Utilizing Mid-circuit Measurements for Quantum Chemistry Initial State Preparation

Future quantum algorithms aiming to compute highly accurate molecular energies, ultraviolet-visible spectra, or other electron-dependent properties rely on the quality of the input electronic state. Initial state preparation is expected to be a crucial aspect to be improved, as it requires a balance between classical and quantum computing resources. Our proposal targets utilizing non-unitary coupled cluster solutions computed on classical computers and generating their corresponding state on a quantum computer for further analysis, such as studying wave function evolution under the time-dependent Schrödinger equation or refining energy estimates with quantum phase estimation (QPE). We compared the accuracy and cost (CNOT and T gate counts) of our method to the unitary coupled-cluster ansatz in the context of a variational quantum eigensolver workflow (VQE-UCC) for several hydrogen chains and small hydrides. Our method produces similar states when considering single and double-electron excitations in the ansatz, while circumventing the need for variational optimization, albeit at the cost of a probabilistic implementation and few ancilla qubits. We further demonstrate that our approach leads to a reduction in the number of CNOT and T gates by an average of 28% and 57%, respectively, compared to the standard VQE-UCCSD protocol.