Optimal control of quantum non-Markovian dissipation: Reduced Liouville-space theory

Xu, Rui-Xue; Yan, YiJing; Ohtsuki, Yukiyoshi; Fujimura, Y.; Rabitz, Herschel

doi:10.1063/1.1665486

Cited by 60 publications

(65 citation statements)

References 85 publications

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“…In order to tackle these challenging quantum engineering tasks, optimal control algorithms are establishing themselves as indispensable tools. They have matured from principles [3] and early implementations [4][5][6] via spectroscopic applications [7][8][9] to advanced numerical algorithms [10,11] for state-to-state transfer and quantumgate synthesis [12] alike.…”

Section: Introductionmentioning

confidence: 99%

Comparing, optimizing, and benchmarking quantum-control algorithms in a unifying programming framework

Machnes¹,

Sander²,

Glaser³

et al. 2011

Phys. Rev. A

236

269

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For paving the way to novel applications in quantum simulation, computation, and technology, increasingly large quantum systems have to be steered with high precision. It is a typical task amenable to numerical optimal control to turn the time course of pulses, i.e. piecewise constant control amplitudes, iteratively into an optimised shape. Here, we present the first comparative study of optimal control algorithms for a wide range of finite-dimensional applications. We focus on the most commonly used algorithms: grape methods which update all controls concurrently, and Krotov-type methods which do so sequentially. Guidelines for their use are given and open research questions are pointed out. -Moreover we introduce a novel unifying algorithmic framework, dynamo (dynamic optimisation platform) designed to provide the quantum-technology community with a convenient matlab-based toolset for optimal control. In addition, it gives researchers in optimal-control techniques a framework for benchmarking and comparing new proposed algorithms to the state-of-the-art. It allows for a mix-and-match approach with various types of gradients, update and step-size methods as well as subspace choices. Open-source code including examples is made available at http://qlib.info.

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Section: Introductionmentioning

confidence: 99%

Comparing, optimizing, and benchmarking quantum-control algorithms in a unifying programming framework

Machnes¹,

Sander²,

Glaser³

et al. 2011

Phys. Rev. A

236

269

View full text Add to dashboard Cite

show abstract

“…To this end, also among the mathematical tools [25,26] optimal control algorithms have been establishing themselves as indispensable [27,28]. They have matured from principles [29] and early implementations [30][31][32] via spectroscopic applications [33][34][35] to advanced numerical algorithms [36,37] for state-to-state transfer and quantumgate synthesis [38][39][40] alike as will be illustrated in more detail.…”

Section: Introductionmentioning

confidence: 99%

Control aspects of quantum computing using pure and mixed states

Schulte‐Herbrüggen

Marx

Fahmy

et al. 2012

Phil. Trans. R. Soc. A.

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Steering quantum dynamics such that the target states solve classically hard problems is paramount to quantum simulation and computation. And beyond, quantum control is also essential to pave the way to quantum technologies. Here, important control techniques are reviewed and presented in a unified frame covering quantum computational gate synthesis and spectroscopic state transfer alike. We emphasize that it does not matter whether the quantum states of interest are pure or not. While pure states underly the design of quantum circuits, ensemble mixtures of quantum states can be exploited in a more recent class of algorithms: it is illustrated by characterizing the Jones polynomial in order to distinguish between different (classes of) knots. Further applications include Josephson elements, cavity grids, ion traps and nitrogen vacancy centres in scenarios of closed as well as open quantum systems.

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“…An alternative approach to realize high-fidelity quantum gate is through the quantum optimal control (QOC) [54][55][56][57][58][59][60][61][62][63][64][65][66][67][68][69][70][71]. A recent study [50] investigated the theoretically achievable fidelities when coherently controlling an effective three-qubit system consisting of a negatively charged ( 15 NV − ) center in diamond with an additional nearby carbon 13 C nuclear spin.…”

Section: Introductionmentioning

confidence: 99%

Optimal control of fast and high-fidelity quantum gates with electron and nuclear spins of a nitrogen-vacancy center in diamond

Chou

Goan

2015

Phys. Rev. A

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A negatively charged nitrogen vacancy (NV) center in diamond has been recognized as a good solid-state qubit. A system consisting of the electronic spin of the NV center and hyperfine-coupled nitrogen and additionally nearby carbon nuclear spins can form a quantum register of several qubits for quantum information processing or as a node in a quantum repeater. Several impressive experiments on the hybrid electron and nuclear spin register have been reported, but fidelities achieved so far are not yet at oor below the thresholds required for fault-tolerant quantum computation (FTQC). Using quantum optimal control theory based on the Krotov method, we show here that fast and high-fidelity single-qubit and two-qubit gates in the universal quantum gate set for FTQC, taking into account the effects of the leakage state, nearby noise qubits and distant bath spins, can be achieved with errors less than those required by the threshold theorem of FTQC.

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Optimal control of quantum non-Markovian dissipation: Reduced Liouville-space theory

Cited by 60 publications

References 85 publications

Comparing, optimizing, and benchmarking quantum-control algorithms in a unifying programming framework

Comparing, optimizing, and benchmarking quantum-control algorithms in a unifying programming framework

Control aspects of quantum computing using pure and mixed states

Optimal control of fast and high-fidelity quantum gates with electron and nuclear spins of a nitrogen-vacancy center in diamond

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