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The variational quantum eigensolver is one of the most promising algorithmsfor near-term quantum computers. It has the potential to solve quantumchemistry problems involving strongly correlated electrons, which are otherwisedifficult to solve on classical computers. The variational eigenstate isconstructed from a number of factorized unitary coupled-cluster terms appliedonto an initial (single-reference) state. Current algorithms for applying oneof these operators to a quantum state require a number of operations thatscales exponentially with the rank of the operator. We exploit a hidden SU($2$)symmetry to allow us to employ the linear combination of unitaries approach,Our \textsc{Prepare} subroutine uses $n+2$ ancilla qubits for a rank-$n$operator. Our \textsc{Select}($\hat U$) scheme uses $\mathcal{O}(n)$\textsc{Cnot} gates. This results in an full algorithm that scales like thecube of the rank of the operator $n^3$, a significant reduction in complexityfor rank five or higher operators. This approach, when combined with otheralgorithms for lower-rank operators (when compared to the standardimplementation, will make the factorized form of the unitary coupled-clusterapproach much more efficient to implement on all types of quantum computers.

symmetry

Efficient application of the factorized form of the unitary  coupled-cluster ansatz for the variational quantum eigensolver algorithm by  using linear combination of unitaries