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QWIRE Practice: Formal Verification of Quantum Circuits in Coq
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We describe an embedding of the QWIRE quantum circuit language in the Coq proof assistant. This allows programmers to write quantum circuits using high-level abstractions and to prove properties of those circuits using Coq's theorem proving features. The implementation uses higher-order abstract syntax to represent variable binding and provides a type-checking algorithm for linear wire types, ensuring that quantum circuits are well-formed. We formalize a denotational semantics that interprets QWIRE circuits as superoperators on density matrices, and prove the correctness of some simple quantum programs.
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ReOC: Compilation of Recursive Quantum Oracles with Recursion-Aware Uncomputation
A compilation framework from the new language RQIMP to the existing RQC++ language compiles recursive quantum oracles with quantum-controlled recursion and adds recursion-aware automatic uncomputation.
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