量子计算机上规范理论的光谱指纹
Spectral Fingerprints of Gauge Theories on a Quantum Computer
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中文总结 AI 辅助
该研究提出最大混态光谱采样算法，在量子计算机上模拟(1+1)维非阿贝尔SO(3)规范理论，利用动态电路减少量子比特数，用于分析基态与热化行为等物理性质。
中文摘要 AI 辅助
最大混态光谱采样是一种无偏量子算法，可从哈密顿量中提取有限分辨率的光谱分布，覆盖能量允许的整个范围。我们展示了如何将其聚焦于光谱的任意期望区域，以获取目标模型的完整“指纹”信息：包括从最低能量得到的基态现象（如量子临界性），以及从中段光谱得到的热化行为。我们在(1+1)维非阿贝尔SO(3)规范理论上具体演示了该技术，全面分析了执行此算法所需的步骤，以及近期超导量子硬件的可行性，采用了深度为78个两量子比特门的电路进行模拟。我们展示了该算法如何利用近期硬件中新兴的动态电路能力，将所需量子比特数大致减半，以及量子读出误差缓解对该方法而言极为简单。在此过程中，我们提出了一种新策略，通过泡利框架优化来编译光谱采样所需的受控时间演化。我们举例说明了量子光谱采样的两种物理应用——无序多体跃迁和中段光谱态密度，以及它们在算法傅里叶输出之外所需的后处理步骤。
英文摘要
Maximally mixed state spectral sampling is an unbiased quantum algorithm that allows for extraction of a finite-resolution spectral distribution from a Hamiltonian over potentially the entire allowed range of energies. We show how it may be focused on any desired area of the spectrum in order to learn about the full \textit{fingerprint} of the model of interest: from its ground state phenomena such as quantum criticality, obtained from the lowest lying energies, to its thermalization behavior, obtained from the mid-spectrum. We demonstrate this technique specifically on a $(1+1)d$ non-Abelian $SO(3)$ gauge theory, providing a comprehensive analysis of the steps necessary for performing this algorithm, as well as what is possible in the near-term with superconducting quantum hardware, performing simulations with circuits that are $78$ two-qubit gates deep. We show how this algorithm is able to take advantage of emerging dynamical circuit capabilities in near-term hardware to roughly halve the number required qubits, as well as how quantum readout error mitigation is trivial for this method. Along the way, we propose a novel strategy for compiling the controlled-time evolutions needed for spectral sampling by means of Pauli-frame optimizations. We illustrate two physical applications of quantum spectral sampling -- disordered many-body transitions, and mid-spectrum densities of states -- and what postprocessing steps they require beyond the Fourier outputs of the algorithm.
