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arXiv · 2003.07351

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

Artur F. Izmaylov·Manuel Díaz-Tinoco·Robert A. Lang
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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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Artur F. Izmaylov, Manuel Díaz-Tinoco, Robert A. Lang. 2020-03-16. On the order problem in construction of unitary operators for the Variational Quantum Eigensolver. https://doi.org/10.1039/d0cp01707h

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