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

arXiv eprints
 Pub Date:
 April 2020
 arXiv:
 arXiv:2004.04151
 Bibcode:
 2020arXiv200404151W
 Keywords:

 Quantum Physics;
 Computer Science  Emerging Technologies