Abstract
We propose to use a quantum adiabatic and simulated-annealing framework to compute theground state of small molecules. The initial Hamiltonian of our algorithms is taken to be themaximum commuting Hamiltonian that consists of a maximal set of commuting terms in the fullHamiltonian of molecules in the Pauli basis. We consider two variants. In the first method, weperform the adiabatic evolution on the obtained time- or path-dependent Hamiltonian with theinitial state as the ground state of the maximum commuting Hamiltonian. However, this methoddoes suffer from the usual problems of adiabatic quantum computation due to degeneracy andenergy-level crossings along the Hamiltonian path. This problem is mitigated by a Zeno method,i.e., via a series of eigenstate projections used in the quantum simulated annealing, with the path-dependent Hamiltonian augmented by a sum of Pauli X terms, whose contribution vanishes at thebeginning and the end of the path. In addition to the ground state, the low lying excited states canbe obtained using this quantum Zeno approach with equal accuracy to that of the ground state.
Highlights
Quantum chemistry concerns the application of quantum mechanics to chemical properties of physical systems, including their electronic structure, spectroscopy, and dynamics [1,2]
In our consideration of molecular Hamiltonians, we find that those terms in the maximum commuting (MC) set are all of the form of a product of Pauli Z and identity operators with a certain weight, such as c I ⊗ σ z ⊗ σ z ⊗ · · · ⊗ I
We note that the simulation of an iterative quantum phase estimation for the ground-state energy of LiH was done in Ref. [10] and the implementation of the variational quantum eigensolver (VQE) on quantum computers was presented in Ref. [15]
Summary
Quantum chemistry concerns the application of quantum mechanics to chemical properties of physical systems, including their electronic structure, spectroscopy, and dynamics [1,2]. Our first variant is the usual adiabatic quantum computation with such a time-dependent Hamiltonian This approach of quantum adiabatic evolution (QAE) yields accurate results of molecular ground-state energies around the equilibrium atomic position or with small perturbations of the bond length, but not at the limit of bond breaking, which is due to the degeneracy of ground and excited states, as well as energylevel crossings. Even though the resultant path-dependent Hamiltonian may not necessarily yield better results under adiabatic evolution, its use in the setting of the quantum simulated annealing [31] does improve the obtained ground-state energy This last is our second variant, which drives the computation via the quantum Zeno-like projection (QZP) to eigenstates of the instantaneous Hamiltonian along the path at discrete time steps [31,32,33].
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