title: Modeling an adiabatic quantum computer via an exact map to a gas of particles.
abstract: We map adiabatic quantum evolution on the classical Hamiltonian dynamics of a 1D gas (Pechukas gas) and simulate the latter numerically. This approach turns out to be both insightful and numerically efficient, as seen from our example of a CNOT gate simulation. For a general class of Hamiltonians we show that the escape probability from the initial state scales no faster than |lambda|gamma, where |lambda| is the adiabaticity parameter. The scaling exponent for the escape probability is gamma=1/2 for all levels, except the edge (bottom and top) ones, where gamma approximately < 1/3. In principle, our method can solve arbitrarily large adiabatic quantum Hamiltonians.
authors.affiliation: Frontier Research System, The Institute of Physical and Chemical Research (RIKEN), Wako-shi, Saitama, Japan.
authors.forename: A M
authors.initials: AM
authors.lastname: Zagoskin
authors.forename: S
authors.initials: S
authors.lastname: Savel'ev
authors.forename: Franco
authors.initials: F
authors.lastname: Nori