What question did this study set out to answer?

This research aims to demonstrate that quantum circuit topology is equivalent to classical network topology through mathematical frameworks.

March 31, 20260 citationsOpen Access

Quantum Circuit Topology Reduces to Classical Transfer Matrices: 24 Theorems on Controlled-Unitary Networks

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MMattson

Key Points

This research aims to demonstrate that quantum circuit topology is equivalent to classical network topology through mathematical frameworks.
Proving 24 theorems connecting quantum and classical topologies.
Conducting over 42,000 tests to validate the findings without any failures.
Developing a topology-aware compiler to enhance network performance by 35%.
Establishment of a universal 4x4 transfer matrix connecting both topologies.
Achieved a 35% improvement in SWAP-count through the new compiler.
Validated hardware compatibility using partial IBM Torino verification.

Abstract

We prove that quantum circuit topology and classical network topology are the same mathematical object, connected by a universal 4x4 transfer matrix with bond dimension 4=2x2. Twenty-four theorems, 42,000+ tests, zero failures. Includes topology-aware compiler (35% improvement over SWAP-count) and partial IBM Torino hardware verification. Paper v17.

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Cite This Study

Mattson (Sun,) studied this question.

synapsesocial.com/papers/69cb6589e6a8c024954b98f5 https://doi.org/https://doi.org/10.5281/zenodo.19313358

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