Using Hoare logic for quantum circuit optimization

By employing quantum mechanical phenomena such as superposition, entanglement, and interference, quantum computers promise to perform certain computations exponentially faster than any classical device. Precise control over these physical systems and proper shielding from unwanted interactions with the environment become more difficult as the space/time volume of the computation grows. Code optimization is thus crucial in order to reduce resource requirements to the greatest extent possible. Besides manual optimization, previous work has successfully adapted classical methods such as constant-folding and common subexpression elimination to the quantum domain. However, such classically-inspired methods fail to exploit certain optimization opportunities that arise due to entanglement. To address this insufficiency, we introduce an optimization methodology which employs Hoare triples in order to identify and exploit these optimization opportunities. We implement the optimizer using the Z3 Theorem Prover and the ProjectQ software framework for quantum computing and show that it is able to reduce the circuit area of our benchmarks by up to 5x.