An efficient framework for implementing the factorized unitary coupled-cluster ansatz circuit for quantum chemistry on a quantum computer using the linear combination of unitaries

The factorized form of the UCC ansatz can be systematically applied to a single-reference state to generate a variational wavefunction for a molecule that is accurate to chemical accuracy. The cost of the ansatz circuit comes mainly from the number of multi-qubit entanglement gates, which grows rapidly with the number of active spin orbitals. In this work, we propose a new framework for implementing the factorized UCC ansatz by directly simulating its alternative form derived from an exact Euler-like SU(2) operator identity for each UCC factor. We include a detailed method for preparing the ancilla bank, as well as a circuit for the select(U) operator for factorized UCC doubles. We then prove that the scheme works for factorized UCC operators of any rank. This result has the potential to prepare the factorized UCC ansatz on near-term hardware with significantly reduced circuit depth.