Modeling an Adiabatic Quantum Computer via an Exact Map to a Gas of Particles
Alexandre M. Zagoskin, Sergey E. Savel'ev, Franco Nori · Physical Review Letters · 2007
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 $|\stackrel{\ifmmode \dot{}\else \textperiodcentered \fi{}}{\ensuremath{\lambda}}{|}^{\ensuremath{\gamma}}$, where $|\stackrel{\ifmmode \dot{}\else \textperiodcentered \fi{}}{\ensuremath{\lambda}}|$ is the adiabaticity parameter. The scaling exponent for the escape probability is $\ensuremath{\gamma}=\frac{1}{2}$ for all levels, except the edge (bottom and top) ones, where $\ensuremath{\gamma}\ensuremath{\lesssim}\frac{1}{3}$. In principle, our method can solve arbitrarily large adiabatic quantum Hamiltonians.