Dissipative Landau-Zener problem and thermally assisted Quantum Annealing

Arceci, Luca; Barbarino, Simone; Fazio, Rosario; Santoro, Giuseppe E.

doi:10.1103/physrevb.96.054301

Cited by 42 publications

(39 citation statements)

References 43 publications

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“…It should be kept in mind that the adiabatic dynamics of a dissipative many-body system is linked to the understanding of the Landau-Zener problem of a two-level system coupled to an environment, which is an extensively studied problem in many different areas [33][34][35][36][37][38].…”

Section: Introductionmentioning

confidence: 99%

Dissipation in adiabatic quantum computers: lessons from an exactly solvable model

et al. 2017

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We introduce and study the adiabatic dynamics of free-fermion models subject to a local Lindblad bath and in the presence of a time-dependent Hamiltonian. The merit of these models is that they can be solved exactly, and will help us to study the interplay between nonadiabatic transitions and dissipation in many-body quantum systems. After the adiabatic evolution, we evaluate the excess energy (the average value of the Hamiltonian) as a measure of the deviation from reaching the final target ground state. We compute the excess energy in a variety of different situations, where the nature of the bath and the Hamiltonian is modified. We find robust evidence of the fact that an optimal working time for the quantum annealing protocol emerges as a result of the competition between the nonadiabatic effects and the dissipative processes. We compare these results with the matrix-productoperator simulations of an Ising system and show that the phenomenology we found also applies for this more realistic case.

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Section: Introductionmentioning

confidence: 99%

Dissipation in adiabatic quantum computers: lessons from an exactly solvable model

et al. 2017

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“…Mediated interactions have attracted interest in several fields, as in quantum simulations [16,17] or driven dissipative systems [18,19]. Similar questions have been addressed in the context of Landau-Zener transition of a single two-level system coupled to several bosonic modes [20,21]. These works indicate that adiabaticity improve or worsen depending on the spin-boson coupling.…”

Section: Introductionmentioning

confidence: 92%

Quantum annealing in spin-boson model: from a perturbative to an ultrastrong mediated coupling

Pino

García-Ripoll

2018

New J. Phys.

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We study a quantum annealer where bosons mediate the Ising-type interactions between qubits. We compare the efficiency of ground state preparation for direct and mediated couplings, for which Ising and spin-boson Hamiltonian are employed respectively. This comparison is done numerically for a small frustrated antiferromagnet, with a careful choice of the optimal adiabatic passage that reveals the features of the boson-mediated interactions. Those features can be explained by taking into account what we called excited solutions: states with the same spin correlations as the ground-state but with a larger bosonic occupancy. For similar frequencies of the bosons and qubits, the performance of quantum annealing depends on how excited solutions interchange population with local spin errors. We report an enhancement of quantum annealing thanks to this interchange under certain circumstances.

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“…The resulting closed system of master equations is solved numerically. [17][18][19][20][21][22][23][24][25] This numerics sometimes reveals a peculiar dependence 20 of the dynamics of the LZ transition on the noise frequency and intensity or, more precisely, on temperature.…”

Section: Introductionmentioning

confidence: 98%

“…Refs. [12][13][14][15][16][17][18][19][20][21][22][23][24][25], the drive is assumed to be strictly linear. The subject of study is the effect of coupling of the qubit levels to the environment on the probability of the LandauZener transition.…”

Section: Introductionmentioning

confidence: 99%

Suppression of the Landau-Zener transition probability by weak classical noise

2017

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When the drive, which causes the level crossing in a qubit, is slow, the probability, PLZ, of the Landau-Zener transition is close to 1. In this regime, which is most promising for applications, the noise due to the coupling to the environment, reduces the average PLZ. At the same time, the survival probability, 1 − PLZ, which is exponentially small for a slow drive, can be completely dominated by noise-induced correction. Our main message is that the effect of a weak classical noise can be captured analytically by treating it as a perturbation in the Schrödinger equation. This allows us to study the dependence of the noise-induced correction to PLZ on the correlation time of the noise. As this correlation time exceeds the bare Landau-Zener transition time, the effect of noise becomes negligible. On the physical level, the mechanism of enhancement of the survival probability can be viewed as an absorption of the "noise quanta" across the gap. With characteristic energy of the quantum governed by the noise spectrum, the slower is the noise, the less is the number of quanta for which the absorption is allowed energetically. We consider two conventional realizations of noise: gaussian noise and telegraph noise.

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Dissipative Landau-Zener problem and thermally assisted Quantum Annealing

Cited by 42 publications

References 43 publications

Dissipation in adiabatic quantum computers: lessons from an exactly solvable model

Dissipation in adiabatic quantum computers: lessons from an exactly solvable model

Quantum annealing in spin-boson model: from a perturbative to an ultrastrong mediated coupling

Suppression of the Landau-Zener transition probability by weak classical noise

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