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:cond-mat/0703005 · Physical Review B

Phase-space theory for dispersive detectors of superconducting qubits

I. Serban, E. Solano, Frank K. Wilhelm

Published Sep 14, 2007• 16 citations
arXivHTMLPDF

Abstract

Motivated by recent experiments, we study the dynamics of a qubit quadratically coupled to its detector, a damped harmonic oscillator. We use a complex-environment approach, explicitly describing the dynamics of the qubit and the oscillator by means of their full Floquet state master equations in phase-space. We investigate the backaction of the environment on the measured qubit and explore several measurement protocols, which include a long-term full readout cycle as well as schemes based on short time transfer of information between qubit and oscillator. We also show that the pointer becomes measurable before all information in the qubit has been lost.

DOI
10.1103/physrevb.76.104510

Related papers

Time-resolved qubit readout via nonlinear Josephson inductance

Georg M Reuther, David Zueco, Peter Hänggi A +1 more

We propose a generalization of dispersive qubit readout that provides the time evolution of a flux qubit observable.Our proposal relies on the nonlinear coupling of the qubit to a harmonic oscillator with high frequency, representing a dc superconducting quantum interference device.Information about the qubit dynamics is obtained by recording the oscillator response to resonant driving and subsequent lock-in detection.The measurement process is simulated for the example of coherent qubit oscillations.This corroborates the underlying measurement relation and also reveals that the measurement scheme possesses low backaction and high fidelity.

arXiv:1105.1105•New Journal of Physics•Sep 12, 2011•6 citations

11 Time-resolved qubit readout via nonlinear Josephsoninductance

Georg M. Reuther, David Zueco, Sigmund Kohler

We propose a generalization of dispersive qubit readout that provides the time evolution of a flux qubit observable. Our proposal relies on the nonlinear coupling of the qubit to a harmonic oscillator with high frequency, representing a dc superconducting quantum interference device. Information about the qubit dynamics is obtained by recording the oscillator response to resonant driving and subsequent lock-in detection. The measurement process is simulated for the example of coherent qubit oscillations. This corroborates the underlying measurement relation and also reveals that the measurement scheme possesses low backaction and high fidelity.

•Aug 17, 2016•4 citations

Non-Markovian qubit decoherence during dispersive readout

Georg M. Reuther, Peter Hänggi A, Sigmund Kohler

We study qubit decoherence under generalized dispersive readout, i.e., we investigate a qubit coupled to a resonantly driven dissipative harmonic oscillator. We provide a complete picture by allowing for arbitrarily large qubit-oscillator detuning and by considering also a coupling to the square of the oscillator coordinate, which is relevant for flux qubits. Analytical results for the decoherence time are obtained by a transformation of the qubit-oscillator Hamiltonian to the dispersive frame and a subsequent master equation treatment beyond the Markov limit. We predict a crossover from Markovian decay to a decay with Gaussian shape. Our results are corroborated by the numerical solution of the full qubit-oscillator master equation in the original frame.

arXiv:1205.2315•Physical Review A•Jun 28, 2012•6 citations

Prediction of Short Time Qubit Readout via Measurement of the Next Quantum Jump of a Coupled Damped Driven Harmonic Oscillator

Massimo Porrati B, Seth Putterman

The dynamics of the next quantum jump for a qubit [two level system] coupled to a readout resonator [damped driven harmonic oscillator] is calculated. A quantum mechanical treatment of readout resonator reveals nonexponential short time behavior which could facilitate detection of the state of the qubit faster than the resonator lifetime.

arXiv:2006.11950•Physical Review Letters•Dec 21, 2020•3 citations

Dispersive reservoir influence on the superconducting phase qubit

H. A. Hessian, A.‐B. A. Mohamed, Ali H. Homid

An analytical description of a superconducting (SC) phase qubit coupled to a torsional resonator, which is damped by a dispersive reservoir, is presented based on the master equation. Therefore, the effect of the qubit phase damping on the dynamical behavior of the entanglement, purity loss and qubit inversion are investigated. It is found that the collapse and revival phenomena of qubit inversion are very sensitive not only to the damping parameter but also to the frequency detuning and the qubit distribution angle of the initial state. It is interesting to note that the purity of the state of the SC-qubit, which is measured by von Neumann entropy, can be completely lost due to the dispersive reservoir parameter. Because of the existence of dispersive reservoir, the von Neumann entropy cannot be a measure for the entanglement in open system. So, the negative eigenvalue of the partially transposed density matrix of qubit-resonator system is used to quantify the entanglement. For certain parameter sets, it is possible to control the degree and the dynamics of entanglement between the qubit and the torsional resonator.

International Journal of Quantum Information•Oct 1, 2015•4 citations

From Qubit Dynamics to Binary Readout: A Pedagogical State-Space Model of Sampling, Measurement Backaction, and Decoherence

Ricardo Adonis Caraccioli Abrego

This tutorial note develops a self-contained engineering-oriented model that connects thecontinuous dynamics of a two-level quantum system to a classical binary readout. The purpose ispedagogical rather than foundational: no new interpretation of quantum mechanics, measurementpostulate, or quantum analog-to-digital conversion protocol is proposed. Instead, establishedelements of open-system dynamics, generalized measurement, stochastic master equations, pointer-state selection, and threshold detection are organized into a single chain that can be simulatedwith conventional state-space tools.A qubit driven by a Hamiltonian H = ℏ(Ωσx + ∆σz )/2 is first described by a Lindbladequation and by the corresponding Bloch equations. Repeated nonselective partial measurementsare represented by a completely positive trace-preserving dephasing channel, from which the exactdiscrete-time coherence decay rate Γϕ = −fs ln (1 − ϵ) is obtained. The distinction between thisensemble-averaged channel and a single experimental realization is then made explicit througha diffusive stochastic master equation. In that conditional description, the detector producesa continuous noisy record; integration over a finite acquisition time and comparison with athreshold yields the final Boolean symbol. The resulting engineering chain is therefore not “wavefunction to bit,” but rather qubit state → detector statistics → analog record → integration →binary decision.Three time scales are emphasized: coherent dynamics, measurement-induced dephasing, andreadout integration. A Nyquist-like sampling inequality is retained only as a temporal-resolutionguideline for ensemble-reconstructed expectation values, not as a sufficient theorem for single-shotquantum-state reconstruction. Finally, the unconditional Bloch equations are mapped ontoan analog state-space macromodel implementable in LTspice. The note includes a correctedreference netlist and a reproducible validation protocol comparing the discrete channel, thecontinuous master equation, averaged stochastic trajectories, and the SPICE realization.

•Jul 10, 2026•0 citations
Motivated by recent experiments, we study the dynamics of a qubit quadratically coupled to its detector, a damped harmonic oscillator. We use a complex-environment approach, explicitly describing the dynamics of the qubit and the oscillator by means of their full Floquet state master equations in phase-space. We investigate the backaction of the environment on the measured qubit and explore several measurement protocols, which include a long-term full readout cycle as well as schemes based on short time transfer of information between qubit and oscillator. We also show that the pointer becomes measurable before all information in the qubit has been lost.
We propose a generalization of dispersive qubit readout that provides the time evolution of a flux qubit observable.Our proposal relies on the nonlinear coupling of the qubit to a harmonic oscillator with high frequency, representing a dc superconducting quantum interference device.Information about the qubit dynamics is obtained by recording the oscillator response to resonant driving and subsequent lock-in detection.The measurement process is simulated for the example of coherent qubit oscillations.This corroborates the underlying measurement relation and also reveals that the measurement scheme possesses low backaction and high fidelity.
We propose a generalization of dispersive qubit readout that provides the time evolution of a flux qubit observable. Our proposal relies on the nonlinear coupling of the qubit to a harmonic oscillator with high frequency, representing a dc superconducting quantum interference device. Information about the qubit dynamics is obtained by recording the oscillator response to resonant driving and subsequent lock-in detection. The measurement process is simulated for the example of coherent qubit oscillations. This corroborates the underlying measurement relation and also reveals that the measurement scheme possesses low backaction and high fidelity.
We study qubit decoherence under generalized dispersive readout, i.e., we investigate a qubit coupled to a resonantly driven dissipative harmonic oscillator. We provide a complete picture by allowing for arbitrarily large qubit-oscillator detuning and by considering also a coupling to the square of the oscillator coordinate, which is relevant for flux qubits. Analytical results for the decoherence time are obtained by a transformation of the qubit-oscillator Hamiltonian to the dispersive frame and a subsequent master equation treatment beyond the Markov limit. We predict a crossover from Markovian decay to a decay with Gaussian shape. Our results are corroborated by the numerical solution of the full qubit-oscillator master equation in the original frame.
An analytical description of a superconducting (SC) phase qubit coupled to a torsional resonator, which is damped by a dispersive reservoir, is presented based on the master equation. Therefore, the effect of the qubit phase damping on the dynamical behavior of the entanglement, purity loss and qubit inversion are investigated. It is found that the collapse and revival phenomena of qubit inversion are very sensitive not only to the damping parameter but also to the frequency detuning and the qubit distribution angle of the initial state. It is interesting to note that the purity of the state of the SC-qubit, which is measured by von Neumann entropy, can be completely lost due to the dispersive reservoir parameter. Because of the existence of dispersive reservoir, the von Neumann entropy cannot be a measure for the entanglement in open system. So, the negative eigenvalue of the partially transposed density matrix of qubit-resonator system is used to quantify the entanglement. For certain parameter sets, it is possible to control the degree and the dynamics of entanglement between the qubit and the torsional resonator.
This tutorial note develops a self-contained engineering-oriented model that connects thecontinuous dynamics of a two-level quantum system to a classical binary readout. The purpose ispedagogical rather than foundational: no new interpretation of quantum mechanics, measurementpostulate, or quantum analog-to-digital conversion protocol is proposed. Instead, establishedelements of open-system dynamics, generalized measurement, stochastic master equations, pointer-state selection, and threshold detection are organized into a single chain that can be simulatedwith conventional state-space tools.A qubit driven by a Hamiltonian H = ℏ(Ωσx + ∆σz )/2 is first described by a Lindbladequation and by the corresponding Bloch equations. Repeated nonselective partial measurementsare represented by a completely positive trace-preserving dephasing channel, from which the exactdiscrete-time coherence decay rate Γϕ = −fs ln (1 − ϵ) is obtained. The distinction between thisensemble-averaged channel and a single experimental realization is then made explicit througha diffusive stochastic master equation. In that conditional description, the detector producesa continuous noisy record; integration over a finite acquisition time and comparison with athreshold yields the final Boolean symbol. The resulting engineering chain is therefore not “wavefunction to bit,” but rather qubit state → detector statistics → analog record → integration →binary decision.Three time scales are emphasized: coherent dynamics, measurement-induced dephasing, andreadout integration. A Nyquist-like sampling inequality is retained only as a temporal-resolutionguideline for ensemble-reconstructed expectation values, not as a sufficient theorem for single-shotquantum-state reconstruction. Finally, the unconditional Bloch equations are mapped ontoan analog state-space macromodel implementable in LTspice. The note includes a correctedreference netlist and a reproducible validation protocol comparing the discrete channel, thecontinuous master equation, averaged stochastic trajectories, and the SPICE realization.