Completeness of Sum-Over-Paths for Toffoli-Hadamard and the Dyadic Fragments of Quantum Computation
| Autor: | Vilmart, Renaud |
|---|---|
| Přispěvatelé: | 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), European Project: 101018180 ,HPCQS(2021) |
| Jazyk: | angličtina |
| Rok vydání: | 2023 |
| Předmět: |
FOS: Computer and information sciences
Quantum Computation Completeness Quantum Physics Computer Science - Logic in Computer Science Sum-Over-Paths Verification FOS: Physical sciences [INFO.INFO-LO]Computer Science [cs]/Logic in Computer Science [cs.LO] Logic in Computer Science (cs.LO) Toffoli-Hadamard Rewrite Strategy TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph] Theory of computation → Quantum computation theory TheoryofComputation_LOGICSANDMEANINGSOFPROGRAMS Computer Science::Logic in Computer Science Theory of computation → Equational logic and rewriting Quantum Physics (quant-ph) |
| Zdroj: | CSL 2023-31st EACSL Annual Conference on Computer Science Logic CSL 2023-31st EACSL Annual Conference on Computer Science Logic, Feb 2023, Warsaw, Poland. pp.36:1--36:17, ⟨10.4230/LIPIcs.CSL.2023.36⟩ |
| DOI: | 10.4230/LIPIcs.CSL.2023.36⟩ |
| Popis: | 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. LIPIcs, Vol. 252, 31st EACSL Annual Conference on Computer Science Logic (CSL 2023), pages 36:1-36:17 |
| Databáze: | OpenAIRE |
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