Mapping a logical representation of TSP to quantum annealing

Silva, Carla; Aguiar, Ana; Lima, Priscila M. V.; Dutra, Inês

doi:10.1007/s11128-021-03321-8

Cited by 10 publications

(3 citation statements)

References 33 publications

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“…A straightforward computation of the expressions X M G 1 v,p X and X M G 1 p,v X produces exactly the same constraints (minus the constant terms) as those given by Equations ( 13) and (14). M G 1 v,p and M G 1 p,v are generic, in the sense that they do not convey any specific information about the graph at hand.…”

Section: The Matrix Qubo Formulationmentioning

confidence: 84%

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Experimental Analysis of Quantum Annealers and Hybrid Solvers Using Benchmark Optimization Problems

2022

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This paper studies the Hamiltonian cycle problem (HCP) and the traveling salesman problem (TSP) on D-Wave quantum systems. Motivated by the fact that most libraries present their benchmark instances in terms of adjacency matrices, we develop a novel matrix formulation for the HCP and TSP Hamiltonians, which enables the seamless and automatic integration of benchmark instances in quantum platforms. We also present a thorough mathematical analysis of the precise number of constraints required to express the HCP and TSP Hamiltonians. This analysis explains quantitatively why, almost always, running incomplete graph instances requires more qubits than complete instances. It turns out that QUBO models for incomplete graphs require more quadratic constraints than complete graphs, a fact that has been corroborated by a series of experiments. Moreover, we introduce a technique for the min-max normalization for the coefficients of the TSP Hamiltonian to address the problem of invalid solutions produced by the quantum annealer, a trend often observed. Our extensive experimental tests have demonstrated that the D-Wave Advantage_system4.1 is more efficient than the Advantage_system1.1, both in terms of qubit utilization and the quality of solutions. Finally, we experimentally establish that the D-Wave hybrid solvers always provide valid solutions, without violating the given constraints, even for arbitrarily big problems up to 120 nodes.

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Section: The Matrix Qubo Formulationmentioning

confidence: 84%

“…D-Wave computers excel at solving quadratic unconstrained binary optimization (QUBO for short) problems. QUBO models involve minimizing a quadratic polynomial function over binary variables [13,14], a hallmark of NP-hardness [15]. The Schrödinger equation is a linear partial differential equation.…”

Section: Introductionmentioning

confidence: 99%

Experimental Analysis of Quantum Annealers and Hybrid Solvers Using Benchmark Optimization Problems

2022

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“…D-Wave quantum annealers are implemented via typically sparse hardware graphs of superconducting flux qubits. Quantum annealing has been used as an experimental physics simulation tool [12][13][14][15][16] and as a computer to sample a wide variety of optimization problems [17][18][19][20] including, to name specific problem types, the graph coloring problem [21,22], semiprime factorization [23][24][25][26][27][28], traveling salesperson problem [29,30], air traffic management [31], maximum clique [32][33][34], graph partitioning [35,36], boolean tensor networks [37][38][39], community detection [40], spanning trees [41], fault detection [42], and maximum cut [43,44]. Following with the theme of sampling optimization problems that are of interest for many possible applications, there have been numerous studies developing methods to improve the capabilities of modern quantum annealers using different parameter tuning techniques and algorithms [44][45][46][47][48][49][50][51].…”

Section: Introductionmentioning

confidence: 99%

Mapping State Transition Susceptibility in Quantum Annealing

Pelofske¹

2022

Preprint

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Quantum annealing is a novel type of analog computation that aims to use quantum mechanical fluctuations to search for optimal solutions of Ising problems. Quantum annealing in the transverse field Ising model, implemented on D-Wave devices, works by applying a time dependent transverse field, which puts all qubits into a uniform state of superposition, and then applying a Hamiltonian over time which describes a user programmed Ising problem. We present a method which utilizes two control features of D-Wave quantum annealers, reverse annealing and an h-gain schedule, to quantify the susceptibility, or the distance, between two classical states of an Ising problem. The starting state is encoded using reverse annealing, and the second state is encoded on the linear terms of problem Hamiltonian. An h-gain schedule is specified which incrementally increases the strength of the linear terms, thus allowing a quantification of the h-gain strength required to transition the anneal into a specific state at the final measurement. By the nature of quantum annealing, the state tends towards global minima and therefore we restrict the second classical state to a minimum solution of the given Ising problem. This susceptibility mapping, when enumerated across all initial states, shows in detail the behavior of the quantum annealer during reverse annealing. The procedure is experimentally demonstrated on three small test Ising's which were embedded in parallel on the D-Wave Advantage system4.1. Analysis of the state transition mapping shows detailed characteristics of the reverse annealing process including intermediate state transition paths, which are visually represented as state transition networks.

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Quantum Annealing and GNN for Solving TSP with QUBO

2024

Lecture Notes in Computer Science

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Mapping a logical representation of TSP to quantum annealing

Cited by 10 publications

References 33 publications

Experimental Analysis of Quantum Annealers and Hybrid Solvers Using Benchmark Optimization Problems

Experimental Analysis of Quantum Annealers and Hybrid Solvers Using Benchmark Optimization Problems

Mapping State Transition Susceptibility in Quantum Annealing

Quantum Annealing and GNN for Solving TSP with QUBO

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