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Quantum Machine Intelligence

Boost clustering with Gaussian Boson Sampling: a quantum-classical hybrid approach

Nicolò Bonaldi, Martina Sofia Rossi, Daniele Mattioli, Michele Grapulin, Blanca Silva Fernandéz, Davide Caputo, Marco Magagnini, Arianna Osti, Fabio Veronese

Published Oct 8, 2024• 4 citations
Publisher

Abstract

Gaussian Boson Sampling (GBS) is a recently developed paradigm of quantum computing consisting of sending a Gaussian state through a linear interferometer and then counting the number of photons in each output mode. When the system encodes a symmetric matrix, GBS can be viewed as a tool to sample subgraphs: the most sampled are those with a large number of perfect matchings, and thus are the densest ones. This property has been the foundation of the novel clustering approach we propose in this work, called GBS-based clustering , which relies solely on GBS, without the need of classical algorithms. The GBS-based clustering has been tested on several datasets and benchmarked with two well-known classical clustering algorithms. Results obtained by using a GBS simulator show that on average, our approach outperforms the two classical algorithms in two out of the three chosen metrics, proposing itself as a viable quantum-classical hybrid clustering option.

DOI
10.1007/s42484-024-00185-w

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Gaussian Boson Sampling (GBS) is a recently developed paradigm of quantum computing consisting of sending a Gaussian state through a linear interferometer and then counting the number of photons in each output mode. When the system encodes a symmetric matrix, GBS can be viewed as a tool to sample subgraphs: the most sampled are those with a large number of perfect matchings, and thus are the densest ones. This property has been the foundation of the novel clustering approach we propose in this work, called GBS-based clustering , which relies solely on GBS, without the need of classical algorithms. The GBS-based clustering has been tested on several datasets and benchmarked with two well-known classical clustering algorithms. Results obtained by using a GBS simulator show that on average, our approach outperforms the two classical algorithms in two out of the three chosen metrics, proposing itself as a viable quantum-classical hybrid clustering option.
Gaussian Boson Sampling (GBS) is a recently developed paradigm of quantum computing consisting of sending a Gaussian state through a linear interferometer and then counting the number of photons in each output mode. When the system encodes a symmetric matrix, GBS can be viewed as a tool to sample subgraphs: the most sampled are those with a large number of perfect matchings, and thus are the densest ones. This property has been the foundation of the novel clustering approach we propose in this work, called GBS-based clustering, which relies solely on GBS, without the need of classical algorithms. The GBS-based clustering has been tested on several datasets and benchmarked with two well-known classical clustering algorithms. Results obtained by using a GBS simulator show that on average our approach outperforms the two classical algorithms in two out of the three chosen metrics, proposing itself as a viable full-quantum clustering option.
Quantum computers solve intractable problems which classically require an exponentially long time to compute. With the development of large-scale experiments that claim quantum advantage, a vital issue has now emerged. What are the errors, and how do they affect the complexity of the problem solved? Large-scale Gaussian boson sampling (GBS) experiments give an example in which random numbers are generated. Despite classical hardness, these have computable benchmarks for checking data validity. While there are other quantum computing architectures, Gaussian boson sampling is uniquely testable at all scales. Several large, pioneering quantum computing (QC) experiments have been carried out to investigate quantum advantage. Here, we introduce a highly scalable but classical algorithm that can solve GBS approximately. Our numerical simulation of the output count data is closer to the exact solution than current experiments up to 1152 modes. This algorithm outperforms all previous classical, approximate algorithms and scales efficiently to larger experiments. Our results show that effects beyond losses can cause the errors that allow classical simulability. This work will lead to more precise algorithms and is a step towards understanding how QC quantum advantage is affected by the underlying physics.
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.
Biclustering is a problem in machine learning and data mining that seeks to group together rows and columns of a dataset according to certain criteria. In this work, we highlight the natural relation that quantum computing models like boson and Gaussian boson sampling (GBS) have to this problem. We first explore the use of boson sampling to identify biclusters based on matrix permanents. We then propose a heuristic that finds clusters in a dataset using Gaussian boson sampling by (i) converting the dataset into a bipartite graph and then (ii) running GBS to find the densest sub-graph(s) within the larger bipartite graph. Our simulations for the above proposed heuristics show promising results for future exploration in this area.
Biclustering is a problem in machine learning and data mining that seeks to group together rows and columns of a dataset according to certain criteria. In this work, we highlight the natural relation that quantum computing models like boson and Gaussian boson sampling (GBS) have to this problem. We first explore the use of boson sampling to identify biclusters based on matrix permanents. We then propose a heuristic that finds clusters in a dataset using Gaussian boson sampling by (i) converting the dataset into a bipartite graph and then (ii) running GBS to find the densest sub-graph(s) within the larger bipartite graph. Our simulations for the above proposed heuristics show promising results for future exploration in this area.
Gaussian boson sampling (GBS) is a model of nonuniversal quantum computation that claims to demonstrate quantum supremacy with current technologies. This model entails sampling photocounting events from a multimode Gaussian state at the outputs of a linear interferometer. In this scheme, collision events—those with more than one photon for each mode—are infrequent. However, they are still used for validation purposes. Therefore, the limitation of realistic detectors to perfectly resolve adjacent photon numbers becomes pivotal. We derive a photocounting probability distribution in GBS schemes which is applicable for use with general detectors and photocounting techniques. This probability distribution is expressed in terms of functionals of the field-quadrature covariance matrix, e.g., Hafnian and Torontonian in the well-known special cases of photon-number-resolving and on-off detectors, respectively. Based on our results, we consider a GBS validation technique involving detectors with realistic photon-number resolution. Published by the American Physical Society 2024