.png){kind=icon}
.png){kind=icon}
Return
Quantum algorithms for equational reasoning
.png){kind=icon}
OA
AI
DOI：10.1126/sciadv.aec2736.png)
.png){kind=icon}
Original request for help.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
As a cornerstone of automated reasoning, equational reasoning finds equivalences between symbolic expressions and fuels advances across scientific disciplines. Yet, its potential remains limited by the exponential growth of equivalent expressions with increasing problem size. We introduce quantum normal form reduction, a quantum computational framework designed to address this challenge. We construct an efficiently implementable quantum Hamiltonian whose ground state encodes all equivalent expressions in a quantum superposition. By preparing and manipulating these states, we tackle fundamental problems in equational reasoning, including verifying and counting equivalent expressions and identifying structural properties of equivalence classes. We demonstrate a quantum-inspired version of the algorithm using tensor networks to solve instances involving up to 1028 equivalent expressions, far beyond the reach of classical graph exploration. This framework opens the path for quantum symbolic computation in areas from circuit design to data compression, computational group theory, linguistics, and macromolecular modeling, unlocking previously inaccessible problems.
Keywords:
quantum algorithms
equational reasoning
symbolic computation
quantum Hamiltonian
tensor networks
Journal
IF:
12.5
Papers:
2.0W
Citations:
18.1W