Circuit pedantry
Andreas Blass, Yuri Gurevich
TL;DR
This paper introduces the concept of syntactic circuits with black-box gates to unify Boolean and quantum circuit semantics, focusing on unitary quantum circuits and exploring their commonalities and differences.
Contribution
It formalizes syntactic circuits supporting multiple semantics and analyzes the relationship between Boolean and quantum circuit structures, especially regarding entanglement.
Findings
Syntactic circuits can model both Boolean and quantum semantics.
Quantum semantics generalize Boolean circuits but are complicated by entanglement.
Focus on unitary quantum circuits for formal analysis.
Abstract
Boolean and quantum circuits have commonalities and differences. To formalize the syntactical commonality we introduce syntactic circuits where the gates are black boxes. Syntactic circuits support various semantics. One semantics is provided by Boolean circuits, another by quantum circuits. Quantum semantics is a generalization of Boolean but, because of entanglement, the generalization is not straightforward. We consider only unitary quantum circuits here.
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Taxonomy
TopicsConflict of Laws and Jurisdiction