Beyond Ansätze: Learning Quantum Circuits as Unitary Operators

03/01/2022

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by   Bálint Máté, et al.

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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.