Related papers: Solving the Graph Isomorphism Problem with a Quant…

We relate the graph isomorphism problem to the solvability of certain systems of linear equations with nonnegative variables. This version replaces the two previous versions of this paper.

Many computational problems are unchanged under some symmetry operation. In classical machine learning, this can be reflected with the layer structure of the neural network. In quantum machine learning, the ansatz can be tuned to correspond…

The graph isomorphism problem is a main problem which has numerous applications in different fields. Thus, finding an efficient and easy to implement method to discriminate non-isomorphic graphs is valuable. In this paper, a new method is…

Over 50 years ago, Lov\'{a}sz proved that two graphs are isomorphic if and only if they admit the same number of homomorphisms from any graph [Acta Math. Hungar. 18 (1967), pp. 321--328]. In this work we prove that two graphs are quantum…

The graph isomorphism is to determine whether two graphs are isomorphic. A closely related problem is automorphism detection, where an isomorphism between two graphs is a bijection between their vertex sets that preserves adjacency, and an…

This paper proposes a quantum computing-based algorithm to solve the single image super-resolution (SISR) problem. One of the well-known classical approaches for SISR relies on the well-established patch-wise sparse modeling of the problem.…

In the past decades for more and more graph classes the Graph Isomorphism Problem was shown to be solvable in polynomial time. An interesting family of graph classes arises from intersection graphs of geometric objects. In this work we show…

Current quantum computing devices have different strengths and weaknesses depending on their architectures. This means that flexible approaches to circuit design are necessary. We address this task by introducing a novel space-efficient…

The graph isomorphism problem is theoretically interesting and also has many practical applications. The best known classical algorithms for graph isomorphism all run in time super-polynomial in the size of the graph in the worst case. An…

Quantum annealing is a powerful tool for solving and approximating combinatorial optimization problems such as graph partitioning, community detection, centrality, routing problems, and more. In this paper we explore the use of quantum…

With the current progress of quantum computing, quantum annealing is being introduced as a powerful method to solve hard computational problems. In this paper, we study the potential capability of quantum annealing in solving the phase…

This paper assesses the performance of the D-Wave 2X (DW) quantum annealer for finding a maximum clique in a graph, one of the most fundamental and important NP-hard problems. Because the size of the largest graphs DW can directly solve is…

Quantum annealers of D-Wave Systems, Inc., offer an efficient way to compute high quality solutions of NP-hard problems. This is done by mapping a problem onto the physical qubits of the quantum chip, from which a solution is obtained after…

Diagnosing the minimal set of faults capable of explaining a set of given observations, e.g., from sensor readouts, is a hard combinatorial optimization problem usually tackled with artificial intelligence techniques. We present the mapping…

The use of quantum computing in graph community detection and regularity checking related to Szemeredi's Regularity Lemma (SRL) are demonstrated with D-Wave Systems' quantum annealer and simulations. We demonstrate the capability of quantum…

It is well-known that the graph isomorphism problem can be posed as an equivalent problem of determining whether an auxiliary graph structure contains a clique of specific order. However, the algorithms that have been developed so far for…

For every integer $g$, isomorphism of graphs of Euler genus at most $g$ can be decided in linear time. This improves previously known algorithms whose time complexity is $n^{O(g)}$ (shown in early 1980's), and in fact, this is the first…

It is known that any quantum algorithm for Graph Isomorphism that works within the framework of the hidden subgroup problem (HSP) must perform highly entangled measurements across Omega(n log n) coset states. One of the only known models…

Hybrid algorithms that combine quantum and classical resources have become commonplace in quantum computing. The variational quantum eigensolver (VQE) is routinely used to solve prototype problems. Currently, hybrid algorithms use no more…

Achieving densely connected hardware graphs is a challenge for most quantum computing platforms today, and a particularly crucial one for the case of quantum annealing applications. In this context, we present a scalable architecture for…