Optimal control for non-Markovian open quantum systems

Hwang, Bin; Goan, Hsi‐Sheng

doi:10.1103/physreva.85.032321

Cited by 62 publications

(61 citation statements)

References 54 publications

(105 reference statements)

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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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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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“…For quantum systems this process can be implemented by making explicit measurements, and processing the resulting classical information using a classical system [54][55][56][57][58]. Alternatively a fully quantum version of this process can be realized by coupling the system to a second quantum system without making explicit measurements [9][10][11][12][13][14]35,62].…”

Section: Example: Non-markovian Coherent Feedback Networkmentioning

confidence: 99%

Non-Markovian quantum input-output networks

Zhang

Liu

et al. 2013

Phys. Rev. A

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Quantum input-output response analysis is a useful method for modeling the dynamics of complex quantum networks, such as those for communication or quantum control via cascade connections. Non-Markovian effects are expected to be important in networks realized using mesoscopic circuits, but such effects have not yet been studied. Here we extend the Markovian input-output network formalism to non-Markovian networks. The general formalism can be applied to various examples: (i) we show how non-Markovian coherent feedback can reduce the speed of decoherence for an atom in an optical cavity; (ii) we examine the effect of finite-cavity bandwidths in a superconducting circuit.

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“…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.…”

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confidence: 99%

“…Efficient schemes for compensating harmful noise in quantum systems have been developed utilizing the quantum Zeno effect [1,2], dynamical decoupling strategies [3]- [5] and optimal control [6], [7]- [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.…”

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confidence: 99%

“…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], [7]- [17].…”

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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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Optimal control for non-Markovian open quantum systems

Cited by 62 publications

References 54 publications

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

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

Non-Markovian quantum input-output networks

Problem of coherent control in non-Markovian open quantum systems

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