门基量子计算的微扰gadget：无子空间限制的非递归构造
Perturbative gadgets for gate-based quantum computing: Non-recursive constructions without subspace restrictions
AI总结：
本文提出了一种通用的非递归、非绝热且无子空间限制的微扰gadget构造方法，将任意多体Hamiltonian编码到三体Hamiltonian的低能子空间中，适用于门基量子计算，并提供了可定制的gadget构造方案。
摘要：
微扰gadget是一种将Hamiltonian的一部分（通常是低能子空间）编码到具有有利性质（例如降低局部性）的不同Hamiltonian中的工具。多年来，人们提出了许多微扰gadget的构造方法。然而，所有这些方法都受到某些限制：要么仅适用于特定类别的Hamiltonian，要么涉及递归来降低局部性，要么仅限于研究gadget Hamiltonian下的时间演化（例如在绝热量子计算中），从而涉及子空间限制。在这项工作中，我们填补了这一空白，引入了一种通用的、非递归的、非绝热的、无子空间限制的微扰gadget构造方法，该方法将任意多体Hamiltonian编码到三体Hamiltonian的低能子空间中，因此适用于门基量子计算。对于包含r项的k体Hamiltonian，我们的构造需要rk个额外量子比特。除了特定的gadget构造外，我们还提供了一种构造类似gadget的方案，该方案可根据不同性质进行定制，对此我们也进行了讨论。
英文摘要：
Perturbative gadgets are a tool to encode part of a Hamiltonian, usually the low-energy subspace, into a different Hamiltonian with favorable properties, for instance, reduced locality. Many constructions of perturbative gadgets have been proposed over the years. Still, all of them are restricted in some ways: Either they apply to some specific classes of Hamiltonians, they involve recursion to reduce locality, or they are limited to studying time evolution under the gadget Hamiltonian, e.g., in the context of adiabatic quantum computing, and thus involve subspace restrictions. In this work, we fill the gap by introducing a versatile universal, non-recursive, non-adiabatic perturbative gadget construction without subspace restrictions, that encodes an arbitrary many-body Hamiltonian into the low-energy subspace of a three-body Hamiltonian and is therefore applicable to gate-based quantum computing. Our construction requires $rk$ additional qubits for a $k$-body Hamiltonian comprising $r$ terms. Besides a specific gadget construction, we also provide a recipe for constructing similar gadgets, which can be tailored to different properties, which we discuss.
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。
