Beyond Ans\" atze: Learning Quantum Circuits as Unitary Operators
arXiv preprint arXiv:2203.00601, 2022•arxiv.org
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 …
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 …
This paper explores the advantages of optimizing quantum circuits on wires as operators in the unitary group . We run gradient-based optimization in the Lie algebra and use the exponential map to parametrize unitary matrices. We argue that 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 wires.
arxiv.org
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