On the order problem in construction of unitary operators for the Variational Quantum Eigensolver

• URL: http://arxiv.org/abs/2003.07351v3
• Date: Tue, 19 May 2020 14:13:13 GMT
• Title: On the order problem in construction of unitary operators for the Variational Quantum Eigensolver
• Abstract summary: One of the main challenges in the Variational Quantum Eigensolver (VQE) framework is construction of the unitary transformation. We propose an approach based on the Lie algebra - Lie group connection and corresponding closure relations that systematically eliminates the order problem.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: One of the main challenges in the Variational Quantum Eigensolver (VQE) framework is construction of the unitary transformation. The dimensionality of the space for unitary rotations of $N$ qubits is $4^N-1$, which makes the choice of a polynomial subset of generators exponentially difficult process. Moreover, due to non-commutativity of generators, the order in which they are used strongly affects results. Choosing the optimal order in a particular subset of generators requires testing the factorial number of combinations. We propose an approach based on the Lie algebra - Lie group connection and corresponding closure relations that systematically eliminates the order problem.

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