Beyond Ans\"atze: Learning Quantum Circuits as Unitary Operators

• URL: http://arxiv.org/abs/2203.00601v2
• Date: Thu, 3 Mar 2022 17:32:10 GMT
• Title: Beyond Ans\"atze: Learning Quantum Circuits as Unitary Operators
• Authors: B\'alint M\'at\'e, Bertrand Le Saux, Maxwell Henderson
• Abstract summary: We run gradient-based optimization in the Lie algebra $mathfrak u(2N)$. We argue that $U(2N)$ is not only more general than the search space induced by ansatz, but in ways easier to work with on classical computers.
• Score: 30.5744362478158
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $\mathfrak u(2^N)$ 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 ans\"atze on $N$ wires.

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