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

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.

References in corpus (2)

• Exact Parameterization of Fermionic Wave Functions via Unitary Coupled Cluster Theory
• Ordering of Trotterization: Impact on Errors in Quantum Simulation of Electronic Structure

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