发表机构
Qilimanjaro Quantum Tech.; Universitat de Barcelona (UB)（乞力马扎罗量子科技公司; 巴塞罗那大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明非单调时变全局横向场伊辛模型可在多项式时间内模拟任意量子电路，从而建立其与门模型的等价性，并推导出经典模拟的不可行性。
AI 中文摘要
近年来，横向场伊辛模型引起了广泛关注，尤其是在量子模拟和量子计算文献中。这种兴趣源于许多模拟量子计算平台，它们实现横向场伊辛模型以解决优化问题，如量子退火。然而，具有全局横向场的伊辛模型是否等价于量子计算的门模型仍然是一个开放问题。本文对非单调时变横向场的情况给出了肯定回答。基于Cesa和Pichler最近关于里德伯原子全局控制的结果，我们提供了一种构造，允许使用具有全局横向场的伊辛模型模拟任意量子电路，其时间、量子比特数和能量标度的开销为多项式。尽管我们建立的多项式开销相对于实际量子硬件上可行的方案较大，但我们的结果激励了使用具有全局横向场的伊辛模型模拟量子电路的更复杂方法的发展。此外，在假设量子计算严格强于经典计算的前提下，我们的结果可作为具有时变全局横向场的横向场伊辛模型无法被高效经典模拟的不可行定理。因此，我们的发现与多个领域相关，从模拟量子模拟和多种平台上的量子优化到复杂性和控制理论。
英文摘要
The transverse-field Ising model has attracted a lot of attention in recent years, especially in the quantum simulation and quantum computation literature. This interest is driven by many platforms for analog quantum computation, which implement the transverse-field Ising model for solving optimization problems, such as quantum annealing. However, it has remained an open question whether the Ising model with a global transverse field is equivalent to the gate model of quantum computation. Here we answer this question affirmatively for the case of a non-monotonic time-dependent transverse field. Building on a recent result by Cesa and Pichler on global control of Rydberg atoms, we provide a construction that allows simulating arbitrary quantum circuits using the Ising model with global transverse field with polynomial overhead in time, qubit number, and energy scale. Although the polynomial overheads we establish here are large relative to what is feasible on real-world quantum hardware, our result motivates the development of more sophisticated methods for simulating quantum circuits using the Ising model with a global transverse field. Additionally, under the assumption that quantum computing is strictly more powerful than classical computing, our result serves as a no-go theorem for efficient classical simulation of the transverse-field Ising model with a time-dependent global transverse field. Therefore, our finding is relevant for multiple communities, from analog quantum simulation and quantum optimization on various platforms to complexity and control theory.
Comments38 pages, 5 figures
