Solving the graph-isomorphism problem with a quantum annealer

Hen, Itay; Young, A. P.

doi:10.1103/physreva.86.042310

Cited by 34 publications

(45 citation statements)

References 44 publications

(91 reference statements)

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“…Because CAM recall using orthogonal memories is expected to be well behaved, we use that case to test the fundamental performance of the D-Wave processor to recall stored memories. The remaining parameters are chosen from the following sets respectively, n ∈ {8, 12,16,20,24,28 For each parameter combination (n, m, θ), 100 problem instances are randomly generated as specified in Section 3.1 and utilizing one of the learning rules to encode the memories into a weight matrix. Each selected problem instance is then programmed and executed N = 1000 times on the D-Wave QPU to calculate the average recall accuracy c.…”

Section: Methodsmentioning

confidence: 99%

“…This finite-temperature, open system model is expected to more accurately describe the dynamics underlying the QPU [8]. Nevertheless, several experimental tests of the D-Wave QPU have been carried out including applications of machine learning, binary classification, protein folding, graph analysis, and network analysis [9][10][11][12][13][14][15][16][17][18]. Demonstrations of enhanced performance using the D-Wave QPU have been found only for a few selected and highly contrived problem instances [19][20][21].…”

Section: Introductionmentioning

confidence: 99%

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Recall Performance for Content-Addressable Memory Using Adiabatic Quantum Optimization

Schrock

McCaskey

Hamilton

et al. 2017

Entropy

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A content-addressable memory (CAM) stores key-value associations such that the key is recalled by providing its associated value. While CAM recall is traditionally performed using recurrent neural network models, we show how to solve this problem using adiabatic quantum optimization. Our approach maps the recurrent neural network to a commercially available quantum processing unit by taking advantage of the common underlying Ising spin model. We then assess the accuracy of the quantum processor to store key-value associations by quantifying recall performance against an ensemble of problem sets. We observe that different learning rules from the neural network community influence recall accuracy but performance appears to be limited by potential noise in the processor. The strong connection established between quantum processors and neural network problems supports the growing intersection of these two ideas.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Recall Performance for Content-Addressable Memory Using Adiabatic Quantum Optimization

Schrock

McCaskey

Hamilton

et al. 2017

Entropy

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“…The distinguishing power of the algorithm increases with the number of walker moving along the graph; the technique, however, is not universal and there are non-isomorphic graphs that cannot be distinguished. A different approach, based on the Adiabatic Quantum Computation paradigm (AQC) [14,15], has been recently proposed in [16,17]. In order to distinguish nonisomorphic graphs, for example, Vinci et al look at the values assumed by a set non-isomorphism witnesses during the adiabatic evolution of the couple of graphs under investigation.…”

Section: Introductionmentioning

confidence: 99%

A quantum-walk-inspired adiabatic algorithm for solving graph isomorphism problems

Tamascelli¹,

Zanetti²

2014

J. Phys. A: Math. Theor.

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We present a 2-local quantum algorithm for graph isomorphism GI based on an adiabatic protocol. By exploiting continuous-time quantum-walks, we are able to avoid a mere diffusion over all possible configurations and to significantly reduce the dimensionality of the visited space. Within this restricted space, the graph isomorphism problem can be translated into the search of a satisfying assignment to a 2-SAT formula without resorting to perturbation gadgets or projective techniques. We present an analysis of the execution time of the algorithm on small instances of the graph isomorphism problem and discuss the issue of an implementation of the proposed adiabatic scheme on current quantum computing hardware.

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“…[1][2][3][4][5][6][7][8][9] This interest is due in a large part to demonstration of the underlying principles of quantum annealing in condensed matter systems 10 and the more recent development of a programmable annealing device by D-Wave Systems Inc. 11,12 Although the niobium superconducting quantum interference device (SQUIDs) which are the basic building blocks of the D-Wave annealer display limited coherence, it has been used to demonstrate that quantum tunneling is an exploitable resource in a computational setting. 13 Furthermore the development of annealers using aluminum SQUIDs with orders-of-magnitude longer coherence lifetimes 14 may enable further improvements in the computational performance of future quantum annealers.…”

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

Circuit design for multi-body interactions in superconducting quantum annealing systems with applications to a scalable architecture

2017

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Quantum annealing provides a way of solving optimization problems by encoding them as Ising spin models which are implemented using physical qubits. The solution of the optimization problem then corresponds to the ground state of the system. Quantum tunneling is harnessed to enable the system to move to the ground state in a potentially high non-convex energy landscape. A major difficulty in encoding optimization problems in physical quantum annealing devices is the fact that many real world optimization problems require interactions of higher connectivity, as well as multi-body terms beyond the limitations of the physical hardware. In this work we address the question of how to implement multi-body interactions using hardware which natively only provides two-body interactions. The main result is an efficient circuit design of such multi-body terms using superconducting flux qubits in which effective N-body interactions are implemented using N ancilla qubits and only two inductive couplers. It is then shown how this circuit can be used as the unit cell of a scalable architecture by applying it to a recently proposed embedding technique for constructing an architecture of logical qubits with arbitrary connectivity using physical qubits which have nearest-neighbor four-body interactions. It is further shown that this design is robust to non-linear effects in the coupling loops, as well as mismatches in some of the circuit parameters.npj Quantum Information (2017) 3:21 ; doi:10.1038/s41534-017-0022-6 INTRODUCTION Solving machine learning and optimization problems by casting them as an Ising spin glass, and then using a physical device to take advantage of quantum fluctuations has been a subject of much recent interest. [1][2][3][4][5][6][7][8][9] This interest is due in a large part to demonstration of the underlying principles of quantum annealing in condensed matter systems 10 and the more recent development of a programmable annealing device by D-Wave Systems Inc.

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Solving the graph-isomorphism problem with a quantum annealer

Cited by 34 publications

References 44 publications

Recall Performance for Content-Addressable Memory Using Adiabatic Quantum Optimization

Recall Performance for Content-Addressable Memory Using Adiabatic Quantum Optimization

A quantum-walk-inspired adiabatic algorithm for solving graph isomorphism problems

Circuit design for multi-body interactions in superconducting quantum annealing systems with applications to a scalable architecture

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