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:1003.5488 · Physical Review A

High-fidelity feedback-assisted parity measurement in circuit QED

Lars Tornberg, Göran Johansson

Published Jul 26, 2010• 41 citations
arXivHTMLPDF

Abstract

We analyze a two-qubit parity measurement based on dispersive readout in circuit quantum electrodynamics. The back action on the qubits has two qualitatively different contributions. One is an unavoidable dephasing in one of the parity subspaces, arising during the transient time of switching on the measurement. The other part is a stochastic rotation of the phase in the same subspace, which persists during the whole measurement. The latter can be determined from the full measurement record using the method of state estimation. Our main result is that the outcome of this phase determination process is independent of the initial state in the state estimation procedure. The procedure can thus be used in a measurement situation where the initial state is unknown. We discuss how this feedback method can be used to achieve a high-fidelity parity measurement for moderate values of the cavity-qubit coupling strength. Finally, we discuss the robustness of the feedback procedure toward errors in the measurement record.

DOI
10.1103/physreva.82.012329

Related papers

Qubit parity measurement by parametric driving in circuit QED

Baptiste Royer, Shruti Puri, Alexandre Blais

Multiqubit parity measurements are essential to quantum error correction. Current realizations of these measurements often rely on ancilla qubits, a method that is sensitive to faulty two-qubit gates and that requires notable experimental overhead. We propose a hardware-efficient multiqubit parity measurement exploiting the bifurcation dynamics of a parametrically driven nonlinear oscillator. This approach takes advantage of the resonator's parametric oscillation threshold, which depends on the joint parity of dispersively coupled qubits, leading to high-amplitude oscillations for one parity subspace and no oscillation for the other. We present analytical and numerical results for two- and four-qubit parity measurements, with high-fidelity readout preserving the parity eigenpaces. Moreover, we discuss a possible realization that can be readily implemented with the current circuit quantum electrodynamics (QED) experimental toolbox. These results could lead to substantial simplifications in the experimental implementation of quantum error correction and notably of the surface code.

arXiv:1802.10112•Science Advances•Nov 2, 2018•30 citations

Towards a heralded eigenstate-preserving measurement of multi-qubit parity in circuit QED

Patrick Huembeli, Simon E. Nigg

Eigenstate-preserving multi-qubit parity measurements lie at the heart of stabilizer quantum error correction, which is a promising approach to mitigate the problem of decoherence in quantum computers. In this work we explore a high-fidelity, eigenstate-preserving parity readout for superconducting qubits dispersively coupled to a microwave resonator, where the parity bit is encoded in the amplitude of a coherent state of the resonator. Detecting photons emitted by the resonator via a current biased Josephson junction yields information about the parity bit. We analyze theoretically the measurement back action in the limit of a strongly coupled fast detector and show that in general such a parity measurement, while approximately quantum nondemolition is not eigenstate preserving. To remediate this shortcoming we propose a simple dynamical decoupling technique during photon detection, which greatly reduces decoherence within a given parity subspace. Furthermore, by applying a sequence of fast displacement operations interleaved with the dynamical decoupling pulses, the natural bias of this binary detector can be efficiently suppressed. Finally, we introduce the concept of a heralded parity measurement, where a detector click guarantees successful multi-qubit parity detection even for finite detection efficiency.

arXiv:1704.08734•Physical Review A•Jul 11, 2017•6 citations

Tunable joint measurements in the dispersive regime of cavity QED

Kevin Lalumière, Jay Gambetta, Alexandre Blais

Joint measurements of multiple qubits open new possibilities for quantum information processing. Here we present an approach based on homodyne detection to realize such measurements in the dispersive regime of cavity or circuit QED. By changing details of the measurement, the readout can be tuned from extracting only single-qubit to extracting only multiqubit properties. We obtain a reduced stochastic master equation describing this measurement and its effect on the qubits. As an example, we present results showing parity measurements of two qubits. In this situation, measurement of an initially unentangled state can yield, with near unit probability, a state of significant concurrence.

arXiv:0911.5322•Physical Review A•Apr 1, 2010•74 citations

Stochastic-master-equation analysis of optimized three-qubit nondemolition parity measurements

Lars Tornberg, Sh. Barzanjeh, David Peter Divincenzo

We analyzea direct parity measurement of the state of three superconducting qubits in circuit quantum electrodynamics. The parity is inferred from a homodyne measurement of the reflected and transmitted microwave radiation, and the measurement is direct in the sense that the parity is measured without the need for any quantum circuit operations or for ancilla qubits. Qubits are coupled to two resonant-cavity modes, allowing the steady state of the emitted radiation to satisfy the necessary conditions to act as a pointer state for the parity. However, the transient dynamics violates these conditions, and we analyze this detrimental effect and show that it can be overcome in the limit of a weak measurement signal. Our analysis shows that, with a moderate degree of postselection, it is possible to achieve postmeasurement states with fidelity of order 95%. We believe that this type of measurement could serve as a benchmark for future error correction protocols in a scalable architecture.

arXiv:1311.1963•Physical Review A•Mar 12, 2014•17 citations

Undoing measurement-induced dephasing in circuit QED

Anton Frisk Kockum, Lars Tornberg, Göran Johansson

We analyze the backaction of homodyne detection and photodetection on superconducting qubits in circuit quantum electrodynamics. Although both measurement schemes give rise to backaction in the form of stochastic phase rotations, which leads to dephasing, we show that this can be perfectly undone provided that the measurement signal is fully accounted for. This result improves on an earlier one [Phys. Rev. A 82, 012329 (2010)], showing that the method suggested can be made to realize a perfect two-qubit parity measurement. We propose a benchmarking experiment on a single qubit to demonstrate the method using homodyne detection. By analyzing the limited measurement efficiency of the detector and bandwidth of the amplifier, we show that the parameter values necessary to see the effect are within the limits of existing technology.

arXiv:1202.2386•Physical Review A•May 24, 2012•29 citations

On-demand maximally entangled states with a parity meter and continuous feedback

Clemens Meyer zu Rheda, Géraldine Haack, Alessandro Romito

Generating on-demand maximally entangled states is one of the cornerstones for quantum information processing. Parity measurements can serve to create Bell states and have been implemented via an electronic Mach-Zehnder interferometer among others. However, the entanglement generation is necessarily harmed by measurement-induced dephasing processes in one of the two parity subspaces. In this work, we propose two different schemes of continuous feedback for a parity measurement. They enable us to avoid both the measurement-induced dephasing process and the experimentally unavoidable dephasing, e.g., due to fluctuations of the gate voltages controlling the initialization of the qubits. We show that we can generate maximally entangled steady states in both parity subspaces. Importantly, the measurement scheme we propose is valid for implementation of parity measurements with feedback loops in various solid-state environments.

arXiv:1407.1159•Physical Review B•Oct 21, 2014•13 citations
We analyze a two-qubit parity measurement based on dispersive readout in circuit quantum electrodynamics. The back action on the qubits has two qualitatively different contributions. One is an unavoidable dephasing in one of the parity subspaces, arising during the transient time of switching on the measurement. The other part is a stochastic rotation of the phase in the same subspace, which persists during the whole measurement. The latter can be determined from the full measurement record using the method of state estimation. Our main result is that the outcome of this phase determination process is independent of the initial state in the state estimation procedure. The procedure can thus be used in a measurement situation where the initial state is unknown. We discuss how this feedback method can be used to achieve a high-fidelity parity measurement for moderate values of the cavity-qubit coupling strength. Finally, we discuss the robustness of the feedback procedure toward errors in the measurement record.
Multiqubit parity measurements are essential to quantum error correction. Current realizations of these measurements often rely on ancilla qubits, a method that is sensitive to faulty two-qubit gates and that requires notable experimental overhead. We propose a hardware-efficient multiqubit parity measurement exploiting the bifurcation dynamics of a parametrically driven nonlinear oscillator. This approach takes advantage of the resonator's parametric oscillation threshold, which depends on the joint parity of dispersively coupled qubits, leading to high-amplitude oscillations for one parity subspace and no oscillation for the other. We present analytical and numerical results for two- and four-qubit parity measurements, with high-fidelity readout preserving the parity eigenpaces. Moreover, we discuss a possible realization that can be readily implemented with the current circuit quantum electrodynamics (QED) experimental toolbox. These results could lead to substantial simplifications in the experimental implementation of quantum error correction and notably of the surface code.
Eigenstate-preserving multi-qubit parity measurements lie at the heart of stabilizer quantum error correction, which is a promising approach to mitigate the problem of decoherence in quantum computers. In this work we explore a high-fidelity, eigenstate-preserving parity readout for superconducting qubits dispersively coupled to a microwave resonator, where the parity bit is encoded in the amplitude of a coherent state of the resonator. Detecting photons emitted by the resonator via a current biased Josephson junction yields information about the parity bit. We analyze theoretically the measurement back action in the limit of a strongly coupled fast detector and show that in general such a parity measurement, while approximately quantum nondemolition is not eigenstate preserving. To remediate this shortcoming we propose a simple dynamical decoupling technique during photon detection, which greatly reduces decoherence within a given parity subspace. Furthermore, by applying a sequence of fast displacement operations interleaved with the dynamical decoupling pulses, the natural bias of this binary detector can be efficiently suppressed. Finally, we introduce the concept of a heralded parity measurement, where a detector click guarantees successful multi-qubit parity detection even for finite detection efficiency.
Joint measurements of multiple qubits open new possibilities for quantum information processing. Here we present an approach based on homodyne detection to realize such measurements in the dispersive regime of cavity or circuit QED. By changing details of the measurement, the readout can be tuned from extracting only single-qubit to extracting only multiqubit properties. We obtain a reduced stochastic master equation describing this measurement and its effect on the qubits. As an example, we present results showing parity measurements of two qubits. In this situation, measurement of an initially unentangled state can yield, with near unit probability, a state of significant concurrence.
We analyzea direct parity measurement of the state of three superconducting qubits in circuit quantum electrodynamics. The parity is inferred from a homodyne measurement of the reflected and transmitted microwave radiation, and the measurement is direct in the sense that the parity is measured without the need for any quantum circuit operations or for ancilla qubits. Qubits are coupled to two resonant-cavity modes, allowing the steady state of the emitted radiation to satisfy the necessary conditions to act as a pointer state for the parity. However, the transient dynamics violates these conditions, and we analyze this detrimental effect and show that it can be overcome in the limit of a weak measurement signal. Our analysis shows that, with a moderate degree of postselection, it is possible to achieve postmeasurement states with fidelity of order 95%. We believe that this type of measurement could serve as a benchmark for future error correction protocols in a scalable architecture.
We analyze the backaction of homodyne detection and photodetection on superconducting qubits in circuit quantum electrodynamics. Although both measurement schemes give rise to backaction in the form of stochastic phase rotations, which leads to dephasing, we show that this can be perfectly undone provided that the measurement signal is fully accounted for. This result improves on an earlier one [Phys. Rev. A 82, 012329 (2010)], showing that the method suggested can be made to realize a perfect two-qubit parity measurement. We propose a benchmarking experiment on a single qubit to demonstrate the method using homodyne detection. By analyzing the limited measurement efficiency of the detector and bandwidth of the amplifier, we show that the parameter values necessary to see the effect are within the limits of existing technology.
Generating on-demand maximally entangled states is one of the cornerstones for quantum information processing. Parity measurements can serve to create Bell states and have been implemented via an electronic Mach-Zehnder interferometer among others. However, the entanglement generation is necessarily harmed by measurement-induced dephasing processes in one of the two parity subspaces. In this work, we propose two different schemes of continuous feedback for a parity measurement. They enable us to avoid both the measurement-induced dephasing process and the experimentally unavoidable dephasing, e.g., due to fluctuations of the gate voltages controlling the initialization of the qubits. We show that we can generate maximally entangled steady states in both parity subspaces. Importantly, the measurement scheme we propose is valid for implementation of parity measurements with feedback loops in various solid-state environments.