无需假设模型准确,也能高效学习量子过程的通用方法。
Agnostic Process Tomography
- 用保罗子谱分析法,从未知量子通道中学习近似通道。
- 对保罗门、低度通道等多类通道实现高效学习,误差可控。
- 适用于量子机器学习与纠错,尤其适合对模型不完全信任的场景。
通过查询访问未知量子通道Φ和已知通道类𝒞,目标是输出一个通道,其性能在𝒞中所有通道里最优,误差可控制。本文首次提出并研究了无差别过程层析(agnostic process tomography),定义了该任务在量子机器学习、量子计量学、经典模拟及误差缓解中的多种应用。针对保罗字符串、保罗通道、量子局域通道、低度通道以及由QAC⁰电路生成的通道等多类概念类,提出了高效的算法。核心技术为算子与超算子的保罗子谱分析。此外,证明了利用辅助量子比特,任何无差别态层析算法可推广至兼容的酉通道类,从而直接获得对克利福德电路、含少量T门的克利福德电路及单量子比特门张量积电路的高效学习算法。结果揭示了将概念类从标准层析扩展到无差别学习所需条件与新算法设计的关键机制。
原文摘要 · Abstract (English)
Characterizing a quantum system by learning its state or evolution is a fundamental problem in quantum physics and learning theory with a myriad of applications. Recently, as a new approach to this problem, the task of agnostic state tomography was defined, in which one aims to approximate an arbitrary quantum state by a simpler one in a given class. Generalizing this notion to quantum processes, we initiate the study of agnostic process tomography: given query access to an unknown quantum channel $Φ$ and a known concept class $\mathcal{C}$ of channels, output a quantum channel that approximates $Φ$ as well as any channel in the concept class $\mathcal{C}$, up to some error. In this work, we propose several natural applications for this new task in quantum machine learning, quantum metrology, classical simulation, and error mitigation. In addition, we give efficient agnostic process tomography algorithms for a wide variety of concept classes, including Pauli strings, Pauli channels, quantum junta channels, low-degree channels, and a class of channels produced by $\mathsf{QAC}^0$ circuits. The main technical tool we use is Pauli spectrum analysis of operators and superoperators. We also prove that, using ancilla qubits, any agnostic state tomography algorithm can be extended to one solving agnostic process tomography for a compatible concept class of unitaries, immediately giving us efficient agnostic learning algorithms for Clifford circuits, Clifford circuits with few T gates, and circuits consisting of a tensor product of single-qubit gates. Together, our results provide insight into the conditions and new algorithms necessary to extend the learnability of a concept class from the standard tomographic setting to the agnostic one.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品;中文卡片由大模型生成,请以原文为准。