发表机构
International School for Advanced Studies (SISSA)（高等研究国际学院（SISSA））
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究从经典密集伊辛模型低温吉布斯分布采样问题，提出用全量子梅特罗波利斯游走及哈密顿量模拟，相比此前量子游走有三次多项式渐近优势，总查询速度六次多项式加速，经测试有实际优势，是实现量子优势的有前途途径。
AI 中文摘要
我们引入了一类新的全量子梅特罗波利斯游走，其中提议和接受步骤本质上都是量子的。与通过量化经典高效马尔可夫链获得的标准量子游走不同，我们的算法采用哈密顿量模拟作为量子原生提议机制，扩展了量子游走的类别。我们针对从经典密集伊辛模型的低温吉布斯分布中采样的问题，在总变差距离上有固定误差。这种方法比以前的量子游走具有约三次多项式的渐近优势，与最佳经典游走相比，总查询速度提高到六次多项式。这表明在量子游走形式体系中，有可能超越广泛假设的二次极限实现加速。我们对所有算法原语进行了完整的容错编译，并与最佳经典马尔可夫链的CPU、GPU和FPGA实现进行了基准测试。在相同硬件假设下，由此产生的优势运行时交叉从传统量子游走的约10³年减少到不到一天。这些结果表明全量子马尔可夫链是实现实际量子优势的一条有前途的途径。
英文摘要
We introduce a new class of fully-quantum Metropolis walks in which both the proposal and acceptance steps are intrinsically quantum. Unlike standard quantum walks obtained by quantizing classically efficient Markov chains, our algorithm employs Hamiltonian simulation as a quantum-native proposal mechanism, enlarging the class of quantum walks beyond classical counterparts. We target the problem of sampling from the low-temperature Gibbs distribution of classical dense Ising models, within a fixed error in total variation distance. This approach achieves about a cubic polynomial asymptotic advantage over previous quantum-walks, resulting in a total sixth-degree polynomial queries speedup compared to the best classical walk. This shows that speedups beyond the widely assumed quadratic limit are possible within the quantum walk formalism. We perform a complete fault-tolerant compilation of all algorithmic primitives and benchmark against CPU, GPU, and FPGA implementations of the best classical Markov chain. Under identical hardware assumptions, the resulting advantage runtime crossover is reduced from approximately $10^3$ years for conventional quantum walks to less than one day. These results identify fully-quantum Markov chains as a promising route toward practical quantum advantage.
CommentsData and notebooks to reproduce the results are publicly available
