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.
Highlights
We show how to apply the quantum adiabatic algorithm directly to the quantum computation of molecular properties
AQC has been applied to classical optimization problems that lie in the complexity class NP
AQC has been applied to structured and unstructured search[20,21], search engine ranking[22] and artificial intelligence problems arising in space exploration[23]. Many of these applications follow naturally from the NP-Completeness of determining the ground state energy of classical Ising spin glasses[24]. This creates an equivalence between a large set of computational problems and a set of models in classical physics
Summary
We show how to apply the quantum adiabatic algorithm directly to the quantum computation of molecular properties. AQC has been applied to structured and unstructured search[20,21], search engine ranking[22] and artificial intelligence problems arising in space exploration[23] Many of these applications follow naturally from the NP-Completeness of determining the ground state energy of classical Ising spin glasses[24]. Just as with adiabatic optimization, it does not matter if molecular electronic structure is QMA-Complete so long as the average instance can be solved (or even approximated) efficiently In this case we have considerable heuristic evidence that molecules are able to find their ground state configurations rapidly: these are the configurations in which they naturally occur. The number of distinct integrals scale as O (n4) in the number of molecular orbitals n
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