Quantum adiabatic search with decoherence in the instantaneous energy eigenbasis

Åberg, Johan; Kult, David; Sjöqvist, Erik

doi:10.1103/physreva.72.042317

Cited by 35 publications

(29 citation statements)

References 19 publications

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“…In particular, we may consider monitoring the populations of the adiabatic levels or of the diabatic levels, with possibly different consequences on the ensuing time evolution. Such selective observation characterizes recently studied models of adiabatic quantum computing [25][26][27][28]. This distinction may come up in specific experimental situations.…”

Section: Introductionmentioning

confidence: 87%

Landau–Zener evolution under weak measurement: manifestation of the Zeno effect under diabatic and adiabatic measurement protocols

2015

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The time evolution and the asymptotic outcome of a Landau-Zener-Stueckelberg-Majorana (LZ) process under continuous weak non-selective measurement is analyzed. We compare two measurement protocols in which the populations of either the adiabatic or the non-adiabatic levels are (continuously and weakly) monitored. The weak measurement formalism, described using a Gaussian Kraus operator, leads to a time evolution characterized by a Markovian dephasing process, which, in the non-adiabatic measurement protocol is similar to earlier studies of LZ dynamics in a dephasing environment. Casting the problem in the language of measurement theory makes it possible for us to compare diabatic and adiabatic measurement scenarios, to consider engineered dephasing as a control device and to examine the manifestation of the Zeno effect under the different measurement protocols. In particular, under measurement of the non-adiabatic populations, the Zeno effect is manifested not as a freezing of the measured system in its initial state, but rather as an approach to equal asymptotic populations of the two diabatic states. This behavior can be traced to the way by which the weak measurement formalism behaves in the strong measurement limit, with a built-in relationship between measurement time and strength.

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Section: Introductionmentioning

confidence: 87%

Landau–Zener evolution under weak measurement: manifestation of the Zeno effect under diabatic and adiabatic measurement protocols

2015

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“…In this Letter, we study the effect of an environment on the adiabatic quantum search (AQS) algorithm [3,15], the adiabatic equivalent of Grover's algorithm [16]. While the AQS algorithm in open systems has been the subject of numerous studies, a complete understanding of its scalability is missing [14,[17][18][19][20][21][22][23][24][25].…”

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confidence: 99%

Adiabatic Quantum Search in Open Systems

et al. 2016

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Adiabatic quantum algorithms represent a promising approach to universal quantum computation. In isolated systems, a key limitation to such algorithms is the presence of avoided level crossings, where gaps become extremely small. In open quantum systems, the fundamental robustness of adiabatic algorithms remains unresolved. Here, we study the dynamics near an avoided level crossing associated with the adiabatic quantum search algorithm, when the system is coupled to a generic environment. At zero temperature, we find that the algorithm remains scalable provided the noise spectral density of the environment decays sufficiently fast at low frequencies. By contrast, higher order scattering processes render the algorithm inefficient at any finite temperature regardless of the spectral density, implying that no quantum speedup can be achieved. Extensions and implications for other adiabatic quantum algorithms will be discussed.

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“…In the closed system setting, starting in the ground state of H(0) and evolving adiabatically, the system is guaranteed to reach the ground state of H I with high probability [15][16][17]. Although adiabatic dynamics is robust against certain forms of decoherence appearing in the more realistic open system setting [10,[18][19][20][21][22][23], it remains susceptible to thermal noise and specification errors [24], which can jeopardize the efficiency of the quantum computation. Therefore, any scalable quantum annealing architecture will require quantum error correction [25].…”

Section: Introductionmentioning

confidence: 99%

Performance of two different quantum annealing correction codes

Mishra

Albash

Lidar

2015

Quantum Inf Process

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Quantum annealing is a promising approach for solving optimization problems, but like all other quantum information processing methods, it requires error correction to ensure scalability. In this work we experimentally compare two quantum annealing correction codes in the setting of antiferromagnetic chains, using two different quantum annealing processors. The lower temperature processor gives rise to higher success probabilities. The two codes differ in a number of interesting and important ways, but both require four physical qubits per encoded qubit. We find significant performance differences, which we explain in terms of the effective energy boost provided by the respective redundantly encoded logical operators of the two codes. The code with the higher energy boost results in improved performance, at the expense of a lower degree encoded graph. Therefore, we find that there exists an important tradeoff between encoded connectivity and performance for quantum annealing correction codes.

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Quantum adiabatic search with decoherence in the instantaneous energy eigenbasis

Cited by 35 publications

References 19 publications

Landau–Zener evolution under weak measurement: manifestation of the Zeno effect under diabatic and adiabatic measurement protocols

Landau–Zener evolution under weak measurement: manifestation of the Zeno effect under diabatic and adiabatic measurement protocols

Adiabatic Quantum Search in Open Systems

Performance of two different quantum annealing correction codes

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