Variational Neural Annealing

Hibat-Allah, Mohamed; Inack, Estelle M.; Wiersema, Roeland; Melko, Roger G.; Carrasquilla, Juan

doi:10.48550/arxiv.2101.10154

Cited by 5 publications

(6 citation statements)

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“…On the one hand, recent advances in quantum science and technology have inspired the development of novel classical algorithms, sometimes dubbed nature-inspired or physics-inspired algorithms (e.g., simulated quantum annealing [10,11] running on conventional CMOS hardware) that have raised the bar for emerging quantum annealing hardware; see, for example, Refs. [12][13][14][15]. On the other hand, in parallel to these algorithmic developments, substantial progress has been made in recent years on the development of programmable special-purpose devices based on alternative technologies, such as the coherent Ising machine based on optical parametric oscillators [16,17], digital MemComputing machines based on self-organizing logic gates [18,19], and the ASIC-based Fujitsu Digital Annealer [20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Combinatorial optimization with physics-inspired graph neural networks

Schuetz

Brubaker²,

Katzgraber

2022

Nat Mach Intell

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Combinatorial optimization problems are pervasive across science and industry. Modern deep learning tools are poised to solve these problems at unprecedented scales, but a unifying framework that incorporates insights from statistical physics is still outstanding. Here we demonstrate how graph neural networks can be used to solve combinatorial optimization problems. Our approach is broadly applicable to canonical NP-hard problems in the form of quadratic unconstrained binary optimization problems, such as maximum cut, minimum vertex cover, maximum independent set, as well as Ising spin glasses and higher-order generalizations thereof in the form of polynomial unconstrained binary optimization problems. We apply a relaxation strategy to the problem Hamiltonian to generate a differentiable loss function with which we train the graph neural network and apply a simple projection to integer variables once the unsupervised training process has completed. We showcase our approach with numerical results for the canonical maximum cut and maximum independent set problems. We find that the graph neural network optimizer performs on par or outperforms existing solvers, with the ability to scale beyond the state of the art to problems with millions of variables.

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Section: Introductionmentioning

confidence: 99%

Combinatorial optimization with physics-inspired graph neural networks

Schuetz

Brubaker²,

Katzgraber

2022

Nat Mach Intell

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“…Also, although the aim of this paper is not to provide a classical algorithm competitive with the best algorithms for finding TSP solutions, several network ar-chitectures can be tested to provide faster solutions. A promising candidate is the class of transformer-like architectures, which have proven to yield interesting results on the TSP 41 as well as on quantum annealing setups to find the ground state of random Ising spin-glasses 42,43 . Furthermore, TSP solvers based on ground state finding can be integrated into meta-heuristic solvers, to solve smaller TSP problems with accuracy.…”

Section: Discussionmentioning

confidence: 99%

Many-Qudit representation for the Travelling Salesman Problem Optimisation

Vargas-Calderón,

Parra-A.,

Vinck-Posada

et al. 2021

Preprint

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We present a map from the travelling salesman problem (TSP), a prototypical NP-complete combinatorial optimisation task, to the ground state associated with a system of many-qudits. Conventionally, the TSP is cast into a quadratic unconstrained binary optimisation (QUBO) problem, that can be solved on an Ising machine. The size of the corresponding physical system's Hilbert space is 2 N 2, where N is the number of cities considered in the TSP. Our proposal provides a manyqudit system with a Hilbert space of dimension 2 N log 2 N , which is considerably smaller than the dimension of the Hilbert space of the system resulting from the usual QUBO map. This reduction can yield a significant speedup in quantum and classical computers. We simulate and validate our proposal using variational Monte Carlo with a neural quantum state, solving the TSP in a linear layout for up to almost 100 cities.

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“…Likewise, by encoding the cost function on n bits as the endpoint of a one-parameter family of quantum Hamiltonians, quantum annealing (QA) [4] attempts to follow a trajectory in Hilbert space, which interpolates, via a sequence of approximate ground states, between the uniform superposition state of n qubits and a state in the linear span of orthonormal basis elements corresponding to valid solutions. More recently, partially inspired by the search for practical utility of noisy intermediate-scale quantum computers, variational implementations of both QA and SA have been advocated, which have been termed quantum approximate optimization algorithm (QAOA) [3] and variational neural annealing (VNA) [7]. These variational algorithms achieve the desired interpolation by optimizing over a space of trial wavefunctions (respectively, probability distributions), which are selected from a variational class by following the gradient of a stochastic objective function, estimated via Monte Carlo sampling.…”

Section: Introductionmentioning

confidence: 99%

“…The use of restricted Boltzmann machines (RBMs) enables for an efficient initialization strategy using the output of the BMZ algorithm. The RBM suffers the disadvantage of depending upon an unknown normalizing constant, which precludes the possibility of utilizing an annealing schedule as discussed in [7]. In this preliminary work, we therefore focus on the limit of zero entropy regularization in which the variational Monte Carlo reduces to natural evolution strategies as discussed in [15].…”

Section: Introductionmentioning

confidence: 99%

Continuous-variable optimization with neural network quantum states

Zhang¹,

Gorsich²,

Jayakumar³

et al. 2021

Preprint

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Inspired by proposals for continuous-variable quantum approximate optimization (CV-QAOA), we investigate the utility of continuous-variable neural network quantum states (CV-NQS) for performing continuous optimization, focusing on the ground state optimization of the classical antiferromagnetic rotor model. Numerical experiments conducted using variational Monte Carlo with CV-NQS indicate that although the non-local algorithm succeeds in finding ground states competitive with the local gradient search methods, the proposal suffers from unfavorable scaling. A number of proposed extensions are put forward which may help alleviate the scaling difficulty.

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Variational Neural Annealing

Cited by 5 publications

References 0 publications

Combinatorial optimization with physics-inspired graph neural networks

Combinatorial optimization with physics-inspired graph neural networks

Many-Qudit representation for the Travelling Salesman Problem Optimisation

Continuous-variable optimization with neural network quantum states

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