Graph theory-based automated quantum algorithm for efficient querying of acyclic and multiloop causal configurations

• URL: http://arxiv.org/abs/2508.04019v1
• Date: Wed, 06 Aug 2025 02:18:08 GMT
• Title: Graph theory-based automated quantum algorithm for efficient querying of acyclic and multiloop causal configurations
• Authors: Salvador A. Ochoa-Oregon, Juan P. Uribe-Ramírez, Roger J. Hernández-Pinto, Selomit Ramírez-Uribe, Germán Rodrigo,
• Abstract summary: We present the Minimum Clique-optimised quantum algorithm (MCA), an automated quantum algorithm designed to efficiently query the causal structures within the Loop-Tree Duality.<n>The MCA quantum algorithm is optimised by exploiting graph theory techniques, specifically, by analogy with the Minimum Clique Partition problem.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum algorithms provide a promising framework in high-energy physics, in particular, for unraveling the causal configurations of multiloop Feynman diagrams by identifying Feynman propagators with qubits, a challenge analogous to querying directed acyclic graphs in graph theory. In this paper, we present the Minimum Clique-optimised quantum Algorithm (MCA), an automated quantum algorithm designed to efficiently query the causal structures within the Loop-Tree Duality. The MCA quantum algorithm is optimised by exploiting graph theory techniques, specifically, by analogy with the Minimum Clique Partition problem. The evaluation of the MCA quantum algorithm is exhibited by analysing the transpiled quantum circuit depth and quantum circuit area.

Related papers

• Quantum querying based on multicontrolled Toffoli gates for causal Feynman loop configurations and directed acyclic graphs [0.0]
  We present a quantum algorithm for querying in both types of applications.<n>The efficiency of the algorithm is evaluated by comparison with a quantum algorithm based on binary clauses.<n>We explicitly analyse three-, four- and five-eloop topologies, which have not previously been explored.
  arXiv  Detail & Related papers  (2024-04-04T15:51:43Z)
• Quantum Subroutine for Variance Estimation: Algorithmic Design and Applications [80.04533958880862]
  Quantum computing sets the foundation for new ways of designing algorithms. New challenges arise concerning which field quantum speedup can be achieved. Looking for the design of quantum subroutines that are more efficient than their classical counterpart poses solid pillars to new powerful quantum algorithms.
  arXiv  Detail & Related papers  (2024-02-26T09:32:07Z)
• Lightcone Bounds for Quantum Circuit Mapping via Uncomplexity [1.0360348400670518]
  We show that a minimal SWAP-gate count for executing a quantum circuit on a device emerges via the minimization of the distance between quantum states. This work constitutes the first use of quantum circuit uncomplexity to practically-relevant quantum computing.
  arXiv  Detail & Related papers  (2024-02-01T10:32:05Z)
• A multiple-circuit approach to quantum resource reduction with application to the quantum lattice Boltzmann method [39.671915199737846]
  We introduce a multiple-circuit algorithm for a quantum lattice Boltzmann method (QLBM) solve of the incompressible Navier--Stokes equations.<n>The presented method is validated and demonstrated for 2D lid-driven cavity flow.
  arXiv  Detail & Related papers  (2024-01-20T15:32:01Z)
• Quantum Clustering with k-Means: a Hybrid Approach [117.4705494502186]
  We design, implement, and evaluate three hybrid quantum k-Means algorithms. We exploit quantum phenomena to speed up the computation of distances. We show that our hybrid quantum k-Means algorithms can be more efficient than the classical version.
  arXiv  Detail & Related papers  (2022-12-13T16:04:16Z)
• Quantum Algorithm for Querying Causality of Multiloop Scattering Amplitudes [0.0]
  The first application of a quantum algorithm to Feynman loop integrals is reviewed. The two on-shell states of a Feynman propagator are naturally encoded in a qubit. The problem to be addressed is the identification of the causal singular configurations of multiloop Feynman diagrams.
  arXiv  Detail & Related papers  (2022-11-10T11:12:10Z)
• Variational quantum eigensolver for causal loop Feynman diagrams and directed acyclic graphs [0.0]
  We present a variational quantum eigensolver (VQE) algorithm for the efficient bootstrapping of the causal representation of multiloop Feynman diagrams. A loop Hamiltonian based on the adjacency matrix describing a multiloop topology, and whose different energy levels correspond to the number of cycles, is minimized by VQE to identify the causal or acyclic configurations.
  arXiv  Detail & Related papers  (2022-10-24T13:42:53Z)
• Compilation of algorithm-specific graph states for quantum circuits [55.90903601048249]
  We present a quantum circuit compiler that prepares an algorithm-specific graph state from quantum circuits described in high level languages. The computation can then be implemented using a series of non-Pauli measurements on this graph state.
  arXiv  Detail & Related papers  (2022-09-15T14:52:31Z)
• 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)
• Quantum Optimization of Maximum Independent Set using Rydberg Atom Arrays [39.76254807200083]
  We experimentally investigate quantum algorithms for solving the Maximum Independent Set problem. We find the problem hardness is controlled by the solution degeneracy and number of local minima. On the hardest graphs, we observe a superlinear quantum speedup in finding exact solutions.
  arXiv  Detail & Related papers  (2022-02-18T19:00:01Z)
• Benchmarking Small-Scale Quantum Devices on Computing Graph Edit Distance [52.77024349608834]
  Graph Edit Distance (GED) measures the degree of (dis)similarity between two graphs in terms of the operations needed to make them identical. In this paper we present a comparative study of two quantum approaches to computing GED.
  arXiv  Detail & Related papers  (2021-11-19T12:35:26Z)
• Synthesis of Quantum Circuits with an Island Genetic Algorithm [44.99833362998488]
  Given a unitary matrix that performs certain operation, obtaining the equivalent quantum circuit is a non-trivial task. Three problems are explored: the coin for the quantum walker, the Toffoli gate and the Fredkin gate. The algorithm proposed proved to be efficient in decomposition of quantum circuits, and as a generic approach, it is limited only by the available computational power.
  arXiv  Detail & Related papers  (2021-06-06T13:15:25Z)
• Quantum algorithm for Feynman loop integrals [0.0]
  We present a novel benchmark application of a quantum algorithm to Feynman loop integrals. The two on-shell states of a Feynman propagator are identified with the two states of a qubit. A quantum algorithm is used to unfold the causal singular configurations of multiloop Feynman diagrams.
  arXiv  Detail & Related papers  (2021-05-18T17:41:56Z)

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.