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Completeness of Sum-Over-Paths for Toffoli-Hadamard and the Dyadic Fragments of Quantum Computation

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  • معلومة اضافية
    • Contributors:
      Laboratoire Méthodes Formelles (LMF); Institut National de Recherche en Informatique et en Automatique (Inria)-CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Ecole Normale Supérieure Paris-Saclay (ENS Paris Saclay); Quantum Computation Structures (QuaCS); Inria Saclay - Ile de France; Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Méthodes Formelles (LMF); Institut National de Recherche en Informatique et en Automatique (Inria)-CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Ecole Normale Supérieure Paris-Saclay (ENS Paris Saclay)-CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Ecole Normale Supérieure Paris-Saclay (ENS Paris Saclay); Institut National de Recherche en Informatique et en Automatique (Inria); ANR-22-PETQ-0007,EPiQ,Etude de la pile quantique : Algorithmes, modèles de calcul et simulation pour l'informatique quantique(2022); ANR-22-PNCQ-0002,HQI – R&D et Support,Initiative Nationale Hybride HPC Quantique – R&D et Support des communautés(2022); European Project: 101018180 ,HPCQS(2021)
    • بيانات النشر:
      HAL CCSD
    • الموضوع:
      2023
    • الموضوع:
      Warsaw; Poland
    • نبذة مختصرة :
      International audience ; The “Sum-Over-Paths” formalism is a way to symbolically manipulate linear maps that describe quantum systems, and is a tool that is used in formal verification of such systems.We give here a new set of rewrite rules for the formalism, and show that it is complete for “Toffoli-Hadamard”, the simplest approximately universal fragment of quantum mechanics. We show that the rewriting is terminating, but not confluent (which is expected from the universality of the fragment). We do so using the connection between Sum-over-Paths and graphical language ZH-Calculus, and also show how the axiomatisation translates into the latter.Finally, we show how to enrich the rewrite system to reach completeness for the dyadic fragments of quantum computation – obtained by adding phase gates with dyadic multiples of π to the Toffoli-Hadamard gate-set – used in particular in the Quantum Fourier Transform.
    • Relation:
      info:eu-repo/semantics/altIdentifier/arxiv/2205.02600v2; info:eu-repo/grantAgreement//101018180 /EU/High Performance Computer and Quantum Simulator hybrid/HPCQS; hal-03654438; https://hal.science/hal-03654438; https://hal.science/hal-03654438v2/document; https://hal.science/hal-03654438v2/file/SOP-TH.pdf; ARXIV: 2205.02600v2
    • الرقم المعرف:
      10.4230/LIPIcs.CSL.2023.36
    • الدخول الالكتروني :
      https://hal.science/hal-03654438
      https://hal.science/hal-03654438v2/document
      https://hal.science/hal-03654438v2/file/SOP-TH.pdf
      https://doi.org/10.4230/LIPIcs.CSL.2023.36
    • Rights:
      info:eu-repo/semantics/OpenAccess
    • الرقم المعرف:
      edsbas.C3914B90