Adiabatic Quantum Simulation of Quantum Chemistry

Abstract

We show how to apply the quantum adiabatic algorithm directly to the quantum computation of molecular properties. We describe a procedure to map electronic structure Hamiltonians to 2-body qubit Hamiltonians with a small set of physically realizable couplings. By combining the Bravyi-Kitaev construction to map fermions to qubits with perturbative gadgets to reduce the Hamiltonian to 2-body, we obtain precision requirements on the coupling strengths and a number of ancilla qubits that scale polynomially in the problem size. Hence our mapping is efficient. The required set of controllable interactions includes only two types of interaction beyond the Ising interactions required to apply the quantum adiabatic algorithm to combinatorial optimization problems. Our mapping may also be of interest to chemists directly as it defines a dictionary from electronic structure to spin Hamiltonians with physical interactions.

Exploiting Locality in Quantum Computation for Quantum Chemistry

“…It is not known to show the same direct dependence on the overlap of the initial guess state as QPE, which may allow it to solve different problems than the quantum phase estimation or variational quantum eigensolver in practice. In [51], Babbush et al show how to scalably embed the eigenspectra of molecular Hamiltonians in a programmable physical system so that the adiabatic algorithm can be applied directly. In this scheme, the molecular Hamiltonian is first written in second quantization using fermionic operators.…”

“…In [51], Babbush et al reduce the locality of interaction terms using perturbative gadgets from the "bit-flip" family, first introduced in [53] and later generalized by [54]. In the supplementary material presented in a later paper analyzing the scaling of gadget constructions [55], it is shown that for bit-flip gadgets, λ k+1 /∆ k = O ( ) and…”

Adiabatic state preparation study of methylene

“…In fact, when implementing ASP directly, i.e. when transforming the Hamiltonian to contain at most 2-qubit interactions, the Bravyi-Kitaev approach is crucial for the efficiency of the algorithm [56].…”

“…It turns out that for the efficient direct implementation of the ASP algorithm, the Bravyi-Kitaev transformation, which balances locality of occupation and parity information [54], is essential. When finishing this paper, we have learned about the very recent paper [56], which in detail describes the efficient algorithm relying on the BravyiKitaev transformation. We will therefore not discuss why use of the Jordan-Wigner transformation is not efficient, but rather refer the reader to [56].…”

“…When finishing this paper, we have learned about the very recent paper [56], which in detail describes the efficient algorithm relying on the BravyiKitaev transformation. We will therefore not discuss why use of the Jordan-Wigner transformation is not efficient, but rather refer the reader to [56].…”