Beyond Ansätze: Learning Quantum Circuits as Unitary Operators

Abstract

This paper explores the advantages of optimizing quantum circuits on 𝑁 wires as operators in the unitary group 𝑈 (2 𝑁 ). We run gradient-based optimization in the Lie algebra 𝔲(2 𝑁 ) and use the exponential map to parametrize unitary matrices. We argue that 𝑈 (2 𝑁 ) is not only more general than the search space induced by an ansatz, but in ways easier to work with on classical computers. The resulting approach is quick, ansatz-free and provides an upper bound on performance over all ansätze on 𝑁 wires.