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 ...

Most of the exact solutions of quantum one-dimensional Hamiltonians are obtained thanks to the success of the Bethe ansatz on its several formulations. According to this ansatz the amplitudes of the eigenfunctions of the Hamiltonian are given by a sum of permutations of appropriate plane waves. In this paper, alternatively, we present a matrix product ansatz that asserts that those amplitudes a...

Quantum computation promises exponential speedup over classical computation by exploiting the quantum mechanical nature of physical processes [1]. In addition to the standard circuit models, surprisingly, local measurement alone provides the same power of computation, given only a prior sufficiently entangled state [2]. Cluster states are the first known resource states for such measurement-bas...

We show that the stochastic dynamics of a large class of one-dimensional interacting particle systems may be presented by integrable quantum spin Hamiltonians. Generalizing earlier work [1, 2] we present an alternative description of these processes in terms of a time-dependent operator algebra with quadratic relations. These relations generate the Bethe ansatz equations for the spectrum and tu...

The (group and spin space) matrix Hamiltonian describing the dynamics of a nonrelativistic spin 1/2 particle moving in a static, but spatially dependent, non-Abelian magnetic field in two spatial dimensions is shown to take the form of an anticommutator of a nilpotent operator and its hermitian conjugate. Consequently, the (group space) matrix Hamiltonians for the two different spin projections...

We describe some field theoretic methods for studying quantum spin systems in one dimension. These include the nonlinear σ-model approach which is particularly useful for large values of the spin, the idea of Luttinger liquids and bosonization which are more useful for small values of spin such as spin-1/2, and the technique of low-energy effective Hamiltonians which can be useful if the system...

Quantum spin liquids are topological states of matter that arise in frustrated quantum magnets at low temperatures. At energies, such exhibit emergent gauge fields and fractionalized quasiparticles can also possess enhanced global symmetries compared to their parent microscopic Hamiltonians. We study the consequences this symmetry structure for hydrodynamics liquids. Specifically, we analyze tw...