Adiabatic theorem in the presence of noise

O'Hara, Michael J.; O’Leary, Dianne P.

doi:10.1103/physreva.77.042319

Cited by 17 publications

(19 citation statements)

References 33 publications

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“…In order to derive equation (25), the three superoperators are ordered in perturbation theory, in the sense that…”

Section: Timescalesmentioning

confidence: 99%

“…Such derivations are valuable and can be made rigorous, but the assumption of periodicity can be excessive, especially in the context of adiabatic quantum computation. Bounds on the validity of the adiabatic approximation for open systems, but without master equations, were presented in [25] (see also [10]). Various authors derived or studied adiabatic master equations limited to the case of a single qubit, where detailed physical considerations are possible [26][27][28].…”

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confidence: 99%

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Quantum adiabatic Markovian master equations

et al. 2012

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Abstract. We develop from first principles Markovian master equations suited for studying the time evolution of a system evolving adiabatically while coupled weakly to a thermal bath. We derive two sets of equations in the adiabatic limit, one using the rotating wave (secular) approximation that results in a master equation in Lindblad form, the other without the rotating wave approximation but not in Lindblad form. The two equations make markedly different predictions depending on whether or not the Lamb shift is included. Our analysis keeps track of the various time and energy scales associated with the various approximations we make, and thus allows for a systematic inclusion of higher order corrections, in particular beyond the adiabatic limit. We use our formalism to study the evolution of an Ising spin chain in a transverse field and coupled to a thermal bosonic bath, for which we identify four distinct evolution phases. While we do not expect this to be a generic feature, in one of these phases dissipation acts to increase the fidelity of the system state relative to the adiabatic ground state.

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“…In order to derive equation (25), the three superoperators are ordered in perturbation theory, in the sense that…”

Section: Timescalesmentioning

confidence: 99%

mentioning

confidence: 99%

Quantum adiabatic Markovian master equations

et al. 2012

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“…As remarked in the introduction, this condition is hardly quantitative due to the intrinsic vagueness of " ," and has been the subject of critique (consistent with its lack of rigor) [19][20][21], justifications [22,23], and rigorous improvements [24][25][26][27][28][29][30][31][32]. Nevertheless, it remains a useful rule of thumb, as long as it is applied with appropriate care.…”

Section: B the Adiabatic Theoremmentioning

confidence: 99%

Accuracy versus run time in an adiabatic quantum search

2010

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Adiabatic quantum algorithms are characterized by their run time and accuracy. The relation between the two is essential for quantifying adiabatic algorithmic performance yet is often poorly understood. We study the dynamics of a continuous time, adiabatic quantum search algorithm and find rigorous results relating the accuracy and the run time. Proceeding with estimates, we show that under fairly general circumstances the adiabatic algorithmic error exhibits a behavior with two discernible regimes: The error decreases exponentially for short times and then decreases polynomially for longer times. We show that the well-known quadratic speedup over classical search is associated only with the exponential error regime. We illustrate the results through examples of evolution paths derived by minimization of the adiabatic error. We also discuss specific strategies for controlling the adiabatic error and run time.

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“…In contrast, they have received relatively little experimental attention. This is a significant concern as data are needed to help clarify the impact of environmental noise upon such approaches to quantum computing [11][12][13][14][15][16][17][18][19] . Experiments have been performed using nuclear magnetic resonance in molecules 20 , but the prospects for scaling this approach to larger systems are limited.…”

Section: Introductionmentioning

confidence: 99%

Experimental investigation of an eight-qubit unit cell in a superconducting optimization processor

Harris¹,

Johnson²,

Lanting³

et al. 2010

Phys. Rev. B

276

287

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A superconducting chip containing a regular array of flux qubits, tunable interqubit inductive couplers, an XY-addressable readout system, on-chip programmable magnetic memory, and a sparse network of analog control lines has been studied. The architecture of the chip and the infrastructure used to control it were designed to facilitate the implementation of an adiabatic quantum optimization algorithm. The performance of an eight-qubit unit cell on this chip has been characterized by measuring its success in solving a large set of random Ising spin glass problem instances as a function of temperature. The experimental data are consistent with the predictions of a quantum mechanical model of an eight-qubit system coupled to a thermal environment. These results highlight many of the key practical challenges that we have overcome and those that lie ahead in the quest to realize a functional large scale adiabatic quantum information processor.

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Adiabatic theorem in the presence of noise

Cited by 17 publications

References 33 publications

Quantum adiabatic Markovian master equations

Quantum adiabatic Markovian master equations

Accuracy versus run time in an adiabatic quantum search

Experimental investigation of an eight-qubit unit cell in a superconducting optimization processor

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