Skip to content
DraconiticResearch
Search Sources API
203,203 studies31 sourcesUpdated 4 min ago
PreprintCC BY 4.0arXiv

A Complete Equational Theory for Quantum Circuits with Generalized Control

  • William Schober
  • Scott Wesley
Open at sourcePDFDOICite

Abstract

Controlled subcircuits are commonplace in quantum algorithms as they represent the quantum analogue of branching statements (if then). We introduce a generalization of controlled subcircuits in the form of a binary operation which sends pairs of unitary quantum circuits to a generalized controlled operation, whose semantics are based on matrix exponentials and logarithms. The family of quantum circuits with generalized controlled operations and circuit exponentiation is denoted HQC for Hierarchical Quantum Circuits. We formalize HQC as a modified prop category using a novel category-theoretic construction, and provide a sound and complete equational theory for diagrammatic reasoning in HQC.

Versions

Related

  1. A complete classification for n-species Lotka-Volterra stably dissipative systems based on a generalized AHU algorithm
    Yajia Du, Zhengyi Lu, Jinya Xu +1
    arXivPreprintCC BY 4.0Full textDynamical systemsarXiv
  2. Reliability Analysis of Isolation Structures for Integrated Circuits Based on the Beta Generalized Weibull Distribution
    Wei Cheng, Hongqing Zheng, Wanqing Song +1
    Fractal and FractionalPeer-reviewedCC BY 4.0Analysis & PDEsCrossref
  3. Generalized Functional ANOVA: A Complete Theoretical Framework
    Baptiste Ferrere, Nicolas Bousquet, Fabrice Gamboa +1
    arXivPreprintCC BY 4.0Full textStatisticsarXiv
  4. Complete mapping criteria for generalized Cesàro operators between Hardy spaces
    Pengcheng Tang, Huayou Xie
    arXivPreprintCC BY-NC-SA 4.0Full textAnalysis & PDEsarXiv
  5. Complete Factorial Asymptotics and Integrable Structure of Generalized Charlier Recurrence Coefficients
    Mahouton Norbert Hounkonnou
    arXivPreprintCC BY 4.0Full textMathematical physicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{schober2026complete,
  title = {{A Complete Equational Theory for Quantum Circuits with Generalized Control}},
  author = {William Schober and Scott Wesley},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.07207},
  eprint = {2611.07207},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.07207},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A Complete Equational Theory for Quantum Circuits with Generalized Control
AU  - William Schober
AU  - Scott Wesley
PY  - 2026
DA  - 2026/11/04
PB  - arXiv
DO  - 10.48550/arxiv.2611.07207
UR  - https://arxiv.org/abs/2611.07207
AB  - Controlled subcircuits are commonplace in quantum algorithms as they represent the quantum analogue of branching statements (if then). We introduce a generalization of controlled subcircuits in the form of a binary operation which sends pairs of unitary quantum circuits to a generalized controlled operation, whose semantics are based on matrix exponentials and logarithms. The family of quantum circuits with generalized controlled operations and circuit exponentiation is denoted HQC for Hierarchical Quantum Circuits. We formalize HQC as a modified prop category using a novel category-theoretic construction, and provide a sound and complete equational theory for diagrammatic reasoning in HQC.
ER  -