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

Physical Review A

Quantum trajectory sensing problem and its solution

Zachary E. Chin, Isaac L. Chuang

Published May 28, 2025• 2 citations
Publisher

Abstract

The quantum trajectory sensing problem seeks quantum sensor states which enable the trajectories of incident particles to be distinguished using a single measurement. For an $n$-qubit sensor state to unambiguously discriminate a set of trajectories with a single projective measurement, all post-trajectory output states must be mutually orthogonal; therefore, the ${2}^{n}$ state coefficients must satisfy a system of constraints which is typically very large. Given that this system is generally challenging to solve directly, we introduce a group-theoretic framework which simplifies the criteria for sensor states and exponentially reduces the number of equations and variables involved when the trajectories obey certain symmetries. These simplified criteria yield general families of trajectory sensor states and provide bounds on the particle-sensor interaction strength required for perfect one-shot trajectory discrimination. Furthermore, we establish a link between trajectory sensing and quantum error correction, recognizing their common motivation to identify perturbations using projective measurements. Our sensor states in fact form quantum codes, and conversely, a number of familiar stabilizer codes (such as toric codes) also provide trajectory sensing capabilities. This connection enables noise-resilient trajectory sensing through the concatenation of sensor states with quantum error-correcting codes.

DOI
10.1103/physreva.111.052447

Related papers

The quantum trajectory sensing problem and its solution

Zachary E. Chin, Isaac L. Chuang

The quantum trajectory sensing problem seeks quantum sensor states which enable the trajectories of incident particles to be distinguished using a single measurement. For an $n$-qubit sensor state to unambiguously discriminate a set of trajectories with a single projective measurement, all post-trajectory output states must be mutually orthogonal; therefore, the $2^n$ state coefficients must satisfy a system of constraints which is typically very large. Given that this system is generally challenging to solve directly, we introduce a group-theoretic framework which simplifies the criteria for sensor states and exponentially reduces the number of equations and variables involved when the trajectories obey certain symmetries. These simplified criteria yield general families of trajectory sensor states and provide bounds on the particle-sensor interaction strength required for perfect one-shot trajectory discrimination. Furthermore, we establish a link between trajectory sensing and quantum error correction, recognizing their common motivation to identify perturbations using projective measurements. Our sensor states in fact form novel quantum codes, and conversely, a number of familiar stabilizer codes (such as toric codes) also provide trajectory sensing capabilities. This connection enables noise-resilient trajectory sensing through the concatenation of sensor states with quantum error-correcting codes.

arXiv:2410.00893•Oct 1, 2024•0 citations

Quantum Entanglement Enables Single-Shot Trajectory Sensing for Weakly Interacting Particles

Zachary E. Chin, David R. Leibrandt, Isaac L. Chuang

Sensors for mapping the trajectory of an incoming particle find important utility in experimental high energy physics and searches for dark matter. For a quantum sensing protocol that uses projective measurements on a multiqubit sensor array to infer the trajectory of an incident particle, we establish that entanglement can dramatically reduce the particle-qubit interaction strength θ required for perfect trajectory discrimination. Within an interval of θ above this reduced threshold, any unentangled sensor requires Θ[log(1/ε)] repetitions of the protocol to estimate a previously unknown particle trajectory with ε error probability, whereas an entangled sensor can succeed with zero error in a single shot. Furthermore, entanglement can enhance trajectory sensing in realistic scenarios where θ varies continuously over the sensor qubits, exemplified by a Gaussian-profile laser pulse propagating through an array of atoms.

arXiv:2405.05888•Physical Review Letters•May 28, 2025•2 citations

Quantum Error Correction and the Limits of Quantum Metrology

Zhuoran Bao, Daniel F. V. James

Quantum metrology has been making amazing progress in the past decades. It is always in researchers' interest to search for new optimal states that improve parameter estimation. In this paper, we point out a connection between the code's error correcting capacity and its ability to act as a sensor. We backed our claim by providing an example that relates the Absorption emission code to the sensor state for arbitrary state rotation. It is hoped that, in building such a unified theory, one can draw inspiration from error correction to develop promising quantum sensors.

quant-pharXiv:2605.24120•May 26, 2026•0 citations

Ancilla-Free Quantum Error Correction Codes for Quantum Metrology

David Layden, Sisi Zhou, Paola Cappellaro +1 more

Quantum error correction has recently emerged as a tool to enhance quantum sensing under Markovian noise. It works by correcting errors in a sensor while letting a signal imprint on the logical state. This approach typically requires a specialized error-correcting code, as most existing codes correct away both the dominant errors and the signal. To date, however, few such specialized codes are known, among which most require noiseless, controllable ancillas. We show here that such ancillas are not needed when the signal Hamiltonian and the error operators commute, a common limiting type of decoherence in quantum sensors. We give a semidefinite program for finding optimal ancilla-free sensing codes in general, as well as closed-form codes for two common sensing scenarios: qubits undergoing dephasing, and a lossy bosonic mode. Finally, we analyze the sensitivity enhancement offered by the qubit code under arbitrary spatial noise correlations, beyond the ideal limit of orthogonal signal and noise operators.

arXiv:1811.01450•Physical Review Letters•Jan 30, 2019•86 citations

Quantum error correction and quantum computation

G. Alber, A. Delgado, M. Mussinger

In order to stabilize quantum algorithms against decoherence one has to fulfill two requirements. Firstly, one has to develop an appropriate quantum error correcting code. Secondly, one has to find a set of suitable unitary quantum transformations acting on the physical qubits which preserve the properties of this error correcting quantum code and which allow the implementation of a universal set of quantum gates. This is a challenging task in particular if we restrict ourselves to a limited class of two-particle interactions by which the physical qubits can be controlled. For the special cases of four and six physical qubits we discuss a set of such quantum gates which satisfy these two conditions for the recently developed detected-jump correcting quantum codes [1]. These quantum codes are capable of stabilizing distinguishable qubits against decoherence arising from spontaneous decay processes.

Laser Physics•Jan 1, 2002•0 citations

Dynamic local single-shot checks for toric codes

Yingjia Lin, Abhinav Anand, Kenneth R. Brown

Quantum error correction typically requires repeated syndrome extraction due to measurement noise, which results in substantial time overhead in fault-tolerant computation. Single-shot error correction aims to suppress errors using only one round of syndrome extraction. However, for most codes, it requires high-weight checks, which significantly degrade, and often eliminate, single-shot performance at the circuit level. In this work, we introduce local single-shot checks, where we impose constraints on check weights. Using a dynamic measurement scheme, we show that the number of required measurement rounds can be reduced by a factor determined by this constraint. As an example, we show through numerical simulation that our scheme can improve decoding performance compared to conventional checks when using sliding-window decoding with a reduced window size under circuit-level noise models for toric codes. Our work provides a new direction for constructing checks that can reduce time overhead in large-scale fault-tolerant quantum computation.

quant-pharXiv:2511.20576•Nov 26, 2025•0 citations
The quantum trajectory sensing problem seeks quantum sensor states which enable the trajectories of incident particles to be distinguished using a single measurement. For an nnn-qubit sensor state to unambiguously discriminate a set of trajectories with a single projective measurement, all post-trajectory output states must be mutually orthogonal; therefore, the 2n{2}^{n}2n state coefficients must satisfy a system of constraints which is typically very large. Given that this system is generally challenging to solve directly, we introduce a group-theoretic framework which simplifies the criteria for sensor states and exponentially reduces the number of equations and variables involved when the trajectories obey certain symmetries. These simplified criteria yield general families of trajectory sensor states and provide bounds on the particle-sensor interaction strength required for perfect one-shot trajectory discrimination. Furthermore, we establish a link between trajectory sensing and quantum error correction, recognizing their common motivation to identify perturbations using projective measurements. Our sensor states in fact form quantum codes, and conversely, a number of familiar stabilizer codes (such as toric codes) also provide trajectory sensing capabilities. This connection enables noise-resilient trajectory sensing through the concatenation of sensor states with quantum error-correcting codes.
The quantum trajectory sensing problem seeks quantum sensor states which enable the trajectories of incident particles to be distinguished using a single measurement. For an nnn-qubit sensor state to unambiguously discriminate a set of trajectories with a single projective measurement, all post-trajectory output states must be mutually orthogonal; therefore, the 2n2^n2n state coefficients must satisfy a system of constraints which is typically very large. Given that this system is generally challenging to solve directly, we introduce a group-theoretic framework which simplifies the criteria for sensor states and exponentially reduces the number of equations and variables involved when the trajectories obey certain symmetries. These simplified criteria yield general families of trajectory sensor states and provide bounds on the particle-sensor interaction strength required for perfect one-shot trajectory discrimination. Furthermore, we establish a link between trajectory sensing and quantum error correction, recognizing their common motivation to identify perturbations using projective measurements. Our sensor states in fact form novel quantum codes, and conversely, a number of familiar stabilizer codes (such as toric codes) also provide trajectory sensing capabilities. This connection enables noise-resilient trajectory sensing through the concatenation of sensor states with quantum error-correcting codes.
Sensors for mapping the trajectory of an incoming particle find important utility in experimental high energy physics and searches for dark matter. For a quantum sensing protocol that uses projective measurements on a multiqubit sensor array to infer the trajectory of an incident particle, we establish that entanglement can dramatically reduce the particle-qubit interaction strength θ required for perfect trajectory discrimination. Within an interval of θ above this reduced threshold, any unentangled sensor requires Θ[log(1/ε)] repetitions of the protocol to estimate a previously unknown particle trajectory with ε error probability, whereas an entangled sensor can succeed with zero error in a single shot. Furthermore, entanglement can enhance trajectory sensing in realistic scenarios where θ varies continuously over the sensor qubits, exemplified by a Gaussian-profile laser pulse propagating through an array of atoms.
Quantum metrology has been making amazing progress in the past decades. It is always in researchers' interest to search for new optimal states that improve parameter estimation. In this paper, we point out a connection between the code's error correcting capacity and its ability to act as a sensor. We backed our claim by providing an example that relates the Absorption emission code to the sensor state for arbitrary state rotation. It is hoped that, in building such a unified theory, one can draw inspiration from error correction to develop promising quantum sensors.
Quantum error correction has recently emerged as a tool to enhance quantum sensing under Markovian noise. It works by correcting errors in a sensor while letting a signal imprint on the logical state. This approach typically requires a specialized error-correcting code, as most existing codes correct away both the dominant errors and the signal. To date, however, few such specialized codes are known, among which most require noiseless, controllable ancillas. We show here that such ancillas are not needed when the signal Hamiltonian and the error operators commute, a common limiting type of decoherence in quantum sensors. We give a semidefinite program for finding optimal ancilla-free sensing codes in general, as well as closed-form codes for two common sensing scenarios: qubits undergoing dephasing, and a lossy bosonic mode. Finally, we analyze the sensitivity enhancement offered by the qubit code under arbitrary spatial noise correlations, beyond the ideal limit of orthogonal signal and noise operators.
In order to stabilize quantum algorithms against decoherence one has to fulfill two requirements. Firstly, one has to develop an appropriate quantum error correcting code. Secondly, one has to find a set of suitable unitary quantum transformations acting on the physical qubits which preserve the properties of this error correcting quantum code and which allow the implementation of a universal set of quantum gates. This is a challenging task in particular if we restrict ourselves to a limited class of two-particle interactions by which the physical qubits can be controlled. For the special cases of four and six physical qubits we discuss a set of such quantum gates which satisfy these two conditions for the recently developed detected-jump correcting quantum codes [1]. These quantum codes are capable of stabilizing distinguishable qubits against decoherence arising from spontaneous decay processes.
Quantum error correction typically requires repeated syndrome extraction due to measurement noise, which results in substantial time overhead in fault-tolerant computation. Single-shot error correction aims to suppress errors using only one round of syndrome extraction. However, for most codes, it requires high-weight checks, which significantly degrade, and often eliminate, single-shot performance at the circuit level. In this work, we introduce local single-shot checks, where we impose constraints on check weights. Using a dynamic measurement scheme, we show that the number of required measurement rounds can be reduced by a factor determined by this constraint. As an example, we show through numerical simulation that our scheme can improve decoding performance compared to conventional checks when using sliding-window decoding with a reduced window size under circuit-level noise models for toric codes. Our work provides a new direction for constructing checks that can reduce time overhead in large-scale fault-tolerant quantum computation.