Efficient Application of the Factorized form of the Unitary Coupled-Cluster Ansatz for the Variational Quantum Eigensolver Algorithm by Using Linear Combination of Unitaries

The variational quantum eigensolver is one of the most promising algorithms for near-term computers. It has potential to solve chemistry problems involving strongly correlated electrons with relatively low-depth circuits, which are otherwise difficult on classical eigenstate constructed from a number factorized unitary coupled-cluster terms applied onto an initial (single-reference) state. Current applying these operators state require operations that scale exponentially rank operator. We exploit hidden SU(2) symmetry allow us employ linear combination unitaries approach, Our Prepare subroutine uses n+2 ancilla qubits rank-n Select(U^) scheme O(n)Cnot gates. This results in full algorithm scales like cube operator n3, significant reduction complexity five or higher operators. when combined other lower-rank (when compared standard implementation), will make form approach much more efficient implement all types