发表机构
IBM Research Europe - Zurich; École Polytechnique Fédérale de Lausanne; Institute for Quantum Information and Matter, California Institute of Technology（IBM 欧洲苏黎世研究中心; 洛桑联邦理工学院; 加州理工学院量子信息与物质研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出QD-HDQI算法，利用量子解码器制备吉布斯态，通过改进解码阈值降低可达温度，超越经典解码器限制。
AI 中文摘要
我们提出了一种利用哈密顿量中代数结构的吉布斯态制备算法。我们的出发点是哈密顿量解码量子干涉测量（HDQI），这是一种近期提出的算法，它将泡利哈密顿量的吉布斯态制备问题简化为纠错码的解码问题。我们引入了量子解码HDQI（QD-HDQI），用能够利用不同错误之间干涉的量子解码器取代了HDQI的相干经典解码器。对于对易的泡利哈密顿量，我们的约简是高效的，相关的量子解码问题对应于在独立同分布纯态经典-量子信道上传输相应的辛码。对于均匀随机哈密顿量符号，高效解码器的消失错误阈值直接决定了我们的算法能够达到的最低温度。即使仅使用经典解码器，这也在可纠正错误分数方面将HDQI可达到的逆温度从线性改进为平方根；量子解码器可以通过容忍更强的噪声来进一步改进。类似的图景也扩展到HDQI先前处理的非对易区域，现在噪声在小的独立块内相关。我们在QD-HDQI吉布斯采样框架中研究了两种这样的量子解码器。第一种基于无歧义状态判别，可高效地处理任意二进制线性码。然而，我们将此策略“去量子化”用于对易哈密顿量，贡献了一个与其温度阈值匹配的经典拒绝采样器。第二种是带量子消息的置信传播（BPQM），这是经典置信传播的量子推广。我们证明，对于某些稀释自旋玻璃，BPQM的解码阈值超过了经典解码的香农极限，达到了我们框架内任何经典解码器都无法企及的温度。
英文摘要
We propose a Gibbs state preparation algorithm that exploits algebraic structure in the Hamiltonian. Our starting point is Hamiltonian Decoded Quantum Interferometry (HDQI), a recent algorithm that reduces Gibbs state preparation for Pauli Hamiltonians to decoding error-correcting codes. We introduce quantum decoding HDQI (QD-HDQI), replacing HDQI's coherent classical decoder by a quantum decoder that can exploit interference between different errors. For commuting Pauli Hamiltonians, our reduction is efficient and the associated quantum decoding problem corresponds to transmitting the associated symplectic code over i.i.d. pure-state classical-quantum channels. For uniformly random Hamiltonian signs, the vanishing-error threshold of an efficient decoder directly determines the lowest temperature that our algorithm can reach. Even using only classical decoders, this improves upon HDQI's achievable inverse temperature from linear to square-root in the correctable error fraction; quantum decoders can improve further by tolerating still stronger noise. A similar picture extends to the noncommuting regime previously handled by HDQI, where now the noise is correlated within small, independent blocks. We study two such quantum decoders in our QD-HDQI Gibbs sampling framework. The first, based on unambiguous state discrimination, works efficiently for arbitrary binary linear codes. However, we "dequantize" this strategy for commuting Hamiltonians, contributing a classical rejection sampler that matches its temperature threshold. The second is belief propagation with quantum messages (BPQM), a quantum generalization of classical belief propagation. We show that for certain dilute spin glasses, BPQM's decoding threshold exceeds the Shannon limit for classical decoding, reaching temperatures inaccessible to any classical decoder within our framework.
Comments49 pages
