PreprintCC BY 4.0arXiv
Simplification Rules for Continuous-Time Quantum Walks on Dynamic Graphs
Abstract
Continuous-time quantum walks (CTQWs) on dynamic graphs realize quantum gates as sequences of time-evolving graph Hamiltonians, but naive constructions produce long sequences with redundancy. Simplification rules, which are graph rewrite rules that shorten a dynamic graph sequence while preserving the unitary it implements, are the CTQW analogue of circuit identities in the gate model. In this work, we give CTQW realizations of the standard single-qubit gates and introduce new graph rewrite rules. We demonstrate the simplification rules through worked circuit reductions and outline their use as transpilation primitives for converting between the circuit model and the dynamic graph framework.
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BibTeX
@misc{atallah2026simplification,
title = {{Simplification Rules for Continuous-Time Quantum Walks on Dynamic Graphs}},
author = {Mostafa Atallah and Daniel Dilley and Jishnu Mahmud and Zain H Saleem and Rebekah Herrman},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18463},
eprint = {2609.18463},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18463},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Simplification Rules for Continuous-Time Quantum Walks on Dynamic Graphs
AU - Mostafa Atallah
AU - Daniel Dilley
AU - Jishnu Mahmud
AU - Zain H Saleem
AU - Rebekah Herrman
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.18463
UR - https://arxiv.org/abs/2609.18463
AB - Continuous-time quantum walks (CTQWs) on dynamic graphs realize quantum gates as sequences of time-evolving graph Hamiltonians, but naive constructions produce long sequences with redundancy. Simplification rules, which are graph rewrite rules that shorten a dynamic graph sequence while preserving the unitary it implements, are the CTQW analogue of circuit identities in the gate model. In this work, we give CTQW realizations of the standard single-qubit gates and introduce new graph rewrite rules. We demonstrate the simplification rules through worked circuit reductions and outline their use as transpilation primitives for converting between the circuit model and the dynamic graph framework.
ER -