Verified compilation of Quantum oracles

Quantum algorithms often apply classical operations, such as arithmetic or predicate checks, over a quantum superposition of data; these so-called oracles are the largest components program. To ease construction efficient, correct oracle functions, this paper presents VQO, high-assurance framework implemented with Coq proof assistant. The core VQO is OQASM, assembly language. OQASM operations move qubits between two different bases via Fourier transform, thus admitting important optimizations, but without inducing entanglement and exponential blowup that comes it. OQASM’s design enabled us to prove VQO’s compilers—from simple imperative language called OQIMP from SQIR, general-purpose language—and allowed efficiently test properties programs using QuickChick property-based testing framework. We have used implement variety geometric operators building blocks for oracles, including those in Shor’s Grover’s algorithms. found QFT-based require fewer qubits, sometimes substantially fewer, than constructed “classical” gates; versions latter were nevertheless on par better (in terms both qubit gate counts) produced by Quipper, state-of-the-art unverified programming platform.