Commuting Local Hamiltonians on Expanders, Locally Testable Quantum codes, and the qPCP conjecture
Dorit Aharonov, Lior Eldar
TL;DR
This paper explores the properties of commuting local Hamiltonians on expander graphs, their relation to quantum error-correcting codes, and implications for the quantum PCP conjecture, advancing understanding in quantum complexity and physics.
Contribution
It introduces new insights into the structure of commuting local Hamiltonians on expanders and their connection to locally testable quantum codes, contributing to the quantum PCP conjecture.
Findings
New connections between CLHs and quantum codes
Implications for the quantum PCP conjecture
Advances in understanding quantum error correction
Abstract
Understanding commuting local Hamiltonians (CLHs) is at the heart of many questions in quantum computational complexity and quantum physics: quantum error correcting codes, quantum NP, the PCP conjecture, topological order and more.
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