Efficiency of quantum controlled non-Markovian thermalization

Mukherjee, Victor; Giovannetti, Vittorio; Fazio, Rosario; Huelga, Susana F.; Calarco, Tommaso; Montangero, Simone

doi:10.1088/1367-2630/17/6/063031

Cited by 44 publications

(56 citation statements)

References 64 publications

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“…Optimization algorithms had to be derived for specific quantum gates [470][471][472], dissipative evolution as seen in the reduced system dynamics [56,113,114,461,473], or exploiting invariants in system-bath models [474], optimization up to local equivalence classes [475], which can also be used for arbitrary perfect entanglers [476,477] or optimizing for many-body entanglement [478]. Moreover, control techniques were adapted to non-linear dynamics as found in a BEC [479][480][481] and to general dynamics, functionals and couplings to be controlled [98].…”

Section: State Of the Artmentioning

confidence: 99%

Training Schrödinger’s cat: quantum optimal control

et al. 2015

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Abstract. It is control that turns scientific knowledge into useful technology: in physics and engineering it provides a systematic way for driving a dynamical system from a given initial state into a desired target state with minimized expenditure of energy and resources. As one of the cornerstones for enabling quantum technologies, optimal quantum control keeps evolving and expanding into areas as diverse as quantumenhanced sensing, manipulation of single spins, photons, or atoms, optical spectroscopy, photochemistry, magnetic resonance (spectroscopy as well as medical imaging), quantum information processing and quantum simulation. In this communication, state-of-the-art quantum control techniques are reviewed and put into perspective by a consortium of experts in optimal control theory and applications to spectroscopy, imaging, as well as quantum dynamics of closed and open systems. We address key challenges and sketch a roadmap for future developments. ForewordThe authors of this paper represent the QUAINT consortium, a European Coordination Action on Optimal Control of Quantum Systems, funded by the European Commission Framework Programme 7, Future Emerging Technologies FET-OPEN programme and the Virtual Facility for Quantum Control (VF-QC). This consortium has considerable expertise in optimal control theory and its applications to quantum systems, both in existing areas, such as spectroscopy and imaging, and in emerging quantum technologies, such as quantum information processing, quantum communication, quantum simulation a e-mail: fwm@lusi.uni-sb.de and quantum sensing. The list of challenges for quantum control has been gathered by a broad poll of leading researchers across the communities of general and mathematical control theory, atomic, molecular-, and chemical physics, electron and nuclear magnetic resonance spectroscopy, as well as medical imaging, quantum information, communication and simulation. 144 experts in these fields have provided feedback and specific input on the state of the art, mid-term and long-term goals. Those have been summarized in this document, which can be viewed as a perspectives paper, providing a roadmap for the future development of quantum control. Because such an endeavour can hardly ever be complete (there are many additional areas of quantum control applications, such as spintronics, nano-optomechanical technologies etc.), this roadmap

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Section: State Of the Artmentioning

confidence: 99%

Training Schrödinger’s cat: quantum optimal control

et al. 2015

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“…A number of results, indeed, support the idea that non-Markovian dynamics is most suitable for quantum communication and information processing purposes [15][16][17][18][19][20][21][22]. Moreover, very recently it has been investigated in [23] how non-Markovianity affects the effectiveness of optimal-control strategies in the case of…”

Section: Introductionmentioning

confidence: 92%

Dynamical decoupling efficiency versus quantum non-Markovianity

et al. 2015

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We investigate the relationship between non-Markovianity and the effectiveness of a dynamical decoupling (DD) protocol for qubits undergoing pure dephasing. We consider an exact model in which dephasing arises due to a bosonic environment with a spectral density of the Ohmic class. This is parametrized by an Ohmicity parameter by changing which we can model both Markovian and non-Markovian environments. Interestingly, we find that engineering a non-Markovian environment is detrimental to the efficiency of the DD scheme, leading to a worse coherence preservation. We show that each DD pulse reverses the flow of quantum information and, on this basis, we investigate the connection between DD efficiency and the reservoir spectral density. Finally, in the spirit of reservoir engineering, we investigate the optimum system-reservoir parameters for achieving maximum stationary coherences.amplitude-damping-type channels, finding the existence of regimes where non-Markovianity can be either beneficial or detrimental.In the present paper we re-examine a simple example of a DD scheme for a decohering channel in the light of the above mentioned new approach to non-Markovianity. In particular we will assess the performance of DD in the presence of information back-flow, a common quantifier of non-Markovianity. Futhermore, in analogy with the perspective which views DD as a way to engineer environment spectra, here we also study if and how the DD pulses change the non-Markovian character of the dynamics, e.g. whether they induce information back-flow, as defined in [24].The structure of the paper is the following. In section 2 we review the basic definitions of non-Markovianity recently adopted by the open quantum systems community, and we motivate this approach. In section 3 we introduce the system of interest, namely the pure dephasing model including its exact solution in presence of PDD. In section 4, we discuss how the DD pulses affect information flow and hence modify the Markovian/non-Markovian character of the dynamics. In section 5, we investigate whether non-Markovian or Markovian dynamics are best suited to DD, i.e., lead to optimal performance. In section 6, we discuss in the spirit of reservoir engineering, the optimum system parameters for achieving maximum stationary coherences. Finally in section 7 we summarize our findings and draw the conclusions.

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“…Specifically, optimal control techniques have been so far studied, almost exclusively, in the so-called Markovian limit, that is whenever the system-environment interaction is weak and the correlations short living. In this case the master equations describing the open system dynamics are found phenomenologically or derived with microscopic approaches using numerous approximations [6] [30].In this article, we expose the difficulties in employing coherent control to compensate for environment-induced decoherence effects in non-Markovian systems. We consider the widespread assumption (fixed dissipator assumption) that the part of the master equation describing dissipation and dephasing does not change when we add a Hamiltonian control term in the unitary dynamics part.…”

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confidence: 99%

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confidence: 99%

“…Since access and control of the environment is often limited, it is still unclear to what extent such an approach can be carried forward. In this context, recently many have wondered whether memory effects combined with external control techniques offer a possibility to design an overall superior technique to combat decoherence [4], [28]- [30]. Unfortunately, contrary to intuitive reasoning, non-Markovianity is not trivially a resource for optimal control and indeed specific cases have been found where memory effects are instead detrimental in the presence of control [4], [30].…”

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confidence: 99%

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Problem of coherent control in non-Markovian open quantum systems

et al. 2016

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We critically evaluate the most widespread assumption in the theoretical description of coherent control strategies for open quantum systems. We show that, for non-Markovian open systems dynamics, this fixed-dissipator assumption leads to a serious pitfall generally causing difficulties in the effective modeling of the controlled system. We show that at present, to avoid these problems, a full microscopic description of the controlled system in the presence of noise may often be necessary. We illustrate our findings with a paradigmatic example. [17]. Generally, the theoretical description of these techniques in the presence of noise is a daunting task, therefore they are typically studied under a number of assumptions concerning the type of environments the system is interacting with as well as the typical time-scales. Specifically, optimal control techniques have been so far studied, almost exclusively, in the so-called Markovian limit, that is whenever the system-environment interaction is weak and the correlations short living. In this case the master equations describing the open system dynamics are found phenomenologically or derived with microscopic approaches using numerous approximations [6] [30].In this article, we expose the difficulties in employing coherent control to compensate for environment-induced decoherence effects in non-Markovian systems. We consider the widespread assumption (fixed dissipator assumption) that the part of the master equation describing dissipation and dephasing does not change when we add a Hamiltonian control term in the unitary dynamics part. This assumption does not change the physicality of the solutions of the master equation in the Markovian case. We show, however, that this is generally not the case for non-Markovian dynamics. Hence the typical theoretical approaches to quantum control theory cannot be used in the framework of non-Markovian open quantum systems, and only a full microscopic derivation leads to physically meaningful results.For the sake of concreteness we focus on a novel concept utilizing Hamiltonian control recently introduced to counteract the detrimental effect of decoherence. In Ref.[6], the goal is to seek the control Hamiltonian that, on asymptotic time scales, optimally upholds a given target property (e.g. coherence, entanglement or fidelity with respect to a target state). The space of Hamiltonians cannot be efficiently parametrized, hence the problem is approached from a different perspective. The key idea is to optimize some target property in the set of stabilizable cycles, comprising all closed periodic trajectories ρ(t) = ρ(t + T ) for which a periodic control Hamiltonian exists such that ρ(t) solves the master equation ( = 1)with a fixed dissipator

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Efficiency of quantum controlled non-Markovian thermalization

Cited by 44 publications

References 64 publications

Training Schrödinger’s cat: quantum optimal control

Training Schrödinger’s cat: quantum optimal control

Dynamical decoupling efficiency versus quantum non-Markovianity

Problem of coherent control in non-Markovian open quantum systems

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