Controllability of open quantum systems with Kraus-map dynamics

Wu, Rong; Pechen, Alexander; Brif, Constantin; Rabitz, Herschel

doi:10.1088/1751-8113/40/21/015

Cited by 107 publications

(124 citation statements)

References 99 publications

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“…The first implication has also been highlighted in [29]. It can be easily derived considering a constant mapping from D(H) to ρ f ∈ D(H), ρ f being the target state.…”

Section: Notions Of Controllabilitymentioning

confidence: 95%

Discrete-time controllability for feedback quantum dynamics

Albertini¹,

Ticozzi²

2011

Automatica

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Controllability properties for discrete-time, Markovian quantum dynamics are investigated. We find that, while in general the controlled system is not finite-time controllable, feedback control allows for arbitrary asymptotic state-to-state transitions. Under further assumption on the form of the measurement, we show that finite-time controllability can be achieved in a time that scales linearly with the dimension of the system, and we provide an iterative procedure to design the unitary control actions.

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“…The first implication has also been highlighted in [29]. It can be easily derived considering a constant mapping from D(H) to ρ f ∈ D(H), ρ f being the target state.…”

Section: Notions Of Controllabilitymentioning

confidence: 95%

Discrete-time controllability for feedback quantum dynamics

Albertini¹,

Ticozzi²

2011

Automatica

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“…There is a large literature studying the control of quantum systems, starting with establishing the connection with geometric control theory [8,16,18,21] until more recent studies for closed (see, e.g., [3,4,9,[23][24][25]) and open (see e.g., [5,13,26]) quantum systems. Nevertheless, an algebraic characterization of indirect controllability is still lacking.…”

Section: Introductionmentioning

confidence: 99%

Indirect Controllability of Quantum Systems; A Study of Two Interacting Quantum Bits

D’Alessandro

Romano

2012

IEEE Trans. Automat. Contr.

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A quantum mechanical system S is indirectly controlled when the control affects an ancillary system A and the evolution of S is modified through the interaction with A only. A study of indirect controllability gives a description of the set of states that can be obtained for S with this scheme. In this paper, we study the indirect controllability of quantum systems in the finite dimensional case. After discussing the relevant definitions, we give a general necessary condition for controllability in Lie algebraic terms. We present a detailed treatment of the case where both systems, S and A, are two-dimensional (qubits). In particular, we characterize the dynamical Lie algebra associated with S+A, extending previous results, and prove that complete controllability of S+A and an appropriate notion of indirect controllability are equivalent properties for this system. We also prove several further indirect controllability properties for the system of two qubits, and illustrate the role of the Lie algebraic analysis in the study of reachable states.

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“…Can inhomogeneous control [31] be extended to qudits, perhaps allowing addressable unitary maps on large arrays [32]? And finally, is it possible to optimize control in the presence of decoherence [33], and perhaps extend it to (non-unitary) completely positive maps [34]? Some of these questions can be explored in our current system, while others await the application of optimal control to scalable architectures of interacting qubits and qudits.…”

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confidence: 99%

Accurate and Robust Unitary Transformations of a High-Dimensional Quantum System

et al. 2015

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Quantum control in large dimensional Hilbert spaces is essential for realizing the power of quantum information processing. For closed quantum systems the relevant inputoutput maps are unitary transformations, and the fundamental challenge becomes how to implement these with high fidelity in the presence of experimental imperfections and decoherence. For two-level systems (qubits) most aspects of unitary control are well understood, but for systems with Hilbert space dimension d>2 (qudits), many questions remain regarding the optimal design of control Hamiltonians 1 and the feasibility of robust implementation 2,3 . Here we show that arbitrary, randomly chosen unitary transformations can be efficiently designed and implemented in a large dimensional Hilbert space (d=16) associated with the electronic ground state of atomic 133 Cs, 4 achieving fidelities above 0.98 as measured by randomized benchmarking 5 . Generalizing the concepts of inhomogeneous control 6 and dynamical decoupling 7 to d>2 systems, we further demonstrate that these qudit unitary maps can be made robust to both static and dynamic perturbations. Potential applications include improved fault-tolerance in universal quantum computation 8 , nonclassical state preparation for high-precision metrology 9 , implementation of quantum simulations 10 , and the study of fundamental physics related to open quantum systems and quantum chaos 11 .The goal of quantum control is to perform a desired transformation through dynamical evolution driven by a control Hamiltonian H C (t) . For example, one common objective is to evolve the system from a known initial state to a desired final state. If the control task is simple or special symmetries are present, it is sometimes possible to find a high-performing control Hamiltonian through intuition, or to construct one using group theoretic methods 12 . In this letter we explore the use of "optimal control" 1 to design control Hamiltonians for tasks of varying complexity, from state-to-state maps to unitary maps on the entire accessible Hilbert space. The basic procedure is well established: the Hamiltonian H C (t) is parameterized by a set of control variables, and a numerical search is performed to find values that optimize the fidelity with which the control objective is achieved. The application of optimal control to quantum systems originated in NMR 13 and physical chemistry 1 , and has since expanded to include, e. g., ultrafast physics 14 , cold atoms 15,16 , biological molecules 17 , spins in condensed matter 18 , and superconducting circuits 19 .We study the efficacy of numerical design and the performance of the resulting control Hamiltonians using a well developed testbed consisting of the electron and nuclear spins of individual 133 Cs atoms driven by radiofrequency (rf) and microwave (µw) magnetic fields (Fig. 1) 16 . Our experiments show that the optimal control strategy is adaptable to a wide range of control tasks, and that it can generate control Hamiltonians with excellent performance even in the prese...

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Controllability of open quantum systems with Kraus-map dynamics

Cited by 107 publications

References 99 publications

Discrete-time controllability for feedback quantum dynamics

Discrete-time controllability for feedback quantum dynamics

Indirect Controllability of Quantum Systems; A Study of Two Interacting Quantum Bits

Accurate and Robust Unitary Transformations of a High-Dimensional Quantum System

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