Related papers: Graph isomorphism and Gaussian boson sampling

Gaussian boson sampling (GBS) is a near-term quantum computation framework that is believed to be classically intractable, but yet rich of potential applications. In this paper we study the intimate relation between distributions defined…

Boson sampling is a fundamentally and practically important task that can be used to demonstrate quantum supremacy using noisy intermediate-scale quantum devices. In this work, we present classical sampling algorithms for single-photon and…

Photonics chips on which one can perform Gaussian Boson Sampling have become accessible on the cloud, in particular the X8 chip of Xanadu. In this technical report, we study its potential use as a first step towards graph classification on…

Scientists in quantum technology aspire to quantum advantage: a computational result unattainable with classical computers. Gaussian boson sampling experiment has been already claimed to achieve this goal. In this setup squeezed light…

Gaussian boson sampling exploits squeezed states to provide a highly efficient way to demonstrate quantum computational advantage. We perform experiments with 50 input single-mode squeezed states with high indistinguishability and squeezing…

We formulate a notion of the quantum automorphism group of a $2$-graph. After some preliminary computations, we define quantum isomorphism between a pair of $2$-graphs. We produce a `non-trivial' example of a pair of $2$-graphs that are not…

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…

We pose a generalized Boson Sampling problem. Strong evidence exists that such a problem becomes intractable on a classical computer as a function of the number of Bosons. We describe a quantum optical processor that can solve this problem…

Many complex questions in biology, physics, and mathematics can be mapped to the graph isomorphism problem and the closely related graph automorphism problem. In particular, these problems appear in the context of network visualization,…

Graph states are key resources for measurement-based quantum computing, which is particularly promising for photonic systems. Fusions are probabilistic Bell state measurements, measuring pairs of parity operators of two qubits. Fusions can…

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…

Boson sampling has emerged as an important tool to demonstrate the difference between quantum and classical computers and has attracted the interest of experimentalists and theoreticians. In this work we study Boson sampling from general,…

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…

In this paper we resolve the complexity of the isomorphism problem on all but finitely many of the graph classes characterized by two forbidden induced subgraphs. To this end we develop new techniques applicable for the structural and…

Gaussian boson sampling constitutes a prime candidate for an experimental demonstration of quantum advantage within reach with current technological capabilities. The original proposal employs photon-number-resolving detectors, however the…

Boson Sampling has emerged as a tool to explore the advantages of quantum over classical computers as it does not require a universal control over the quantum system, which favours current photonic experimental platforms.Here, we introduce…

We show that any two Hadamard graphs on the same number of vertices are quantum isomorphic. This follows from a more general recipe for showing quantum isomorphism of graphs arising from certain association schemes. The main result is built…

We present a conceptually new approach to describe state-of-the-art photonic quantum experiments using Graph Theory. There, the quantum states are given by the coherent superpositions of perfect matchings. The crucial observation is that…

The graph isomorphism problem remains a fundamental challenge in computer science, driving the search for efficient decision algorithms. Due to its ambiguous computational complexity, heuristic approaches such as simulated annealing are…

We show how phase-space simulations of Gaussian quantum states in a photonic network permit verification of measurable correlations of Gaussian boson sampling (GBS) quantum computers. Our results agree with experiments for up to 100-th…