Open-System Quantum Annealing in Mean-Field Models with Exponential Degeneracy

Kechedzhi, Kostyantyn; Smelyanskiy, Vadim

doi:10.1103/physrevx.6.021028

Cited by 30 publications

(29 citation statements)

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“…The role of temperature and external noise was further considered in the context of the AQC in several papers, showing that in some cases it may be beneficial to reach the target ground state. Work has been done on comparing the AQC and classical approaches using thermal hopping [27], on the use of quantum diffusion, showing better performance than closed-system quantum annealing [28], and on the crucial role of noiseinduced thermalisation in the AQC, which can outperform simulated annealing [29]. In addition, the relation of thermally assisted tunnelling to the quantum Monte Carlo has been studied in [30], and the effect of the noise of a thermal environment [31] as well as decoherence [32] have been studied as well.…”

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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“…In specific cases, however, it has been suggested that the external environment may be even beneficial in reaching the target ground state showing better performance than closed-system quantum annealing [26][27][28][29][30]. The point here is that the evolution of a far-from-thermal equilibrium spin system coupled to a large set of oscillators describing the external environment is not fully understood.…”

Section: Introductionmentioning

confidence: 99%

Dissipative environment may improve the quantum annealing performances of the ferromagnetic p -spin model

et al. 2018

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We investigate the quantum annealing of the ferromagnetic p-spin model in a dissipative environment (p = 5 and p = 7). This model, in the large p limit, codifies the Grover's algorithm for searching in an unsorted database. The dissipative environment is described by a phonon bath in thermal equilibrium at finite temperature. The dynamics is studied in the framework of a Lindblad master equation for the reduced density matrix describing only the spins. Exploiting the symmetries of our model Hamiltonian, we can describe many spins and extrapolate expected trends for large N , and p. While at weak system bath coupling the dissipative environment has detrimental effects on the annealing results, we show that in the intermediate coupling regime, the phonon bath seems to speed up the annealing at low temperatures. This improvement in the performance is likely not due to thermal fluctuation but rather arises from a correlated spin-bath state and persists even at zero temperature. This result may pave the way to a new scenario in which, by appropriately engineering the system-bath coupling, one may optimize quantum annealing performances below either the purely quantum or classical limit.

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“…Recently speedup problem extensively has been discussed in the framework of quantum computation purposed to accelerate the solution of familiar optimization problems by using quantum hardware [71,72]. However, predicting a quantum speedup in this hardware represents a complex problem that depends on many physical parameters including size and topology of the system [73][74][75][76].…”

Section: Discussionmentioning

confidence: 99%

Predicting quantum advantage by quantum walk with convolutional neural networks

2019

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Quantum walks are at the heart of modern quantum technologies. They allow to deal with quantum transport phenomena and are an advanced tool for constructing novel quantum algorithms. Quantum walks on graphs are fundamentally different from classical random walks analogs, in particular, they walk faster than classical ones on certain graphs, enabling in these cases quantum algorithmic applications and quantum-enhanced energy transfer. However, little is known about the possible advantages on arbitrary graphs not having explicit symmetries. For these graphs one would need to perform simulations of classical and quantum walk dynamics to check if the speedup occurs, which could take a long computational time. Here we present a new approach for the solution of the quantum speedup problem, which is based on a machine learning algorithm that predicts the quantum advantage by just 'looking' at a graph. The convolutional neural network, which we designed specifically to learn from graphs, observes simulated examples and learns complex features of graphs that lead to a quantum advantage, allowing to identify graphs that exhibit quantum advantage without performing any quantum walk or random walk simulations. The performance of our approach is evaluated for line and random graphs, where classification was always better than random guess even for the most challenging cases. Our findings pave the way to an automated elaboration of novel largescale quantum circuits utilizing quantum walk based algorithms, and to simulating high-efficiency energy transfer in biophotonics and material science.Computational speedup is one of the keystone problems both in classical and quantum computer sciences [1,2]. Although quantum parallelism, in general, represents necessary ingredient for an acceleration of computational algorithms on quantum 'hardware', sufficient criterion is still unknown in many cases. Strictly speaking, speedup problem might be recognized for certain computational tasks for which definite classical and/or quantum algorithms are used, see [3,4]. In the paper we attack the speedup problem with random and quantum walks in a quite general form by using advanced machine learning approaches.Random walks on graphs are widely used as subroutines in computational algorithms [5][6][7][8][9], and as a model for processes in nature [10][11][12][13][14]. Quantum walks [15][16][17][18], quantum analogs of classical walks, replace a classical particle with a quantum one. This change makes a fundamental difference in the walker's dynamics due to quantum interference. Due to interference, quantum walks of single and multiple particles can be employed as a tool for quantum information processing and quantum algorithms [19][20][21][22][23][24][25][26], for quantum machine learning [27,28], and as a part of a model of photosynthetic energy transfer [29,30]. Especially in the energy transport problem, see, e.g. [31][32][33], it is important that quantum particles hit target vertices of certain graphs faster than classical particles.It is, h...

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Open-System Quantum Annealing in Mean-Field Models with Exponential Degeneracy

Cited by 30 publications

References 50 publications

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

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

Dissipative environment may improve the quantum annealing performances of the ferromagnetic p -spin model

Predicting quantum advantage by quantum walk with convolutional neural networks

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