Resource-Optimized Fermionic Local-Hamiltonian Simulation on a Quantum Computer for Quantum Chemistry

The ability to simulate a fermionic system on quantum computer is expected revolutionize chemical engineering, materials design, nuclear physics, name few. Thus, optimizing the simulation circuits of significance in harnessing power computers. Here, we address this problem two aspects. In fault-tolerant regime, optimize $\rzgate$ and $\tgate$ gate counts along with ancilla qubit required, assuming use product-formula algorithm for implementation. We obtain savings ratio eleven number qubits required over state art. pre-fault tolerant two-qubit counts, variational eigensolver (VQE) approach. Specific latter, present framework that enables bootstrapping VQE progression towards convergence ground-state energy system. This framework, based perturbation theory, capable improving estimate at each cycle progression, by about factor three closer known compared standard approach test-bed, classically-accessible water molecule. improved turn results commensurate level resources, such as gates, be within pre-specified tolerance from energy. also explore suite generalized transformations fermion operators show resource-requirement up more than $20\%$, small instances, possible.