标题： 量子电路复杂性在早期时间的普适增长 显示英文标题

标题： Universal Early-Time Growth in Quantum Circuit Complexity

摘要： 我们证明了对于任意无时间依赖性的哈密顿量的幺正时间演化算符，量子电路复杂度在早期时服从线性增长，且这一结果独立于基本门和代价度量的选择。偏离线性早期增长的行为源于门的交换代数，并且对任何电路而言均为负值，这降低了线性增长率，从而在早期时对电路复杂度的增长率设定了一个界限。 我们通过将其应用于量子比特系统和谐振子系统（包括耦合和非简谐振子）来说明这一一般性结果。 通过对自由场和相互作用标量场理论在格点上的离散化，我们还能够在连续极限下提取这些场论的早期行为以及复杂度对格点间距的依赖关系，展示了这种方法如何适用于之前难以用现有量子电路复杂度技术研究的系统。 显示英文摘要

摘要： We show that quantum circuit complexity for the unitary time evolution operator of any time-independent Hamiltonian is bounded by linear growth at early times, independent of any choices of the fundamental gates or cost metric. Deviations from linear early-time growth arise from the commutation algebra of the gates and are manifestly negative for any circuit, decreasing the linear growth rate and leading to a bound on the growth rate of complexity of a circuit at early times. We illustrate this general result by applying it to qubit and harmonic oscillator systems, including the coupled and anharmonic oscillator. By discretizing free and interacting scalar field theories on a lattice, we are also able to extract the early-time behavior and dependence on the lattice spacing of complexity of these field theories in the continuum limit, demonstrating how this approach applies to systems that have been previously difficult to study using existing techniques for quantum circuit complexity.