Adiabatic state preparation study of methylene

Abstract

Quantum computers attract much attention as they promise to outperform their classical counterparts in solving certain type of problems. One of them with practical applications in quantum chemistry is simulation of complex quantum systems. An essential ingredient of efficient quantum simulation algorithms are initial guesses of the exact wave functions with high enough fidelity. As was proposed in [Aspuru-Guzik et al., Science 309, 1704], the exact ground states can in principle be prepared by the adiabatic state preparation method. Here, we apply this approach to preparation of the lowest lying multireference singlet electronic state of methylene and numerically investigate preparation of this state at different molecular geometries. We then propose modifications that lead to speeding up the preparation process. Finally, we decompose the minimal adiabatic state preparation employing the direct mapping in terms of two-qubit interactions.

Exploiting Locality in Quantum Computation for Quantum Chemistry

“…Some of these results have already appeared in the quantum computation literature in the context of in depth studies of state preparation [24,25]. A general review of quantum simulation [26,27] and one on quantum computation for chemistry [28] cover these topics in more depth.…”

“…Moreover, one would not expect the problem to be easier in general cases where interactions between subsystems are allowed. As a result, further developments in variational methods [13], quantum cooling [50], and adiabatic state preparation [7,25,51] will be of key importance in this area. Moreover improvements in the ansatze used to prepare the wave function such as multi-configurational self consistent field calculations(MCSCF) [24,25] or unitary coupled cluster (UCC) [10] will be integral parts of any practical quantum computing for quantum chemistry effort.…”

“…Their argument is based on the observation that molecular systems are typically stable in their electronic ground states and the natural processes which produce these states should be efficient to simulate with a quantum device. Subsequently, Veis and Pittner analyzed adiabatic state preparation for a set of small chemical systems and observed that for all configurations of these systems, the minimum gap occurs at the very end of the evolution when the state preparation is initialized in an eigenstate given by a CAS (complete active space) ground state [25]. The notion that the minimum gap could be bounded by the physical HOMO (highest occupied molecular orbital) -LUMO (lowest unoccupied molecular orbital) gap lends support to the hypothesis put forward by Babbush et al…”

Hamiltonian gadgets with reduced resource requirements

“…Apart from the physical relevance to quantum computation, gadgets have been central to many results in quantum complexity theory [4,8,11,12]. Hamiltonian gadgets were also used to characterize the complexity of density functional theory [13] and are required components in current proposals related to error correction on an adiabatic quantum computer [14] and the adiabatic and ground state quantum simulator [9,10]. Since these works employ known gadgets which we provide improved constructions of here, our results hence imply a reduction of the resources required in these past works.…”

“…Oliveira and Terhal further reduced the problem, showing completeness when otherwise arbitrary 2-body Hamiltonians were restricted to act on a square lattice [3]. The form of the simplest QMA-complete Hamiltonian is reduced to physically relevant models in [4] (see also [8]), e.g.Although this model contains only physically accessible terms, programming problems into a universal adiabatic quantum computer [4] or an adiabatic quantum simulator [9,10] involves several types of kbody interactions (for bounded k). To reduce from k-body interactions to 2-body is accomplished through * cao23@purdue.…”