Quantum Speedups for Exponential-Time Dynamic Programming Algorithms

Ambainis, Andris; Balodis, Kaspars; Iraids, Janis; Kokainis, Martins; Prūsis, Krišjānis; Vihrovs, Jevgēnijs

doi:10.48550/arxiv.1807.05209

Cited by 3 publications

(4 citation statements)

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“…3SAT is the canonical example of so-called NP-complete problems, which are believed to be exponentially difficult even for quantum computers. Nevertheless, quantum computers can still accelerate their solution [1,2], and given their ubiquity, they may become one of the most important applications of quantum computers. However, the best quantum algorithms, which essentially "quantumenhance" classical SAT solvers [1], require a large number of qubits, and are not directly applicable given a quantum computer of limited size.…”

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confidence: 99%

Computational Speedups Using Small Quantum Devices

Dunjko

Cirac

2018

Phys. Rev. Lett.

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Suppose we have a small quantum computer with only M qubits. Can such a device genuinely speed up certain algorithms, even when the problem size is much larger than M ? Here we answer this question to the affirmative. We present a hybrid quantum-classical algorithm to solve 3SAT problems involving n ≫ M variables that significantly speeds up its fully classical counterpart. This question may be relevant in view of the current quest to build small quantum computers.

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confidence: 99%

Computational Speedups Using Small Quantum Devices

Dunjko

Cirac

2018

Phys. Rev. Lett.

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“…Then, it is possible to solve an HCP with an algorithm for TSP, putting in the (i, j) element of W the cost 1 if the edge from i to j exists, and 2 or more otherwise, and then verifying if the total cost of a TSP solution is equal to the number of nodes of the given graph, or not. Finally, we can apply Bellman-Held-Karp algorithm [13], which has complexity O (2 n ), or the algorithm designed in [14]. This latter is a quantum algorithm with complexity O (1.728 n ).…”

Section: Related Workmentioning

confidence: 99%

“…Consequently, our study of time complexity is valid also for perfectly Markov random walks, not based on previous choices. Furthermore, to outperform respectively the best-known classical [13] and quantum [14] algorithm for HCP, the following conditions must be true:…”

Section: Corollary 1 Considering the Rate Of Success Of Our Algorithm...mentioning

confidence: 99%

Comparison among Classical, Probabilistic and Quantum Algorithms for Hamiltonian Cycle Problem

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2023

Journal of Quantum Computing

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The Hamiltonian cycle problem (HCP), which is an NP-complete problem, consists of having a graph G with n nodes and m edges and finding the path that connects each node exactly once. In this paper we compare some algorithms to solve a Hamiltonian cycle problem, using different models of computations and especially the probabilistic and quantum ones. Starting from the classical probabilistic approach of random walks, we take a step to the quantum direction by involving an ad hoc designed Quantum Turing Machine (QTM), which can be a useful conceptual project tool for quantum algorithms. Introducing several constraints to the graphs, our analysis leads to not-exponential speedup improvements to the best-known algorithms. In particular, the results are based on bounded degree graphs (graphs with nodes having a maximum number of edges) and graphs with the right limited number of nodes and edges to allow them to outperform the other algorithms.

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“…In this work we demonstrate how the two most developed and popular current paradigms, universal quantum computing (UQC) and quantum annealing (QA), can be integrated into the QLS framework and utilized to solve problems of practical size. Both paradigms have demonstrated great potential on a number of important problems [2,[17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Network Community Detection on Small Quantum Computers

et al. 2019

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In recent years, a number of quantum computing devices with small numbers of qubits have become available. A hybrid quantum local search (QLS) approach that combines a classical machine and a small quantum device to solve problems of practical size is presented. The proposed approach is applied to the network community detection problem. QLS is hardware-agnostic and easily extendable to new quantum computing devices as they become available. It is demonstrated to solve the 2-community detection problem on graphs of sizes of up to 410 vertices using the 16-qubit IBM quantum computer and D-Wave 2000Q, and compare their performance with the optimal solutions. The results herein demonstrate that QLS performs similarly in terms of quality of the solution and the number of iterations to convergence on both types of quantum computers and it is capable of achieving results comparable to state-of-the-art solvers in terms of quality of the solution including reaching the optimal solutions.

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Quantum Speedups for Exponential-Time Dynamic Programming Algorithms

Cited by 3 publications

References 0 publications

Computational Speedups Using Small Quantum Devices

Computational Speedups Using Small Quantum Devices

Comparison among Classical, Probabilistic and Quantum Algorithms for Hamiltonian Cycle Problem

Network Community Detection on Small Quantum Computers

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