Universal Dynamical Control of Open Quantum Systems (original) (raw)

Quantum control via encoded dynamical decoupling

Physical Review A, 2002

I revisit the ideas underlying dynamical decoupling methods within the framework of quantum information processing, and examine their potential for direct implementations in terms of encoded rather than physical degrees of freedom. The usefulness of encoded decoupling schemes as a tool for engineering both closed-and open-system encoded evolutions is investigated based on simple examples.

Universal Control of Decoupled Quantum Systems

Physical Review Letters, 1999

It is shown that if one can perform a restricted set of fast manipulations on a quantum system, one can implement a large class of dynamical evolutions by effectively removing or introducing selected Hamiltonians. The procedure can be used to achieve universal noise-tolerant control based on purely unitary open-loop transformations of the dynamics. As a result, it is in principle possible to perform noise-protected universal quantum computation using no extra space resources. 03.67.Lx, 89.70.+c The desire to shape quantum evolution according to precisely controlled dynamics is shared by various areas of contemporary physics and engineering . A problem commonly encountered in the task of controlling the dynamical behavior of a quantum system is the need for removing unwanted interactions present in the full Hamiltonian: historically, one of the first solutions was provided by Nuclear Magnetic Resonance spectroscopy, where a variety of decoupling techniques have been developed to simplify spectra by effectively eliminating selected contributions to the nuclear Hamiltonian . Once suppression of a given term is obtained, the corresponding Hamiltonian may no longer be directly available for control. From the perspective of attaining universal dynamical control, this raises the question of devising ways for introducing or re-introducing Hamiltonian control compatible with the prescribed decoupling action.

Dynamical Decoupling of Open Quantum Systems

Physical Review Letters, 1999

We propose a novel dynamical method for beating decoherence and dissipation in open quantum systems. We demonstrate the possibility of filtering out the effects of unwanted (not necessarily known) system-environment interactions and show that the noise-suppression procedure can be combined with the capability of retaining control over the effective dynamical evolution of the open quantum system. Implications for quantum information processing are discussed. 03.65.-w, 03.67.-a, 05.30.-d

Uniaxial Dynamical Decoupling for an Open Quantum System

Physical Review Letters, 2019

Dynamical decoupling (DD) is an active and effective method for suppressing decoherence of a quantum system from its environment. In contrast to the nominal biaxial DD, this work presents a uniaxial decoupling protocol that requires a significantly reduced number of pulses and a much lower bias field satisfying the "magic" condition. We show this uniaxial DD protocol works effectively in a number of model systems of practical interests, e.g., a spinor atomic Bose-Einstein condensate in stray magnetic fields (classical noise), or an electron spin coupled to nuclear spins (quantum noise) in a semiconductor quantum dot. It requires only half the number of control pulses and a 10-100 times lower bias field for decoupling as normally employed in the above mentioned illustrative examples, and the overall efficacy is robust against rotation errors of the control pulses. The uniaxial DD protocol we propose shines new light on coherent controls in quantum computing and quantum information processing, quantum metrology, and low field nuclear magnetic resonance.

Dynamical suppression of decoherence in two-state quantum systems

Physical Review A, 1998

The dynamics of a decohering two-level system driven by a suitable control Hamiltonian is studied. The control procedure is implemented as a sequence of radiofrequency pulses that repetitively flip the state of the system, a technique that can be termed quantum "bang-bang" control after its classical analog. Decoherence introduced by the system's interaction with a quantum environment is shown to be washed out completely in the limit of continuous flipping and greatly suppressed provided the interval between the pulses is made comparable to the correlation time of the environment. The model suggests a strategy to fight against decoherence that complements existing quantum error-correction techniques. 03.65.-w, 03.67.-a, 05.30.-d I. INTRODUCTION

Random Decoupling Schemes for Quantum Dynamical Control and Error Suppression

Physical Review Letters, 2005

We present a general control-theoretic framework for constructing and analyzing random decoupling schemes, applicable to quantum dynamical control of arbitrary finitedimensional composite systems. The basic idea is to design the control propagator according to a random rather than deterministic path on a group. We characterize the performance of random decoupling protocols, and identify control scenarios where they can significantly weaken time scale requirements as compared to cyclic counterparts. Implications for reliable quantum computation are discussed. PACS numbers: 03.67.-a, 03.67.Pp, 03.65.Yz, 89.70.+c

Randomized dynamical decoupling techniques for coherent quantum control

Journal of Modern Optics, 2006

The need for strategies able to accurately manipulate quantum dynamics is ubiquitous in quantum control and quantum information processing. We investigate two scenarios where randomized dynamical decoupling techniques become more advantageous with respect to standard deterministic methods in switching off unwanted dynamical evolution in a closed quantum system: when dealing with decoupling cycles which involve a large number of control actions and/or when seeking long-time quantum information storage. Highly effective hybrid decoupling schemes, which combine deterministic and stochastic features are discussed, as well as the benefits of sequentially implementing a concatenated method, applied at short times, followed by a hybrid protocol, employed at longer times. A quantum register consisting of a chain of spin-1/2 particles interacting via the Heisenberg interaction is used as a model for the analysis throughout.

Evaluation of Decoherence for Quantum Control and Computing

Journal of Computational and Theoretical Nanoscience, 2004

Different approaches in quantifying environmentally-induced decoherence are considered. We identify a measure of decoherence, derived from the density matrix of the system of interest, that quantifies the environmentally induced error, i.e., deviation from the ideal isolated-system dynamics. This measure can be shown to have several useful features. Its behavior as a function of time has no dependence on the initial conditions, and is expected to be insensitive to the internal dynamical time scales of the system, thus only probing the decoherence-related time dependence.

Single-bit feedback and quantum-dynamical decoupling

Physical Review A, 2006

Synthesizing an effective identity evolution in a target system subjected to unwanted unitary or non-unitary dynamics is a fundamental task for both quantum control and quantum information processing applications. Here, we investigate how single-bit, discrete-time feedback capabilities may be exploited to enact or to enhance quantum procedures for effectively suppressing unwanted dynamics in a finite-dimensional open quantum system. An explicit characterization of the joint unitary propagators correctable by a single-bit feedback strategy for arbitrary evolution time is obtained. For a two-dimensional target system, we show how by appropriately combining quantum feedback with dynamical decoupling methods, concatenated feedback-decoupling schemes may be built, which can operate under relaxed control assumptions and can outperform purely closed-loop and open-loop protocols.

Controlling quantum systems in the presence of an environment

The ability to optimally control quantum systems in the presence of environmentally-induced decoherence is important for many physical and chemical problems. We discuss both theoretical and experimental aspects of optimal control of open quantum systems. The theoretical analysis is based on fundamental concepts of open-system controllability and control landscapes. These theoretical advances lay the groundwork for practical applications, including numerical simulations and experimental implementations of adaptive feedback control. In particular, the adaptive approach was utilized to implement coherent control of decoherence, which uses coherent (unitary) preparation and manipulation of an open quantum system to significantly alter its incoherent (non-unitary) dynamics caused by coupling to an environment. We also discuss other applications, including optimal dynamic discrimination of similar quantum systems and optimal control of high-fidelity quantum gates in the presence of decoherence.