Quantum chemistry is an important area of application for quantum computation. In particular, quantum algorithms applied to the electronic structure problem promise exact, efficient methods for determination of the electronic energy of atoms and molecules. The Bravyi-Kitaev transformation is a method of mapping the occupation state of a fermionic system onto qubits. This transformation maps the Hamiltonian of n interacting fermions to an Oðlog nÞ-local Hamiltonian of n qubits. This is an improvement in locality over the JordanWigner transformation, which results in an O(n)-local qubit Hamiltonian. We present the Bravyi-Kitaev transformation in detail, introducing the sets of qubits which must be acted on to change occupancy and parity of states in the occupation number basis. We give recursive definitions of these sets and of the transformation and inverse transformation matrices, which relate the occupation number basis and the BravyiKitaev basis. We then compare the use of the Jordan-Wigner and Bravyi-Kitaev Hamiltonians for the quantum simulation of methane using the STO-6G basis.

We develop a generalized framework for constructing many-body-interaction operations either in linear time, or in logarithmic time with a linear number of ancilla qubits. Exact gate decompositions are given in particular for Pauli strings, many-control Toffoli gates, number-and parity-conserving interactions, Unitary Coupled Cluster operations, and sparse matrix generators. We provide a linear time protocol that works by creating a superposition of exponentially many different possible operator strings and then uses dynamical decoupling methodology to undo all the unwanted terms. A logarithmic time protocol overcomes the speed limit of the first by using ancilla registers to condition evolution to the support of the desired many-body interaction before using parallel chaining operations to expand the string length. The two techniques improve substantially on current strategies (reductions in time and space can range from linear to exponential), are applicable to different physical interaction mechanisms such as CNOT, XX, and XX +Y Y , and generalize to a wide range of many-body operators.

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In this work, we test a recently developed method to enhance classical auxiliary-field quantum Monte Carlo (AFQMC) calculations with quantum computers against examples from chemistry and material science, representative of classes of industry-relevant systems. As molecular test cases, we calculate the energy curve of H4 and the relative energies of ozone and singlet molecular oxygen with respect to triplet molecular oxygen, which is industrially relevant in organic oxidation reactions. We find that trial wave functions beyond single Slater determinants improve the performance of AFQMC and allow it to generate energies close to chemical accuracy compared to full configuration interaction or experimental results. In the field of material science, we study the electronic structure properties of cuprates through the quasi-1D Fermi–Hubbard model derived from CuBr2, where we find that trial wave functions with both significantly larger fidelities and lower energies over a mean-field solution do not necessarily lead to AFQMC results closer to the exact ground state energy.