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An Exponential Quantum Projection Filter for Open Quantum Systems [article]

Qing Gao, Guofeng Zhang, Ian R. Petersen
2018 arXiv   pre-print
An approximate exponential quantum projection filtering scheme is developed for a class of open quantum systems described by Hudson- Parthasarathy quantum stochastic differential equations, aiming to reduce  ...  , and an exponential quantum projection filter is then formulated as a number of stochastic differential equations satisfied by the finite-dimensional coordinate system of this manifold.  ...  The convergence capability of the exponential quantum projection filter for a special class of open quantum systems is also discussed.  ... 
arXiv:1705.09114v2 fatcat:wcpl6rdazfbkfiqlwqyldupc3m

Exponential stabilization of quantum systems under continuous non-demolition measurements [article]

Gerardo Cardona, Alain Sarlette, Pierre Rouchon
2019 arXiv   pre-print
Such reduced filters should play an increasing role towards advanced quantum technologies.  ...  We present a novel continuous-time control strategy to exponentially stabilize an eigenstate of a Quantum Non-Demolition (QND) measurement operator.  ...  The open-loop system for a continuous-time quantum measurement with a single measurement channel is governed by the Itō stochastic differential equations [5] : dρ t = D L (ρ t )dt + √ ηM L (ρ t )dW t  ... 
arXiv:1906.07403v1 fatcat:3lac2zaoibgolanamwbuvrwma4

Efficient state initialization by a quantum spectral filtering algorithm

François Fillion-Gourdeau, Steve MacLean, Raymond Laflamme
2017 Physical Review A  
This algorithm would be useful for the initialization phase of the simulation of quantum systems on digital quantum computers.  ...  This is performed by introducing a nondeterministic quantum implementation of a standard spectral filtering procedure combined with an apodization technique, allowing for accurate state initialization.  ...  Dumont for carefully revising earlier versions of the manuscript.  ... 
doi:10.1103/physreva.95.042331 fatcat:uqoarfopqbey7ndymy67b25ppm

An Improved Quantum Projection Filter [article]

Qing Gao and Guofeng Zhang and Ian R. Petersen
2019 arXiv   pre-print
This work extends the previous quantum projection filtering scheme in [Gao Q., Zhang G., Petersen I. R. (2019). An exponential quantum projection filter for open quantum systems.  ...  Simulation results for a qubit example demonstrate better approximation performance for the new quantum projection filter.  ...  In our recent work [Gao et al. (2019) ], we proposed an exponential quantum projection filtering approach that is applicable to general open quantum systems.  ... 
arXiv:1909.13524v1 fatcat:ihfn664jlvco7jnhr7xvh3vpwu

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

Gerardo Cardona, Alain Sarlette, Pierre Rouchon
2018 2018 IEEE Conference on Decision and Control (CDC)  
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.  ...  In open loop, such system converges stochastically to one of the eigenstates of the measurement operator.  ...  We recall the asymptotic behavior for the open loop system and provide an exponential convergence rate for a general QND system, via an original Lyapunov function, under a non-degeneracy condition.  ... 
doi:10.1109/cdc.2018.8618681 dblp:conf/cdc/CardonaSR18 fatcat:fsjlbyu3qzdlvhbc5thkht76qi

Quantum Stochastic Stability [article]

Javad Sharifi, Hamidreza Momeni
2009 arXiv   pre-print
the stability criterion is constructed for open quantum systems which govern by quantum stochastic differential equations (QSDE) both for quantum observable flow and the stochastic density operator.  ...  We derive stability criteria (local, asymptotic and exponential stability) for those QSDE.  ...  Acknowledgement We appreciate Ramon Van Handel for some helpful discussion on stochastic process and to introducing some helpful references.  ... 
arXiv:0907.3452v1 fatcat:faztfmbwazdrfgrvfuiruqwrx4

Contraction and observer design on cones

Silvere Bonnabel, Alessandro Astolfi, Rodolphe Sepulchre
2011 IEEE Conference on Decision and Control and European Control Conference  
Two main applications are discussed : positive observers for systems defined in the positive orthant, and positive observers on the cone of positive semi-definite matrices with a view on quantum systems  ...  We consider the problem of positive observer design for positive systems defined on solid cones in Banach spaces.  ...  Quantum filtering as a positive observer problem An interesting linear system on K is the evolution of the density matrix characterizing a state in a quantum channel.  ... 
doi:10.1109/cdc.2011.6161268 dblp:conf/cdc/BonnabelAS11 fatcat:vjnqzwc23bcspgai7twlv4ldie

qopt: An experiment-oriented Qubit Simulation and Quantum Optimal Control Package [article]

Julian D. Teske, Pascal Cerfontaine, Hendrik Bluhm
2021 arXiv   pre-print
Realistic modeling of qubit systems including noise and constraints imposed by control hardware is required for performance prediction and control optimization of quantum processors.  ...  The software easily interfaces with QuTip, is published under an open source license, well-tested and features a detailed documentation.  ...  We also thank Alexander Willmes, Christian Gorjaew, Paul Surrey, Frederike Butt and Jiaqi Ai for testing qopt and providing feedback.  ... 
arXiv:2110.05873v1 fatcat:7thz7x6ww5eedkikqkomlajvza

Employing Trapped Cold Ions to Verify the Quantum Jarzynski Equality

Gerhard Huber, Ferdinand Schmidt-Kaler, Sebastian Deffner, Eric Lutz
2008 Physical Review Letters  
Trapped ions therefore represent an ideal tool for investigating the Jarzynski equality in open and closed quantum systems.  ...  Uniquely to our system, we show how an ion may be immersed in an engineered laser--field reservoir.  ...  So far only studied theoretically, the Jarzynski equation holds in its classical form for closed quantum systems [7] , while quantum corrections appear in the case of open systems due to the coupling  ... 
doi:10.1103/physrevlett.101.070403 pmid:18764513 fatcat:d2qfmgzmxfeqjavwxb7eayhhsa

Model robustness for feedback stabilization of open quantum systems [article]

Weichao Liang, Nina H. Amini
2022 arXiv   pre-print
In addition, we show that with an approximate diagonal filter whose state is a N-dimensional vector, the exponential stabilization toward target subspaces is still ensured.  ...  This paper generalizes the results in [32] concerning feedback stabilization of target states for N-level quantum angular momentum systems undergoing quantum non-demolition measurements (QND) in absence  ...  Here we show an exponential quantum state reduction for the actual system with providing explicit convergence rate.  ... 
arXiv:2205.01961v1 fatcat:hdus4smysjfbpe2qyrhsfr5dqe

Continuous-time Quantum Error Correction with Noise-assisted Quantum Feedback [article]

Gerardo Cardona, Alain Sarlette, Pierre Rouchon
2019 arXiv   pre-print
We address the standard quantum error correction using the three-qubit bit-flip code, yet in continuous-time. This entails rendering a target manifold of quantum states globally attractive.  ...  We further present a reduced-order filter formulation with classical probabilities.  ...  Martin for early discussions on continuous-time QEC.  ... 
arXiv:1902.00115v4 fatcat:d6t47z2j3vhxdj63pen2eefjhy

Page 1089 of Mathematical Reviews Vol. , Issue 93b [page]

1993 Mathematical Reviews  
Summary: “We prove that a regularized projection operator on the physical subspace %nys C 4(Q) can be defined for a symplectic manifold Q = T*M equipped with an ‘almost-K4hler’ structure, provided that  ...  It was developed originally as a mathematical theory of quantum noise in open systems and its first applications in mathematical physics were the construction of unitary dilations of quantum dynamical  ... 

Hybrid Filtering for a Class of Quantum Systems with Classical Disturbances [article]

Qi Yu, Daoyi Dong, Ian R. Petersen, Qing Gao
2017 arXiv   pre-print
A filtering problem for a class of quantum systems disturbed by a classical stochastic process is investigated in this paper.  ...  Quantum filtering theory and a quantum extended Kalman filter method are employed to estimate the states of the combined quantum system.  ...  Quantum filtering theory We use quantum stochastic differential equations (QSDEs) to describe the dynamics of an open quantum system with driving noises.  ... 
arXiv:1703.08976v1 fatcat:n5652ynnv5egxoaedfyjrzmvzu

Resonator reset in circuit QED by optimal control for large open quantum systems

Samuel Boutin, Christian Kraglund Andersen, Jayameenakshi Venkatraman, Andrew J. Ferris, Alexandre Blais
2017 Physical Review A  
We study an implementation of the open GRAPE (Gradient Ascent Pulse Engineering) algorithm well suited for large open quantum systems.  ...  While typical implementations of optimal control algorithms for open quantum systems rely on explicit matrix exponential calculations, our implementation avoids these operations leading to a polynomial  ...  JV would like to thank MITACS Globalink Program for financial assistance.  ... 
doi:10.1103/physreva.96.042315 fatcat:y54emgs2wbhwpp3bziejse2iga

On the robustness of stabilizing feedbacks for quantum spin-1/2 systems [article]

Weichao Liang, Nina H. Amini, Paolo Mason
2020 arXiv   pre-print
We provide sufficient conditions on the feedback controller and a valid domain of estimated parameters which ensure exponential stabilization of the coupled system.  ...  In this paper, we consider stochastic master equations describing the evolution of quantum spin-1/2 systems interacting with electromagnetic fields undergoing continuous-time measurements.  ...  ACKNOWLEDGEMENTS This work is supported by the Agence Nationale de la Recherche projects Q-COAST ANR-19-CE48-0003 and QUACO ANR-17-CE40-0007. The authors thank Pierre Rouchon for helpful discussions.  ... 
arXiv:2004.05638v1 fatcat:6w7kl6aauvdixe4ic6mzlixm4u
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