Feedback-controlled adiabatic quantum computation

Wilson, Richard D.; Zagoskin, A. M.; Savel’ev, Sergey; Everitt, Mark J.; Nori, Franco

doi:10.1103/physreva.86.052306

Cited by 14 publications

(8 citation statements)

References 27 publications

(34 reference statements)

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“…In particular, the validity of the adiabatic theorem has been under intensive studies both theoretically and experimentally since it was proposed, and much of these efforts were devoted to the rigorous description of the sufficient quantitative conditions of adiabatic theorem, and the estimation of the error accumulated over a long time [10,14,15,16]. Once the exact knowledge on the adiabatic process is available, it is straightforward to apply the results to the optimal design of adiabatic control on specific systems [17,18]. The most interesting progress is that the validity of the adiabatic theorem itself has been challenged in the recent decade [19,20,21,22,23,24,25,26,27], both by strict analysis and counterexamples.…”

Section: Introductionmentioning

confidence: 99%

Interpolation approach to Hamiltonian-varying quantum systems and the adiabatic theorem

Pan¹,

Zhang²,

Amini³

et al. 2015

EPJ Quantum Technol.

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Quantum control could be implemented by varying the system Hamiltonian. According to adiabatic theorem, a slowly changing Hamiltonian can approximately keep the system at the ground state during the evolution if the initial state is a ground state. In this paper we consider this process as an interpolation between the initial and final Hamiltonians. We use the mean value of a single operator to measure the distance between the final state and the ideal ground state. This measure resembles the excitation energy or excess work performed in thermodynamics, which can be taken as the error of adiabatic approximation. We prove that under certain conditions, this error can be estimated for an arbitrarily given interpolating function. This error estimation could be used as guideline to induce adiabatic evolution. According to our calculation, the adiabatic approximation error is not linearly proportional to the average speed of the variation of the system Hamiltonian and the inverse of the energy gaps in many cases. In particular, we apply this analysis to an example in which the applicability of the adiabatic theorem is questionable.

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Section: Introductionmentioning

confidence: 99%

Interpolation approach to Hamiltonian-varying quantum systems and the adiabatic theorem

Pan¹,

Zhang²,

Amini³

et al. 2015

EPJ Quantum Technol.

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“…The stochastic Pechukas equations, Eq. ( 6) is independent of any assumptions on the nature of the noise, therefore applicable to a wide range of stochastic systems 16,23 . Using this formalism, we investigate the conditions for the applicability of the Landau-Zener model We further extend this description to explore the impacts of external noise on these conditions.…”

Section: The Pechukas Model and The Evolution Of Eigenstate Coefficientsmentioning

confidence: 99%

Pechukas-Yukawa formalism for Landau-Zener transitions in the presence of external noise

et al. 2018

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Quantum systems are prone to decoherence due to both intrinsic interactions as well as random fluctuations from the environment. Using the Pechukas-Yukawa formalism, we investigate the influence of noise on the dynamics of an adiabatically evolving Hamiltonian which can describe a quantum computer. Under this description, the level dynamics of a parametrically perturbed quantum Hamiltonian are mapped to the dynamics of 1D classical gas. We show that our framework coincides with the results of the classical Landau-Zener transitions upon linearisation. Furthermore, we determine the effects of external noise on the level dynamics and its impact on Landau-Zener transitions.arXiv:1803.05034v2 [cond-mat.stat-mech]

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“…The contribution from the parametrically evolved term λ (t) ZH b , is determined through the Pechukas equations [8][9][10][11][12][13][14][20][21][22] . Taking the Hamiltonian that describes the Pechukas gas as H(λ(t)) = (xm−xn) 2 , with unit mass, one can derive a closed set of first order ordinary differential equations that describe the "position" (x m ), "velocity" (v m ) and "relative angular momentum" (l mn ), as expressed in Eq.…”

Section: Pechukas Equationsmentioning

confidence: 99%

Section: Pechukas Equationsmentioning

confidence: 99%

Bogoliubov-Born-Green-Kirkwood-Yvon chain and kinetic equations for the level dynamics in an externally perturbed quantum system

et al. 2017

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Theoretical description and simulation of large quantum coherent systems out of equilibrium remains a daunting task. Here we are developing a new approach to it based on the Pechukas-Yukawa formalism, which is especially convenient in the case of an adiabatically slow external perturbation though not restircted to adiabatic systems. In this formalism the dynamics of energy levels in an externally perturbed quantum system as a function of the perturbation parameter is mapped on that of a fictitious one-dimensional classical gas of particles with repulsive potential. Equilibrium statistical mechanics of this Pechukas gas allows to reproduce the random matrix theory of energy levels. In the present work, we develop the non-equilibrium statistical mechanics of the Pechukas gas, starting with the derivation of the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) chain of equations for the appropriate generalized distribution functions. Sets of approximate kinetic equations can be consistently obtained by breaking this chain at a particular point (i.e. approximating all higher-order distribution functions by the products of the lower-order ones). When complemented by the equations for the level occupation numbers and inter-level transition amplitudes, they allow to describe the non-equilibrium evolution of the quantum state of the system, which can describe better a large quantum coherent system than the currently used approaches. In particular, we find that corrections to the factorized approximation of the distribution function scale as 1/N, where N is the number of the "Pechukas gas particles" (i.e., energy levels in the system).

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Feedback-controlled adiabatic quantum computation

Cited by 14 publications

References 27 publications

Interpolation approach to Hamiltonian-varying quantum systems and the adiabatic theorem

Interpolation approach to Hamiltonian-varying quantum systems and the adiabatic theorem

Pechukas-Yukawa formalism for Landau-Zener transitions in the presence of external noise

Bogoliubov-Born-Green-Kirkwood-Yvon chain and kinetic equations for the level dynamics in an externally perturbed quantum system

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