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 fault-tolerant regime, we optimize the $\rzgate$ gate counts and depths, assuming the use of a product-formula algorithm for implementation. In the pre-fault tolerant regime, we optimize the two-qubit gate counts, assuming the use of variational quantum eigensolver (VQE) approach. Specifically to the latter, we present a framework that enables bootstrapping the VQE progression towards the convergence of the ground-state energy of the fermionic system. This framework, based on perturbation theory, also improves the energy estimate at each cycle of the VQE progression dramatically, resulting in significant savings of quantum resources required to be within a pre-specified tolerance from the known ground-state energy in the test-bed, classically-accessible system of the water molecule. We also explore a suite of generalized transformations of fermion to qubit operators and show that resource-requirement savings of up to nearly 20\% is possible.

}, url = {https://arxiv.org/abs/2004.04151}, author = {Qingfeng Wang and Ming Li and Christopher Monroe and Yunseong Nam} }