带截断的无界哈密顿量的量子绝热定理及其在超导电路中的应用
Quantum adiabatic theorem for unbounded Hamiltonians with a cutoff and its application to superconducting circuits
AI总结：
本文提出一种新的量子绝热定理，消除了绝热时间尺度中的 2^n 因子和截断依赖，并将其应用于超导电路，给出通量量子比特的绝热时间尺度对电路参数的显式依赖，同时证明量子退火末段泄漏不可避免。
摘要：
我们提出一个新的量子绝热定理，该定理允许对多种系统（包括由无界哈密顿量描述的系统）的绝热时间尺度进行严格界定。我们的界面向超导电路的量子比特近似，并给出了在 n 个量子比特的电路模型中保持在 2^n 维量子比特子空间内的充分条件。该绝热定理的新颖之处在于，与以往严格结果不同，它在绝热时间尺度中不包含 2^n 作为因子，并且允许获得与电路哈密顿量的无限维希尔伯特空间的截断无关的绝热时间尺度表达式。作为应用，我们给出了超导通量量子比特的该时间尺度对电路参数的显式依赖关系，并证明在量子退火接近结束时，随着隧穿势垒升高，泄漏出量子比特子空间是不可避免的。我们还讨论了一种获得 2^n×2^n 有效哈密顿量的方法，该有效哈密顿量能最佳地近似由缓慢变化的电路控制参数所诱导的真实动力学。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
