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:1506.08165 · Comptes Rendus Physique

Quantum trajectories of superconducting qubits

Steven J. Weber, Kater W. Murch, Mollie E. Schwartz, Nicolas Roch, Irfan A. Siddiqi

Published Aug 1, 2016• 28 citations
arXivHTMLPDF

Abstract

In this review, we discuss recent experiments that investigate how the quantum sate of a superconducting qubit evolves during measurement. We provide a pedagogical overview of the measurement process, when the qubit is dispersively coupled to a microwave frequency cavity, and the qubit state is encoded in the phase of a microwave tone that probes the cavity. A continuous measurement record is used to reconstruct the individual quantum trajectories of the qubit state, and quantum state tomography is performed to verify that the state has been tracked accurately. Furthermore, we discuss ensembles of trajectories, time-symmetric evolution, two-qubit trajectories, and potential applications in measurement-based quantum error correction.

DOI
10.1016/j.crhy.2016.07.007

Related papers

Observing Single Quantum Trajectories of a Superconducting Qubit

Irfan A. Siddiqi, Steven J. Weber, K. W. Murch +3 more

We monitor the quantum trajectory of a superconducting qubit as it evolves under a continuous weak measurement. We verify the trajectory using quantum state tomography and investigate statistical properties of ensembles of trajectories.

Research in Optical Sciences•Jan 1, 2014•5 citations

Measurement-based synthesis of multiqubit entangled states in superconducting cavity QED

Ferdinand Helmer, Florian Marquardt

Entangled multiqubit states may be generated through a dispersive collective quantum nondemolition measurement of superconducting qubits coupled to a microwave transmission line resonator. Using the quantum trajectory approach, we analyze the stochastic measurement traces that would be observed in experiments. We illustrate the synthesis of three-qubit $W$ and Greenberger-Horne-Zeilinger states, and we analyze how the fidelity and the entanglement evolve in time during the measurement. We discuss the influence of decoherence and relaxation, as well as of imperfect control over experimental parameters. We show that the desired states can be generated on time scales much faster than the qubit decoherence rates.

arXiv:0902.0341•Physical Review A•May 20, 2009•45 citations

Quantum Measurements with Superconducting Circuits

Tanay Roy, A. M. Vadiraj, Madhavi Chand +4 more

We measure the state of a superconducting quantum bit (qubit) coupled to a microwave cavity by scattering a microwave signal from the cavity. The scattered signal is amplified using a low-noise Josephson parametric amplifier. We carried out measurements to infer the coherence properties of the qubit. In the strong measurement regime, we observe quantum jumps between the qubit states in real time, while we observe stochastic quantum trajectories in the weak measurement regime. The coherence times and measurement fidelity obtained are sufficient for implementing quantum error correction.

Current Science•Dec 1, 2015•2 citations

Continuous measurements for control of superconducting quantum circuits

Shay Hacohen-Gourgy, L. S. Martin

Developments over the last two decades have opened the path towards quantum technologies in many quantum systems, such as cold atoms, trapped ions, cavity-quantum electrodynamics (QED), and circuit-QED. However, the fragility of quantum states to the effects of measurement and decoherence still poses one of the greatest challenges in quantum technology. An imperative capability in this path is quantum feedback, as it enhances the control possibilities and allows for prolonging coherence times through quantum error correction. While changing parameters from shot to shot of an experiment or procedure can be considered feedback, quantum mechanics also allows for the intriguing possibility of performing feedback operations during the measurement process itself. This broader approach to measurements leads to the concepts of weak measurement, quantum trajectories, and numerous types of feedback with no classical analogs. These types of processes are the primary focus of this review. We introduce the concept of quantum feedback in the context of circuit-QED, an experimental platform with significant potential in quantum feedback and technology. We then discuss several experiments and see how they elucidate the concepts of continuous measurements and feedback. We conclude with an overview of coherent feedback, with application to fault-tolerant error correction.

arXiv:2009.07297•Advances in Physics X•Jan 1, 2020•18 citations

Observing quantum trajectories based on the fluorescence and dispersive measurement records of a superconducting qubit

Quentin Ficheux, S. Jézouin, Philippe Campagne-Ibarcq +2 more

We show the interplay of the backaction of two incompatible weak measurements of a superconducting qubit, its fluorescence and the transmission of a coupled cavity. The associated quantum trajectories reveal Zeno and diffusive dynamics.

Quantum Information and Measurement (QIM)•Jan 1, 2017•3 citations

Quantum Back-Action of an Individual Variable-Strength Measurement

Michael Hatridge, Shyam Shankar, Mazyar Mirrahimi +9 more

Measuring a quantum system can randomly perturb its state. The strength and nature of this back-action depend on the quantity that is measured. In a partial measurement performed by an ideal apparatus, quantum physics predicts that the system remains in a pure state whose evolution can be tracked perfectly from the measurement record. We demonstrated this property using a superconducting qubit dispersively coupled to a cavity traversed by a microwave signal. The back-action on the qubit state of a single measurement of both signal quadratures was observed and shown to produce a stochastic operation whose action is determined by the measurement result. This accurate monitoring of a qubit state is an essential prerequisite for measurement-based feedback control of quantum systems.

arXiv:1903.11732•Science•Jan 10, 2013•278 citations
In this review, we discuss recent experiments that investigate how the quantum sate of a superconducting qubit evolves during measurement. We provide a pedagogical overview of the measurement process, when the qubit is dispersively coupled to a microwave frequency cavity, and the qubit state is encoded in the phase of a microwave tone that probes the cavity. A continuous measurement record is used to reconstruct the individual quantum trajectories of the qubit state, and quantum state tomography is performed to verify that the state has been tracked accurately. Furthermore, we discuss ensembles of trajectories, time-symmetric evolution, two-qubit trajectories, and potential applications in measurement-based quantum error correction.
Entangled multiqubit states may be generated through a dispersive collective quantum nondemolition measurement of superconducting qubits coupled to a microwave transmission line resonator. Using the quantum trajectory approach, we analyze the stochastic measurement traces that would be observed in experiments. We illustrate the synthesis of three-qubit WWW and Greenberger-Horne-Zeilinger states, and we analyze how the fidelity and the entanglement evolve in time during the measurement. We discuss the influence of decoherence and relaxation, as well as of imperfect control over experimental parameters. We show that the desired states can be generated on time scales much faster than the qubit decoherence rates.
We measure the state of a superconducting quantum bit (qubit) coupled to a microwave cavity by scattering a microwave signal from the cavity. The scattered signal is amplified using a low-noise Josephson parametric amplifier. We carried out measurements to infer the coherence properties of the qubit. In the strong measurement regime, we observe quantum jumps between the qubit states in real time, while we observe stochastic quantum trajectories in the weak measurement regime. The coherence times and measurement fidelity obtained are sufficient for implementing quantum error correction.
Developments over the last two decades have opened the path towards quantum technologies in many quantum systems, such as cold atoms, trapped ions, cavity-quantum electrodynamics (QED), and circuit-QED. However, the fragility of quantum states to the effects of measurement and decoherence still poses one of the greatest challenges in quantum technology. An imperative capability in this path is quantum feedback, as it enhances the control possibilities and allows for prolonging coherence times through quantum error correction. While changing parameters from shot to shot of an experiment or procedure can be considered feedback, quantum mechanics also allows for the intriguing possibility of performing feedback operations during the measurement process itself. This broader approach to measurements leads to the concepts of weak measurement, quantum trajectories, and numerous types of feedback with no classical analogs. These types of processes are the primary focus of this review. We introduce the concept of quantum feedback in the context of circuit-QED, an experimental platform with significant potential in quantum feedback and technology. We then discuss several experiments and see how they elucidate the concepts of continuous measurements and feedback. We conclude with an overview of coherent feedback, with application to fault-tolerant error correction.
Measuring a quantum system can randomly perturb its state. The strength and nature of this back-action depend on the quantity that is measured. In a partial measurement performed by an ideal apparatus, quantum physics predicts that the system remains in a pure state whose evolution can be tracked perfectly from the measurement record. We demonstrated this property using a superconducting qubit dispersively coupled to a cavity traversed by a microwave signal. The back-action on the qubit state of a single measurement of both signal quadratures was observed and shown to produce a stochastic operation whose action is determined by the measurement result. This accurate monitoring of a qubit state is an essential prerequisite for measurement-based feedback control of quantum systems.