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:1509.00860 · Physical Review X

Comparing and Combining Measurement-Based and Driven-Dissipative Entanglement Stabilization

Y. Liu, Shyam Shankar, Nissim Ofek, Michael Hatridge, A. Narla, Katrina Sliwa, Luigi Frunzio, Robert J. Schoelkopf, Michel Devoret

Published Mar 3, 2016• 80 citations
arXivHTMLPDF

Abstract

We demonstrate and contrast two approaches to the stabilization of qubit entanglement by feedback.Our demonstration is built on a feedback platform consisting of two superconducting qubits coupled to a cavity, which are measured by a nearly quantum-limited measurement chain and controlled by high-speed classical logic circuits.This platform is used to stabilize entanglement by two nominally distinct schemes: a "passive" reservoir engineering method and an "active" correction based on conditional parity measurements.In view of the instrumental roles that these two feedback paradigms play in quantum error correction and quantum control, we directly compare them on the same experimental setup.Furthermore, we show that a second layer of feedback can be added to each of these schemes, which heralds the presence of a high-fidelity entangled state in real time.This "nested" feedback brings about a marked entanglement fidelity improvement without sacrificing success probability.

DOI
10.1103/physrevx.6.011022

Related papers

Stabilizing two-qubit entanglement with dynamically decoupled active feedback

Sacha Greenfield, Leigh S. Martin, Felix Motzoi +3 more

We propose and analyze a protocol for stabilizing a maximally entangled state of two noninteracting qubits using active state-dependent feedback from a continuous two-qubit half-parity measurement in coordination with a concurrent, noncommuting dynamical decoupling drive. We demonstrate that such a drive can be simultaneous with the measurement and feedback, while also playing a key part in the feedback protocol itself. We show that robust stabilization with near-unit fidelity can be achieved even in the presence of realistic nonidealities, such as time delay in the feedback loop, imperfect state-tracking, inefficient measurements, dephasing from $1/f$-distributed qubit-frequency noise, and relaxation. We mitigate feedback-delay error by introducing a forward-state-estimation strategy in the feedback controller that tracks the effects of control signals already in transit. More generally, the steady state is globally attractive without the need for ancillas, regardless of the error state, in contrast to most known feedback and error-correction schemes.

arXiv:2308.03923•Physical Review Applied•Feb 12, 2024•8 citations

Entanglement stabilization using ancilla-based parity detection and real-time feedback in superconducting circuits

Christian Kraglund Andersen, Ants Remm, Stefania Lazar +6 more

Abstract Fault-tolerant quantum computing relies on the ability to detect and correct errors, which in quantum error correction codes is typically achieved by projectively measuring multi-qubit parity operators and by conditioning operations on the observed error syndromes. Here, we experimentally demonstrate the use of an ancillary qubit to repeatedly measure the ZZ and XX parity operators of two data qubits and to thereby project their joint state into the respective parity subspaces. By applying feedback operations conditioned on the outcomes of individual parity measurements, we demonstrate the real-time stabilization of a Bell state with a fidelity of F ≈ 74% in up to 12 cycles of the feedback loop. We also perform the protocol using Pauli frame updating and, in contrast to the case of real-time stabilization, observe a steady decrease in fidelity from cycle to cycle. The ability to stabilize parity over multiple feedback rounds with no further reduction in fidelity provides strong evidence for the feasibility of executing stabilizer codes on timescales much longer than the intrinsic coherence times of the constituent qubits.

arXiv:1902.06946•npj Quantum Information•Aug 15, 2019•91 citations

Feedback control of superconducting quantum circuits

Diego Ristè

Superconducting circuits have recently risen to the forefront of the solid-state prototypes for quantum computing. Reaching the stage of robust quantum computing requires closing the loop between measurement and control of quantum bits (qubits). This thesis presents the realization of feedback control of superconducting qubits based on projective measurement, with initial applications. The first application is a reset operation which initializes a qubit in the ground state fast and on demand. In a second experiment, we transform a cavity into a two-qubit parity meter, which is capable of generating entanglement starting from an unentangled superposition state. We then employ feedback to turn the generation of entanglement from probabilistic to deterministic, thus combining two key ingredients - parity measurement and feedback - of quantum error correction. As a third application, we transform a superconducting qubit into a charge-parity detector to investigate the limits of quasiparticle tunneling to qubit coherence. We find room for at least a tenfold increase in qubit coherence times before quasiparticles become the bottleneck. Finally, we present our latest results towards implementing the bit-flip error correction code in a five-qubit processor and discuss the role of feedback control in the future development of superconducting quantum circuits.

•Jan 1, 2014•2 citations

Measurement-and Feedback-Driven Non-Equilibrium Phase Transitions on a Quantum Processor

Zhiyi Wu, Xuandong Sun, Songlei Wang +8 more

Mid-circuit measurements and feedback operations conditioned on the measurement outcomes are essential for implementing quantum error-correction on quantum hardware. When integrated in quantum many-body dynamics, they can give rise to novel non-equilibrium phase transitions both at the level of each individual quantum trajectory and the averaged quantum channel. Experimentally resolving both transitions on realistic devices has been challenging due to limitations on the fidelity and the significant latency for performing mid-circuit measurements and feedback operations in real time. Here, we develop a superconducting quantum processor that enables global mid-circuit measurement with an average quantum non-demolition (QND) fidelity of 98.7% and fast conditional feedback with a 200 ns real-time decision latency. Using this platform, we demonstrate the coexistence of an absorbing-state transition in the quantum channel and a measurement-induced entanglement transition at the level of individual quantum trajectories. For the absorbing-state transition, we experimentally extract a set of critical exponents at the transition point, which is in excellent agreement with the directed percolation universality class. Crucially, the two transitions occur at distinct values of the tuning parameter. Our results demonstrate that adaptive quantum circuits provide a powerful platform for exploring non-equilibrium quantum many-body dynamics.

quant-pharXiv:2512.07966•Physical Review Letters•Dec 10, 2025•0 citations

Purification and switching protocols for dissipatively stabilized entangled qubit states

Sven M. Hein, Camille Aron, Hakan E. Türeci

Pure dephasing processes limit the fidelities achievable in driven-dissipative schemes for stabilization of entangled states of qubits. We propose a scheme which, combined with already existing entangling methods, purifies the desired entangled state by driving out of equilibrium auxiliary dissipative cavity modes coupled to the qubits. We lay out the specifics of our scheme and compute its efficiency in the particular context of two superconducting qubits in a cavity-QED architecture, where the strongly coupled auxiliary modes provided by collective cavity excitations can drive and sustain the qubits in maximally entangled Bell states with fidelities reaching 90% for experimentally accessible parameters.

arXiv:1604.07198•Physical Review A•Jun 23, 2016•11 citations

Hardware-efficient stabilization of entanglement via engineered dissipation in superconducting circuits

C. H. Chen, Kai Tang, Yuxuan Zhou +8 more

Generation and preservation of quantum entanglement are among the primary tasks in quantum information processing. State stabilization via quantum bath engineering offers a resource-efficient approach to achieve this objective. However, current methods for engineering dissipative channels to stabilize target entangled states often require specialized hardware designs, complicating experimental realization and hindering their compatibility with scalable quantum computation architectures. In this work, we propose and experimentally demonstrate a stabilization protocol readily implementable in the mainstream integrated superconducting quantum circuits. The approach utilizes a Raman process involving a resonant (or nearly resonant) superconducting qubit array and the qubits' dedicated readout resonators to effectively develop nonlocal dissipative channels. Leveraging individual controllability of the qubits and resonators, the protocol stabilizes two-qubit Bell states with a fidelity of 90.7 % , marking the highest reported value in solid-state platforms to date. Furthermore, by extending this strategy to include three qubits, an entangled W state is achieved with a fidelity of 86.2 % . This demonstrates the protocol's extensibility beyond two-qubit systems. Notably, the protocol is of practical interest since it only utilizes existing hardware common to standard operations in the underlying superconducting circuits, thereby facilitating the exploration of many-body quantum entanglement with dissipative resources.

arXiv:2407.13321•Physical Review Research•Apr 16, 2025•10 citations
We demonstrate and contrast two approaches to the stabilization of qubit entanglement by feedback.Our demonstration is built on a feedback platform consisting of two superconducting qubits coupled to a cavity, which are measured by a nearly quantum-limited measurement chain and controlled by high-speed classical logic circuits.This platform is used to stabilize entanglement by two nominally distinct schemes: a "passive" reservoir engineering method and an "active" correction based on conditional parity measurements.In view of the instrumental roles that these two feedback paradigms play in quantum error correction and quantum control, we directly compare them on the same experimental setup.Furthermore, we show that a second layer of feedback can be added to each of these schemes, which heralds the presence of a high-fidelity entangled state in real time.This "nested" feedback brings about a marked entanglement fidelity improvement without sacrificing success probability.
We propose and analyze a protocol for stabilizing a maximally entangled state of two noninteracting qubits using active state-dependent feedback from a continuous two-qubit half-parity measurement in coordination with a concurrent, noncommuting dynamical decoupling drive. We demonstrate that such a drive can be simultaneous with the measurement and feedback, while also playing a key part in the feedback protocol itself. We show that robust stabilization with near-unit fidelity can be achieved even in the presence of realistic nonidealities, such as time delay in the feedback loop, imperfect state-tracking, inefficient measurements, dephasing from 1/f1/f1/f-distributed qubit-frequency noise, and relaxation. We mitigate feedback-delay error by introducing a forward-state-estimation strategy in the feedback controller that tracks the effects of control signals already in transit. More generally, the steady state is globally attractive without the need for ancillas, regardless of the error state, in contrast to most known feedback and error-correction schemes.
Abstract Fault-tolerant quantum computing relies on the ability to detect and correct errors, which in quantum error correction codes is typically achieved by projectively measuring multi-qubit parity operators and by conditioning operations on the observed error syndromes. Here, we experimentally demonstrate the use of an ancillary qubit to repeatedly measure the ZZ and XX parity operators of two data qubits and to thereby project their joint state into the respective parity subspaces. By applying feedback operations conditioned on the outcomes of individual parity measurements, we demonstrate the real-time stabilization of a Bell state with a fidelity of F ≈ 74% in up to 12 cycles of the feedback loop. We also perform the protocol using Pauli frame updating and, in contrast to the case of real-time stabilization, observe a steady decrease in fidelity from cycle to cycle. The ability to stabilize parity over multiple feedback rounds with no further reduction in fidelity provides strong evidence for the feasibility of executing stabilizer codes on timescales much longer than the intrinsic coherence times of the constituent qubits.
Superconducting circuits have recently risen to the forefront of the solid-state prototypes for quantum computing. Reaching the stage of robust quantum computing requires closing the loop between measurement and control of quantum bits (qubits). This thesis presents the realization of feedback control of superconducting qubits based on projective measurement, with initial applications. The first application is a reset operation which initializes a qubit in the ground state fast and on demand. In a second experiment, we transform a cavity into a two-qubit parity meter, which is capable of generating entanglement starting from an unentangled superposition state. We then employ feedback to turn the generation of entanglement from probabilistic to deterministic, thus combining two key ingredients - parity measurement and feedback - of quantum error correction. As a third application, we transform a superconducting qubit into a charge-parity detector to investigate the limits of quasiparticle tunneling to qubit coherence. We find room for at least a tenfold increase in qubit coherence times before quasiparticles become the bottleneck. Finally, we present our latest results towards implementing the bit-flip error correction code in a five-qubit processor and discuss the role of feedback control in the future development of superconducting quantum circuits.
Mid-circuit measurements and feedback operations conditioned on the measurement outcomes are essential for implementing quantum error-correction on quantum hardware. When integrated in quantum many-body dynamics, they can give rise to novel non-equilibrium phase transitions both at the level of each individual quantum trajectory and the averaged quantum channel. Experimentally resolving both transitions on realistic devices has been challenging due to limitations on the fidelity and the significant latency for performing mid-circuit measurements and feedback operations in real time. Here, we develop a superconducting quantum processor that enables global mid-circuit measurement with an average quantum non-demolition (QND) fidelity of 98.7% and fast conditional feedback with a 200 ns real-time decision latency. Using this platform, we demonstrate the coexistence of an absorbing-state transition in the quantum channel and a measurement-induced entanglement transition at the level of individual quantum trajectories. For the absorbing-state transition, we experimentally extract a set of critical exponents at the transition point, which is in excellent agreement with the directed percolation universality class. Crucially, the two transitions occur at distinct values of the tuning parameter. Our results demonstrate that adaptive quantum circuits provide a powerful platform for exploring non-equilibrium quantum many-body dynamics.
Pure dephasing processes limit the fidelities achievable in driven-dissipative schemes for stabilization of entangled states of qubits. We propose a scheme which, combined with already existing entangling methods, purifies the desired entangled state by driving out of equilibrium auxiliary dissipative cavity modes coupled to the qubits. We lay out the specifics of our scheme and compute its efficiency in the particular context of two superconducting qubits in a cavity-QED architecture, where the strongly coupled auxiliary modes provided by collective cavity excitations can drive and sustain the qubits in maximally entangled Bell states with fidelities reaching 90% for experimentally accessible parameters.
Generation and preservation of quantum entanglement are among the primary tasks in quantum information processing. State stabilization via quantum bath engineering offers a resource-efficient approach to achieve this objective. However, current methods for engineering dissipative channels to stabilize target entangled states often require specialized hardware designs, complicating experimental realization and hindering their compatibility with scalable quantum computation architectures. In this work, we propose and experimentally demonstrate a stabilization protocol readily implementable in the mainstream integrated superconducting quantum circuits. The approach utilizes a Raman process involving a resonant (or nearly resonant) superconducting qubit array and the qubits' dedicated readout resonators to effectively develop nonlocal dissipative channels. Leveraging individual controllability of the qubits and resonators, the protocol stabilizes two-qubit Bell states with a fidelity of 90.7 % , marking the highest reported value in solid-state platforms to date. Furthermore, by extending this strategy to include three qubits, an entangled W state is achieved with a fidelity of 86.2 % . This demonstrates the protocol's extensibility beyond two-qubit systems. Notably, the protocol is of practical interest since it only utilizes existing hardware common to standard operations in the underlying superconducting circuits, thereby facilitating the exploration of many-body quantum entanglement with dissipative resources.