论文标题
在冷凝问题问题中寻找量子古典交叉
Hunting for quantum-classical crossover in condensed matter problems
论文作者
论文摘要
从计算复杂性方面,对量子优势的强烈追求进一步导致了一个现代化的关键问题:{\ it何时何时以及如何表现量子计算机?}下一个里程碑无疑是实现实践问题中量子加速的实现。在这里,我们提供了一个明确的证据和论点,表明主要目标可能是凝结物理学。我们的主要贡献总结如下:1)基于张量的网络对最先进的经典算法进行系统错误/运行时分析的建议; 2)在可执行逻辑指令级别执行的量子资源的专用和高分辨率分析; 3)澄清地面模拟的量子古典跨点仅在数小时的运行时间内使用2D海森贝格和2D Fermi-Hubbard模型的数十亿个物理Qubits,假设逻辑Qubits通过表面代码编码,则具有$ P = 10^{ - 3} $的物理错误率。据我们所知,我们认为,凝结物问题提供了最早的平台,以证明实用量子优势,而量化顺序比以往任何时候都更可行,就Qubit计数和总运行时而言。
The intensive pursuit for quantum advantage in terms of computational complexity has further led to a modernized crucial question: {\it When and how will quantum computers outperform classical computers?} The next milestone is undoubtedly the realization of quantum acceleration in practical problems. Here we provide a clear evidence and arguments that the primary target is likely to be condensed matter physics. Our primary contributions are summarized as follows: 1) Proposal of systematic error/runtime analysis on state-of-the-art classical algorithm based on tensor networks; 2) Dedicated and high-resolution analysis on quantum resource performed at the level of executable logical instructions; 3) Clarification of quantum-classical crosspoint for ground-state simulation to be within runtime of hours using only a few hundreds of thousand physical qubits for 2d Heisenberg and 2d Fermi-Hubbard models, assuming that logical qubits are encoded via the surface code with the physical error rate of $p=10^{-3}$. To our knowledge, we argue that condensed matter problems offer the earliest platform for demonstration of practical quantum advantage that is order-of-magnitude more feasible than ever known candidates, in terms of both qubit counts and total runtime.