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

Qureshi, Mumnuna A.; Zhong, Johnny; Mason, P.; Betouras, Joseph J.; Zagoskin, A. M.

doi:10.1103/physreva.98.012128

Cited by 1 publication

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References 35 publications

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“…For example, such a definition was adopted in a recent paper [17] to study the effect of noise on the quantum system. The derivation of the formula is based on the idea that in the neighborhood of s * the behavior of these two energy levels can be described by degenerate perturbation theory: the energy levels are eigenvalues of the 2 × 2 matrix…”

Section: A Parametrization Definition Of An Anti-crossingmentioning

confidence: 99%

The effects of the problem Hamiltonian parameters on the minimum spectral gap in adiabatic quantum optimization

Choi¹

2020

Quantum Inf Process

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We study the relation between the Ising problem Hamiltonian parameters and the minimum spectral gap (min-gap) of the system Hamiltonian in the Ising-based quantum annealer. The main argument we use in this paper to assess the performance of a QA algorithm is the presence or absence of an anti-crossing during quantum evolution. For this purpose, we introduce a new parametrization definition of the anti-crossing. Using the Maximum-weighted Independent Set (MIS) problem in which there are flexible parameters (energy penalties J between pairs of edges) in an Ising formulation as the model problem, we construct examples to show that by changing the value of J, we can change the quantum evolution from one that has an anti-crossing (that results in an exponential small min-gap) to one that does not have, or the other way around, and thus drastically change (increase or decrease) the min-gap. However, we also show that by changing the value of J alone, one can not avoid the anti-crossing. We recall a polynomial reduction from an Ising problem to an MIS problem to show that the flexibility of changing parameters without changing the problem to be solved can be applied to any Ising problem. As an example, we show that by such a reduction alone, it is possible to remove the anti-crossing and thus increase the min-gap. Our anti-crossing definition is necessarily scaling invariant as scaling the problem Hamiltonian does not change the nature (i.e. presence or absence) of an anti-crossing. As a side note, we show exactly how the min-gap is scaled if we scale the problem Hamiltonian by a constant factor.

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Section: A Parametrization Definition Of An Anti-crossingmentioning

confidence: 99%

The effects of the problem Hamiltonian parameters on the minimum spectral gap in adiabatic quantum optimization

Choi¹

2020

Quantum Inf Process

View full text Add to dashboard Cite

show abstract

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

Cited by 1 publication

References 35 publications

The effects of the problem Hamiltonian parameters on the minimum spectral gap in adiabatic quantum optimization

The effects of the problem Hamiltonian parameters on the minimum spectral gap in adiabatic quantum optimization

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