm where time itself is directly sensed. This work details a theoretical framework for such a system, outlining key components, potential challenges, and the anticipated improvements in accuracy compared to existing technologies. We propose a system utilizing a macroscopic quantum clock, exploiting the precisely controlled evolution of quantum superposition states to determine time intervals with potentially sub-picosecond resolution. The design emphasizes the minimization of decoherence effects—a critical factor in realizing the full potential of quantum time measurement—and introduces novel strategies for signal processing and calibration. This research contributes to the emerging field of quantum metrology and lays the groundwork for future advancements in high-precision timekeeping and fundamental physics research. ---

•Aug 29, 2026•0 citations
Time-resolution protocol of quantum sensing aims to measure the fast temporal variation of an external field and demands a high field sensitivity in a short interrogation time \ensuremathτ\ensuremath{\tau}\ensuremathτ. Since any operation that evolves the quantum state takes time and is counted as part of the interrogation, evaluating the performance of the time-resolution protocol requires a complete end-to-end description of the measurement process. In particular, the initial state has to be one of the quantum sensor's eigenstates in the absence of external fields, and the final projective measurements must be performed in the same eigenstate basis. Building upon prior works which proposed limits for time-resolved sensing using a quantum sensor, we apply optimal control theory to optimize the time-resolution protocol. Our analysis indicates that there exists a critical interrogation time T∗{T}^{*}T∗: When \ensuremathτ<T∗\ensuremath{\tau}<{T}^{*}\ensuremathτ<T∗ the optimal protocol is a purely bang-bang strategy; when \ensuremathτ>T∗\ensuremath{\tau}>{T}^{*}\ensuremathτ>T∗ the optimal protocol involves a singular control during the interrogation. In the short-\ensuremathτ\ensuremath{\tau}\ensuremathτ regime, which is relevant to high time resolution, we propose a detune protocol that involves only smooth control during the entire interrogation. As the discontinuities of control pose the main obstacles to experimental realization, we expect the presented detune protocol to be practically useful. In the long-\ensuremathτ\ensuremath{\tau}\ensuremathτ regime, the optimal protocol closely resembles the Ramsey sequence; protocols based on maximizing quantum Fisher information are constructed to highlight the difference between the theoretically optimal and practically implementable measurements. Effective use of the time-resolution protocol requires a setup where the unknown time-domain signal of interest can be identically and repeatedly generated. As a potentially relevant application, we outline the calibration of baseband flux pulse distortion in the control of superconducting qubits.
Quantum sensors capitalize on advanced control sequences for maximizing sensitivity and precision. However, protocols are not usually optimized for temporal resolution. Here, we establish the limits for time-resolved sensing of dynamical signals using qubit probes. We show that the best possible time resolution is closely related to the quantum speed limit (QSL), which describes the minimum time needed to transform between basis states. We further show that a composite control sequence consisting of two phase-shifted pulses reaches the QSL. Practical implementation is discussed based on the example of the spin-1 qutrit of a nitrogen-vacancy center in diamond.
Optimal control theory is applied to analyze the time-optimal solution with a single scalar control knob in a two-level quantum system without quantum decoherence. Emphasis is placed on the dependence on the maximum control strength umax{u}_{\text{max}}umax​. General constraints on the optimal protocol are derived and used to rigorously parametrize the time-optimal solution. Two concrete problems are investigated. For generic state preparation problems, both multiple bang-bang and bang-singular-bang are legitimate and should be considered. Generally, the optimal is bang-bang for small umax{u}_{\text{max}}umax​, and there exists a state-dependent critical amplitude above which singular control emerges. For the X-gate operation of a qubit, the optimal protocol is exclusively multiple bang-bang. The minimum gate time is about 80% of that based on the resonant Rabi $\ensuremath{\pi}$-pulse over a wide range of control strength; in the ${u}_{\text{max}}\ensuremath{\rightarrow}0$ limit, this ratio is derived to be $\ensuremath{\pi}/4$. To develop practically feasible protocols, we present methods to smooth the abrupt changes in the bang-bang control while preserving perfect gate fidelity. The presence of bang-bang segments in the time-optimal protocol indicates that the high-frequency components and a full calculation (instead of the commonly adopted rotating wave approximation) are essential for the ultimate quantum speed limit.
Measurement noise is a major source of noise in quantum metrology.Here, we explore preprocessing protocols that apply quantum controls to the quantum sensor state prior to the final noisy measurement (but after the unknown parameter has been imparted), aiming to maximize the estimation precision.We define the quantum preprocessing-optimized Fisher information, which determines the ultimate precision limit for quantum sensors under measurement noise, and conduct a thorough investigation into optimal preprocessing protocols.First, we formulate the preprocessing optimization problem as a biconvex optimization using the error observable formalism, based on which we prove that unitary controls are optimal for pure states and derive analytical solutions of the optimal controls in several practically relevant cases.Then we prove that for classically mixed states (whose eigenvalues encode the unknown parameter) under commuting-operator measurements, coarse-graining controls are optimal, while unitary controls are suboptimal in certain cases.Finally, we demonstrate that in multiprobe systems where noisy measurements act independently on each probe, the noiseless precision limit can be asymptotically recovered using global controls for a wide range of quantum states and measurements.Applications to noisy Ramsey interferometry and thermometry are presented, as well as explicit circuit constructions of optimal controls.
Temporal resolution is a critical figure of merit in quantum sensing. This study combines the distinguishable condition of quantum states with quantum speed limits to establish a lower bound on interrogation time. When the interrogation time falls below this bound, the output state becomes statistically indistinguishable from the input state, and the information will inevitably be lost in noise. Without loss of generality, we extend these conclusions to time-dependent signal Hamiltonian. In theory, leveraging certain quantum control techniques allows us to calculate the minimum interrogation time for arbitrary signal Hamiltonian. Finally, we illustrate the impact of quantum speed limits on magnetic field measurements and temporal resolution.
Abstract Quantum sensors promise revolutionary advances in medical imaging, energy production, mass detection, geodesy, foundational physics research, and a host of other fields. In many sensors, the signal takes the form of a changing qubit frequency, which is detected with a Ramsey interference measurement. Unfortunately, environmental noise decoheres the qubit state, reducing signal. Here we introduce a protocol for enhancing the sensitivity of a measurement of a qubit's frequency in the presence of decoherence. We use a continuous drive to stabilize one component of the qubit's Bloch vector, enhancing the effect of a small static frequency shift. We demonstrate our protocol on a superconducting qubit, enhancing sensitivity per measurement shot by 1.65x and sensitivity per qubit evolution time by 1.09x compared to standard Ramsey interferometry. We explore the protocol theoretically and numerically, finding maximum enhancements of 1.96x and 1.18x, respectively. We also show that the protocol is robust to parameter miscalibrations. Our protocol provides an unconditional enhancement in signal-to-noise ratio compared to standard Ramsey interferometry. It requires no feedback and no extra control or measurement resources, and can be immediately applied in a wide variety of quantum computing and quantum sensor technologies to enhance their sensitivities.
This paper explores the potential of quantum sensors for achieving unprecedented levels of precision in time measurement. The core concept leverages the inherent sensitivity of quantum systems to external perturbations, particularly quantum entanglement and coherence, to directly measure the passage of time. Traditional timekeeping methods rely on periodic phenomena like atomic oscillations, which introduce systematic errors and limitations. Quantum sensors, however, offer a fundamentally different approach, promising a shift towards a measurement paradigm where time itself is directly sensed. This work details a theoretical framework for such a system, outlining key components, potential challenges, and the anticipated improvements in accuracy compared to existing technologies. We propose a system utilizing a macroscopic quantum clock, exploiting the precisely controlled evolution of quantum superposition states to determine time intervals with potentially sub-picosecond resolution. The design emphasizes the minimization of decoherence effects—a critical factor in realizing the full potential of quantum time measurement—and introduces novel strategies for signal processing and calibration. This research contributes to the emerging field of quantum metrology and lays the groundwork for future advancements in high-precision timekeeping and fundamental physics research. ---