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 quantum devices. In order to achieve this goal, we study the generated samples of the graph embedding method which leads to feature vectors. This is done on a restricted class of unweighted, undirected and loop-free graphs. Hardware constraints are matched to properties of graphs that can be encoded. We report experiments on the X8 chip as well as comparisons to numerical simulations on a classical computer and analytical solutions. We conclude this technical report by trying to take photon loss into account and explain the observed results accordingly.
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 quantum devices. In order to achieve this goal, we study the generated samples of the graph embedding method which leads to feature vectors. This is done on a restricted class of unweighted, undirected and loop-free graphs. Hardware constraints are matched to properties of graphs that can be encoded. We report experiments on the X8 chip as well as comparisons to numerical simulations on a classical computer and analytical solutions. We conclude this technical report by trying to take photon loss into account and explain the observed results accordingly.
Quantum computers, due to their superposition and entanglement properties, provide significant advantages in solving certain problems compared with classical computers. Therefore, it is crucial to identify issues that can be efficiently solved by noisy intermediate-scale quantum (NISQ) systems. Xanadu has introduced the X8 quantum chip, based on integrated photonic technology, along with important photonic platforms such as Strawberry Fields and Gaussian Boson Sampling (GBS), to solve specific computational problems. In this review article, after reviewing Boson Sampling (BS) and Gaussian Boson Sampling (GBS), we discuss the relationship between GBS and graph theory, including how graphs can be encoded in GBS. Some applications of GBS, particularly molecular docking and molecular vibrations, are also considered. The future goal of this study is to identify problems that can be represented as small graphs and solved using GBS with a limited number of optical modes.
Gaussian boson sampling (GBS) is a tool for demonstrating quantum computational utilities and also exhibits mathematical connections to specific graph-related and quantum chemistry problems. It has been suggested that the samples generated from GBS could be utilized to improve stochastic algorithms in searching for certain graph features. In this study, we employed X8, a noisy intermediate-scale quantum computer, to address graph problems. The samples were produced from a 4-mode quantum photonic processor. This research represents a step toward analyzing Gaussian boson sampling as a tool for solving real-world problems using existing noisy intermediate-scale quantum computers and aims to encourage the development of quantum algorithms.
Gaussian Boson Sampling (GBS) generates random samples of photon-click patterns from a class of probability distributions that are hard for a classical computer to sample from. Despite heroic demonstrations of quantum supremacy using GBS, Boson Sampling, and instantaneous quantum polynomial (IQP) algorithms, systematic evaluations of the power of these quantum-enhanced random samplers when applied to provably hard problems, and performance comparisons with best-known classical algorithms have been lacking. We propose a hybrid quantum-classical algorithm using the GBS for the NP-complete problem of determining if two graphs are a vertex minor of one another. The graphs are encoded in GBS and the generated random samples serve as feature vectors in a support vector machine (SVM) classifier. We find a graph embedding that allows trading between the one-shot classification accuracy and the amount of input squeezing, a hard-to-produce quantum resource, followed by repeated trials and a majority vote to reach an overall desired accuracy. We introduce a new classical algorithm based on graph spectra, which we show outperforms various well-known graph-similarity algorithms. We compare the performance of our algorithm with this classical algorithm and analyze their time versus problem-size scaling, to yield a desired classification accuracy. Our simulation results suggest that with a near-term realizable GBS device—5 dB pulsed squeezers, 12-mode unitary, and reasonable assumptions on coupling efficiency, on-chip losses, and detection efficiency of photon number resolving detectors—we can solve 12-node vertex-minor instances with about 103fold lower time compared to a powerful desktop computer.
Quantum generative modeling has emerged as a promising application of quantum computers, aiming to model complex probability distributions beyond the reach of classical methods. In practice, however, training such models often requires costly gradient estimation performed directly on the quantum hardware. Crucially, for certain structured quantum circuits, expectation values of local observables can be efficiently evaluated on a classical computer, enabling classical training without calls to the quantum hardware in the optimization loop. In these models, sampling from the resulting circuits can still be classically hard, so inference must be performed on a quantum device, yielding a potential computational advantage. In this work, we introduce a photonic quantum generative model built on parametrized Gaussian Boson Sampling circuits. The training is based on the efficient classical evaluation of expectation values enabled by the Gaussian structure of the state, allowing scalable optimization of the model parameters through the maximum mean discrepancy loss function. We demonstrate the effectiveness of the approach through numerical experiments on photonic systems with up to 805 modes and over a million trainable parameters, highlighting its scalability and suitability for near-term photonic quantum devices.
Abstract Gaussian Boson Sampling (GBS) is a non-universal model for quantum computing inspired by the original formulation of the Boson Sampling (BS) problem. Nowadays, it represents a paradigmatic quantum platform to reach the quantum advantage regime in a specific computational model. Indeed, thanks to the implementation in photonics-based processors, the latest GBS experiments have reached a level of complexity where the quantum apparatus has solved the task faster than currently up-to-date classical strategies. In addition, recent studies have identified possible applications beyond the inherent sampling task. In particular, a direct connection between photon counting of a genuine GBS device and the number of perfect matchings in a graph has been established. In this work, we propose to exploit such a connection to benchmark GBS experiments. We interpret the properties of the feature vectors of the graph encoded in the device as a signature of correct sampling from the true input state. Within this framework, two approaches are presented. The first method exploits the distributions of graph feature vectors and classification via neural networks. The second approach investigates the distributions of graph kernels. Our results provide a novel approach to the actual need for tailored algorithms to benchmark large-scale Gaussian Boson Samplers.
Abstract Photonic Quantum Computers provide several benefits over the discrete qubit-based paradigm of quantum computing. By using the power of continuous-variable computing we build an anomaly detection model to use on searches for New Physics. Our model uses Gaussian Boson Sampling, a #P-hard problem and thus not efficiently accessible to classical devices. This is used to create feature vectors from graph data, a natural format for representing data of high-energy collision events. A simple K-means clustering algorithm is used to provide a baseline method of classification. We then present a novel method of anomaly detection, combining the use of Gaussian Boson Sampling and a quantum extension to K-means known as Q-means. This is found to give equivalent results compared to the classical clustering version while also reducing the O O complexity, with respect to the sample’s feature-vector length, from O(N) O N to O(log(N)) O log N .