论文标题
基于哈密顿最小化的计算量子模型的数学结构
On the mathematical structure of quantum models of computation based on Hamiltonian minimisation
论文作者
论文摘要
确定自旋汉密尔顿人的基态的性质仍然是连接数学，理论和应用物理学学科的中心相关性的话题。在过去的几十年中，物理系统的基态特性越来越被视为计算资源。本文开发了数学设备的一部分，以创建（程序）基础状态与量子和经典计算相关。本文（现在已经过去了十年）中提出的核心发现，包括（i）逻辑操作（门）可以嵌入Ising旋转的低能力部门中，而三个（及更高的）体型交互项可以通过2和1-body Ising术语的最小化来模仿，但需要对iSing ising slack sallake sallake sblack spindsss进行介绍； （ii）扰动理论的小工具能够仿真给定的汉密尔顿人中不存在的相互作用，例如，可以从$ zz $，$ xx $中实现〜$ yy $互动，该论文包含2007年的结果，该论文的结果表明，物理上相关的两体模型Hamiltonian患有QMA HADD STAND STATE ENTARE ENGENT STATE能源决策问题。与其他结果合并，确定这些模型为基态量子计算提供了通用资源。最新的发现包括以下证据：当代量子算法的理想化版本可以实现量子计算的通用模型。其他相关的结果也与基态量子计算相关，并通过量子电路最小化哈密顿量。涵盖的主题包括：iSing模型降低，图形上的随机与量子过程，量子门和电路，作为张量网络，变异量子算法和汉密尔顿小工具。
Determining properties of ground states of spin Hamiltonians remains a topic of central relevance connecting disciplines of mathematical, theoretical and applied physics. In the last few decades, ground state properties of physical systems have been increasingly considered as computational resources. This thesis develops parts of the mathematical apparatus to create (program) ground states relevant for quantum and classical computation. The core findings presented in this thesis (now over a decade old) including that (i) logic operations (gates) can be embedded into the low-energy sector of Ising spins whereas three (and higher) body Ising interaction terms can be mimicked through the minimisation of 2- and 1-body Ising terms yet require the introduction of slack spins; (ii) Perturbation theory gadgets enable the emulation of interactions not present in a given Hamiltonian, e.g.~$YY$ interactions can be realized from $ZZ$, $XX$, the thesis contains a result from 2007 showing that physically relevant two-body model Hamiltonian's have a QMA-hard ground state energy decision problem. Merged with other results, this established that these models provide a universal resource for ground state quantum computation. More recent findings include the proof that an idealised version of the contemporary variational approach to quantum algorithms enables a universal model of quantum computation. Other related results are also presented as they relate to ground state quantum computation and the minimisation of Hamiltonians by quantum circuits. The topics covered include: Ising model reductions, stochastic versus quantum processes on graphs, quantum gates and circuits as tensor networks, variational quantum algorithms and Hamiltonian gadgets.
