用微扰小工具简化量子双哈密顿量

拓扑量子码的非微扰小工具

Non-perturbative gadget for topological quantum codes

多体纠缠系统，特别是拓扑有序的自旋系统被提出作为量子信息处理任务的资源，通常涉及高度非局域相互作用项。虽然可以通过微扰的两体相互作用来近似这样的系统，但是这些方法在实践中具有许多缺点。在这里，我们提出了一个方案来模拟多体自旋哈密顿与两体哈密顿非微扰。与以前的方法不同，我们的哈密顿量不仅是精确的基态简并精确可解，而且还支持完全局域化的准粒子激发，这是理想的量子信息处理任务。我们的构造仅限于模拟复曲面码和量子双模型，但推广到其他非局域自旋哈密顿量是可能的。

通过在物质相内插值得到多项式交互强度的类量子模拟

Analogue quantum simulation with polylogarithmic interaction strengths by extrapolating within phases of matter

本文通过在物质相内插值得到多项式交互强度的类量子模拟，展示如何通过经典后处理减少非临界系统所需的交互强度缩放。

二维晶格上局部stoquastic哈密顿量的复杂性

The Complexity of Local Stoquastic Hamiltonians on 2D Lattices

研究证明二维正方形量子比特晶格上的2-局部stoquastic哈密顿量问题属于StoqMA完备问题，通过扩展Oliveira和Terhal的空间稀疏电路构造以及Bravyi等人扰动工具，展示空间稀疏StoqMA电路和无粒子维度增加的几何扰动工具的构建。

Simulating highly nonlocal Hamiltonians with less nonlocal Hamiltonians

The need for Hamiltonians with many-body interactions arises in various applications of quantum computing. However, interactions beyond two-body are difficult to realize experimentally. Perturbative gadgets were introduced to obtain arbitrary many-body effective interactions using Hamiltonians with two-body interactions only. Although valid for arbitrary $k$-body interactions, their use is limited to small $k$ because the strength of interaction is $k$'th order in perturbation theory. In this paper we develop a nonperturbative technique for obtaining effective $k$-body interactions using Hamil…

Perturbative 2-body Parent Hamiltonians for Projected Entangled Pair States

We construct parent Hamiltonians involving only local 2-body interactions for a broad class of Projected Entangled Pair States (PEPS). Making use of perturbation gadget techniques, we define a perturbative Hamiltonian acting on the virtual PEPS space with a finite order low energy effective Hamiltonian that is a gapped, frustration-free parent Hamiltonian for an encoded version of a desired PEPS. For topologically ordered PEPS, the ground space of the low energy effective Hamiltonian is shown to be in the same phase as the desired state to all orders of perturbation theory. An encoded parent H…

关于引导式Berry相位估计的计算复杂性

On the Computational Complexity of Guided Berry Phase Estimation

本文证明给定与基态有重叠的引导态时，判定2-局域量子比特哈密顿量的Berry相位是BQP完全的，并扩展到加权海森堡相互作用及二维晶格，利用Schrieffer-Wolff变换建立1-局域与2-局域间的复杂性转变。

EPR哈密顿量中的复杂性相变

A complexity phase transition at the EPR Hamiltonian

研究2局部哈密顿量问题的计算复杂性，发现其属于三种复杂性阶段：QMA完全、StoqMA完全和可归约至新问题EPR*。EPR*问题被推测在BPP中，从而完成复杂性分类。

量子化学的绝热量子模拟

Adiabatic Quantum Simulation of Quantum Chemistry

我们展示了如何将量子绝热算法直接应用于分子性质的量子计算。我们描述了一个程序，以映射电子结构的哈密顿量的2-本地量子比特哈密顿量与一个小的物理可实现的耦合。通过结合Bravyi-Kitaev构造将费米子映射到量子位，并使用微扰小工具将哈密顿量降低到2-本地，我们获得了耦合强度和一些辅助量子位的精度要求，这些量子位在问题大小中呈多项式形式。因此，我们的映射是有效的。所需的一组可控的相互作用，包括只有两种类型的相互作用以外的伊辛相互作用所需的量子绝热算法的组合优化问题。我们的映射也可能是化学家直接感兴趣的，因为它定义了一个字典，从电子结构到自旋哈密顿与物理相互作用。

Precision of quantum simulation of all-to-all coupling in a local architecture

We present a simple 2d local circuit that implements all-to-all interactions via perturbative gadgets. We find an analytic relation between the values $J_{ij}$ of the desired interaction and the parameters of the 2d circuit, as well as the expression for the error in the quantum spectrum. For the relative error to be a constant $ε$, one requires an energy scale growing as $n^6$ in the number of qubits, or equivalently a control precision up to $ n^{-6}$. Our proof is based on the Schrieffer-Wolff transformation and generalizes to any hardware. In the architectures available today, $5$ digits o…

Translationally-Invariant Universal Quantum Hamiltonians in 1D

Recent work has characterised rigorously what it means for one quantum system to simulate another, and demonstrated the existence of universal Hamiltonians -- simple spin lattice Hamiltonians that can replicate the entire physics of any other quantum many body system. Previous universality results have required proofs involving complicated `chains' of perturbative `gadgets'. In this paper, we derive a significantly simpler and more powerful method of proving universality of Hamiltonians, directly leveraging the ability to encode quantum computation into ground states. This provides new insight…

局域两体相互作用下的有效量子记忆哈密顿量

Effective quantum memory Hamiltonian from local two-body interactions

在[Phys.Rev.A88，062313（2013）]中，我们提出并研究了一种自校正量子存储器的模型，其中在存储器中引入缺陷的能量成本作为系统大小的函数无限制地增长。这种积极的行为是由于有吸引力的长程相互作用介导的玻色子场的记忆耦合。实现这种记忆的关键因素是玻色子场的物理实现以及记忆和玻色子场的稳定算子之间的局部五体相互作用。在这里，我们表明，这两个成分出现在一个低能量的有效理论的哈密顿量，只涉及两个相邻的自旋之间的相互作用。特别是，我们认为低能量，长波长激发的有序海森堡铁磁体（磁振子）的玻色子场的实现。此外，我们提出了微扰小工具产生所需的五自旋运营商。因此，我们的哈密顿量只涉及局部两体相互作用，预计将表现出自校正特性，只要影响它的噪声是在有效的低能量描述仍然有效的制度。