标题： 量子电路复杂度的普遍早期增长 显示英文标题

标题： Universal Early-Time Growth in Quantum Circuit Complexity

摘要： 我们证明，对于任何时间独立哈密顿量的幺正时间演化算子，量子电路复杂度在早期时间是线性增长的，这与基本门的选择或成本度量无关。 早期时间增长偏离线性增长是由门的对易代数引起的，并且对于任何电路来说都是明显负的，从而降低了线性增长速率，并导致了早期时间电路复杂度增长速率的界限。 我们通过将这一一般结果应用于自旋和谐振子系统，包括耦合和非谐振子系统来说明这一结果。 通过对格点上的自由和相互作用标量场理论进行离散化，我们还能够提取这些场理论在连续极限下的早期时间行为和与格点间距的依赖关系，展示了这种方法如何应用于之前难以使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 linear in time 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.