Gaussian Boson Sampling to Accelerate NP-Complete Vertex-Minor Graph Classification

• URL: http://arxiv.org/abs/2402.03524v1
• Date: Mon, 5 Feb 2024 21:24:11 GMT
• Title: Gaussian Boson Sampling to Accelerate NP-Complete Vertex-Minor Graph Classification
• Authors: Mushkan Sureka, Saikat Guha
• Abstract summary: We propose a hybrid quantum-classical algorithm for the NP-complete problem of determining if two graphs are minor of one another. We find a graph embedding that allows trading between the one-shot classification accuracy and the amount of input squeezing. We introduce a new classical algorithm based on graph spectra, which we show outperforms various well-known graph-similarity algorithms.
• Score: 0.9935277311162707
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Gaussian Boson Sampling (GBS) generate 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 for quantum supremacy using GBS, Boson Sampling, and instantaneous quantum polynomial (IQP) algorithms, systematic evaluations of the power of these quantum-enhanced random samples 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 vertex minor of one another. The graphs are encoded in GBS and the generated random samples serve as feature vectors in the 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 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 vs problem-size scaling, to yield a desired classification accuracy. Our simulation suggests that with a near-term realizable GBS device- $5$ dB pulsed squeezer, $12$-mode unitary, and reasonable assumptions on coupling efficiency, on-chip losses and detection efficiency of photon number resolving detectors-we can solve a $12$-node vertex minor instances with about $10^3$ fold lower time compared to a powerful desktop computer.

Related papers

• Generalized Hybrid Search and Applications to Blockchain and Hash Function Security [50.16790546184646]
  We first examine the hardness of solving various search problems by hybrid quantum-classical strategies. We then construct a hybrid quantum-classical search algorithm and analyze its success probability.
  arXiv  Detail & Related papers  (2023-11-07T04:59:02Z)
• Solving Graph Problems Using Gaussian Boson Sampling [22.516585968074146]
  We use a noisy intermediate-scale quantum computer to solve graph problems. We experimentally observe the presence of GBS enhancement with large photon-click number and an enhancement under certain noise. Our work is a step toward testing real-world problems using the existing intermediate-scale quantum computers.
  arXiv  Detail & Related papers  (2023-02-02T08:25:47Z)
• Sample efficient graph classification using binary Gaussian boson sampling [0.0]
  We present a variation of a quantum algorithm for the machine learning task of classification with graph-structured data. Our setup only requires binary (light/no light) detectors, as opposed to photon number resolving detectors.
  arXiv  Detail & Related papers  (2023-01-03T17:23:43Z)
• Validation tests of GBS quantum computers give evidence for quantum advantage with a decoherent target [62.997667081978825]
  We use positive-P phase-space simulations of grouped count probabilities as a fingerprint for verifying multi-mode data. We show how one can disprove faked data, and apply this to a classical count algorithm.
  arXiv  Detail & Related papers  (2022-11-07T12:00:45Z)
• A single $T$-gate makes distribution learning hard [56.045224655472865]
  This work provides an extensive characterization of the learnability of the output distributions of local quantum circuits. We show that for a wide variety of the most practically relevant learning algorithms -- including hybrid-quantum classical algorithms -- even the generative modelling problem associated with depth $d=omega(log(n))$ Clifford circuits is hard.
  arXiv  Detail & Related papers  (2022-07-07T08:04:15Z)
• Entanglement and coherence in Bernstein-Vazirani algorithm [58.720142291102135]
  Bernstein-Vazirani algorithm allows one to determine a bit string encoded into an oracle. We analyze in detail the quantum resources in the Bernstein-Vazirani algorithm. We show that in the absence of entanglement, the performance of the algorithm is directly related to the amount of quantum coherence in the initial state.
  arXiv  Detail & Related papers  (2022-05-26T20:32:36Z)
• Certification of Gaussian Boson Sampling via graph theory [4.063872661554895]
  We exploit a connection between photon counting of a genuine Gaussian Boson Sampling device and the number of perfect matchings in a graph. Within this framework, two approaches that exploit the distributions of graph feature vectors and graph kernels are presented.
  arXiv  Detail & Related papers  (2022-02-15T20:22:28Z)
• The Boundary for Quantum Advantage in Gaussian Boson Sampling [44.62475518267084]
  State-of-the-art quantum photonics experiments would require 600 million years to simulate using the best pre-existing classical algorithms. We present substantially faster classical GBS simulation methods, including speed and accuracy improvements. This reduces the run-time of simulating state-of-the-art GBS experiments to several months -- a nine orders of magnitude improvement over previous estimates.
  arXiv  Detail & Related papers  (2021-08-03T16:49:40Z)
• Unsupervised Event Classification with Graphs on Classical and Photonic Quantum Computers [0.0]
  Photonic Quantum Computers provides several benefits over the discrete qubit-based paradigm of quantum computing. We build an anomaly detection model to use on searches for New Physics. We 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.
  arXiv  Detail & Related papers  (2021-03-05T19:02:31Z)
• Hybrid quantum-classical algorithms for approximate graph coloring [65.62256987706128]
  We show how to apply the quantum approximate optimization algorithm (RQAOA) to MAX-$k$-CUT, the problem of finding an approximate $k$-vertex coloring of a graph. We construct an efficient classical simulation algorithm which simulates level-$1$ QAOA and level-$1$ RQAOA for arbitrary graphs.
  arXiv  Detail & Related papers  (2020-11-26T18:22:21Z)
• Quantum Sampling Algorithms for Near-Term Devices [0.0]
  We introduce a family of quantum algorithms that provide unbiased samples by encoding the entire Gibbs distribution. We show that this approach leads to a speedup over a classical Markov chain algorithm. It opens the door to exploring potentially useful sampling algorithms on near-term quantum devices.
  arXiv  Detail & Related papers  (2020-05-28T14:46:20Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.