# Continuous-time Quantum Error Correction with Noise-assisted Quantum Feedback

@article{Cardona2019ContinuoustimeQE, title={Continuous-time Quantum Error Correction with Noise-assisted Quantum Feedback}, author={Gerardo Cardona and Alain Sarlette and Pierre Rouchon}, journal={IFAC-PapersOnLine}, year={2019} }

## 10 Citations

Exponential stabilization of quantum systems subject to non-demolition measurements in continuous time

- Mathematics
- 2019

This thesis develops control methods to stabilize quantum systems in continuous-time subject to quantum nondemolition measurements and proposes the use of control laws and of reduced-order filters which only track classical characteristics of the system, corresponding to the populations on the measurement eigenbasis.

Exponential stabilization of quantum systems under continuous non-demolition measurements

- MathematicsAutom.
- 2020

Always-On Quantum Error Tracking with Continuous Parity Measurements

- Computer ScienceQuantum
- 2020

This work investigates quantum error correction using continuous parity measurements to correct bit-flip errors with the three-qubit code and discusses an unnormalized (linear) Bayesian filter, with improved computational efficiency compared to the related Wonham filter introduced by Mabuchi.

Model robustness for feedback stabilization of open quantum systems

- Mathematics
- 2022

This paper generalizes the results in [32] concerning feedback stabilization of target states for N -level quantum angular momentum systems undergoing quantum nondemolition measurements (QND) in…

Quantum Error Detection Without Using Ancilla Qubits

- Physics
- 2022

In this paper, we describe and experimentally demonstrate an error detection scheme that does not employ ancilla qubits or mid-circuit measurements. This is achieved by expanding the Hilbert space…

Experimental demonstration of continuous quantum error correction

- PhysicsNature communications
- 2022

The storage and processing of quantum information are susceptible to external noise, resulting in computational errors. A powerful method to suppress these effects is quantum error correction.…

Quantum computation with cat qubits

- Physics
- 2022

These are the lecture notes from the 2019 Les Houches Summer School on “Quantum Information Machines”. After a brief introduction to quantum error correction and bosonic codes, we focus on the case…

Continuous quantum error correction for evolution under time-dependent Hamiltonians

- Physics
- 2020

The results suggest that a continuous implementation is suitable for quantum error correction in the presence of encoded time-dependent Hamiltonians, opening the possibility of many applications in quantum simulation and quantum annealing.

Entanglement-preserving limit cycles from sequential quantum measurements and feedback

- PhysicsPhysical Review A
- 2020

Entanglement generation and preservation is a key task in quantum information processing, and a variety of protocols exist to entangle remote qubits via measurement of their spontaneous emission. We…

## References

SHOWING 1-10 OF 19 REFERENCES

Continuous quantum error correction as classical hybrid control

- Computer Science
- 2009

A focused case study is presented, connecting continuous QEC with elements of hybrid control theory, showing that canonical methods of the latter engineering discipline can be applied fruitfully in the design of separated controller structures for quantum memories based on coding and continuous syndrome measurement.

Exponential Stochastic Stabilization of a Two-Level Quantum System via Strict Lyapunov Control

- Mathematics2018 IEEE Conference on Decision and Control (CDC)
- 2018

This article provides a novel continuous-time state feedback control strategy to stabilize an eigenstate of the Hermitian measurement operator of a two-level quantum system and shows that this leads to a global exponential convergence property with a strict Lyapunov function.

Quantum error correction for continuously detected errors

- Physics
- 2003

We show that quantum feedback control can be used as a quantum-error-correction process for errors induced by a weak continuous measurement. In particular, when the error model is restricted to one,…

Continuous quantum error correction via quantum feedback control

- Physics
- 2002

We describe a protocol for continuously protecting unknown quantum states from decoherence that incorporates design principles from both quantum error correction and quantum feedback control. Our…

Practical scheme for error control using feedback

- Physics
- 2004

We describe a scheme for quantum-error correction that employs feedback and weak measurement rather than the standard tools of projective measurement and fast controlled unitary gates. The advantage…

Extending the lifetime of a quantum bit with error correction in superconducting circuits

- PhysicsNature
- 2016

A QEC system that reaches the break-even point by suppressing the natural errors due to energy loss for a qubit logically encoded in superpositions of Schrödinger-cat states of a superconducting resonator is demonstrated.

Locally optimal measurement-based quantum feedback with application to multiqubit entanglement generation

- PhysicsPhysical Review A
- 2020

Application of the PaQS approach to generation of N-qubit W, general Dicke and GHZ states shows that such entangled states can be efficiently generated with high fidelity, for up to N = 100 in some cases.

Realization of three-qubit quantum error correction with superconducting circuits

- PhysicsNature
- 2012

This work encodes a quantum state, induce errors on the qubits and decode the error syndrome, which is used as the input to a three-qubit gate that corrects the primary qubit if it was flipped, and demonstrates the predicted first-order insensitivity to errors.

Repetition cat-qubits: fault-tolerant quantum computation with highly reduced overhead

- Physics
- 2019

This work builds, at the level of the repetition cat-qubit, a universal set of fully protected logical gates, which includes single qubit preparations and measurements, NOT, controlled-NOT and controlled-controlled-NOT (Toffoli) gates.

Quantum Trajectories and Measurements in Continuous Time: The Diffusive Case

- Physics
- 2009

I General theory.- The Stochastic Schr#x00F6 dinger Equation.- The Stochastic Master Equation: Part I.- Continuous Measurements and Instruments.- The Stochastic Master Equation: Part II.- Mutual…