Zagoskin A M, Savel'ev S, Nori Franco
Frontier Research System, The Institute of Physical and Chemical Research (RIKEN), Wako-shi, Saitama, Japan.
Phys Rev Lett. 2007 Mar 23;98(12):120503. doi: 10.1103/PhysRevLett.98.120503.
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.
我们将绝热量子演化映射到一维气体（佩楚卡斯气体）的经典哈密顿动力学上，并对后者进行数值模拟。从我们对CNOT门模拟的例子可以看出，这种方法既具有启发性又在数值上高效。对于一般类别的哈密顿量，我们表明从初始状态的逃逸概率的增长速度不超过|λ|γ，其中|λ|是绝热参数。除了边缘（底部和顶部）能级外，所有能级的逃逸概率的标度指数γ = 1/2，在边缘能级处γ约< 1/3。原则上，我们的方法可以求解任意大的绝热量子哈密顿量。
