论文标题
无界哈密顿量的量子绝热定理，其截止量及其应用于超导电路
Quantum adiabatic theorem for unbounded Hamiltonians with a cutoff and its application to superconducting circuits
论文作者
论文摘要
我们提出了一种新的量子绝热定理，该定理允许人们严格绑定绝热时间尺度的各种系统，包括无限型汉密尔顿人所描述的系统。我们的界限旨在用于超导电路的量子近似，并提出了足够的条件，可以在$ n $ Qubits的电路模型的$ 2^n $维二维Qubit子空间内。这种绝热定理的新颖性是，与以前的严格结果不同，它不包含$ 2^n $作为绝热时间尺度的一个因素，并且它允许人们获得绝热时间表的表达，而与汉密尔顿电路的无限二维希尔伯特空间无关。作为应用程序，我们提出了该时间尺度对超导通量量子的电路参数的明确依赖性，并证明，由于隧道屏障在量子退火的末端升高，因此不可避免地会泄漏量子空间。我们还讨论了一种获得$ 2^n \ times 2^n $有效哈密顿量的方法，该方法最能通过缓慢变化的电路控制参数近似于真正的动力学。
We present a new quantum adiabatic theorem that allows one to rigorously bound the adiabatic timescale for a variety of systems, including those described by unbounded Hamiltonians. Our bound is geared towards the qubit approximation of superconducting circuits, and presents a sufficient condition for remaining within the $2^n$-dimensional qubit subspace of a circuit model of $n$ qubits. The novelty of this adiabatic theorem is that unlike previous rigorous results, it does not contain $2^n$ as a factor in the adiabatic timescale, and it allows one to obtain an expression for the adiabatic timescale independent of the cutoff of the infinite-dimensional Hilbert space of the circuit Hamiltonian. As an application, we present an explicit dependence of this timescale on circuit parameters for a superconducting flux qubit, and demonstrate that leakage out of the qubit subspace is inevitable as the tunnelling barrier is raised towards the end of a quantum anneal. We also discuss a method of obtaining a $2^n\times 2^n$ effective Hamiltonian that best approximates the true dynamics induced by slowly changing circuit control parameters.
