论文标题
基于量子估计理论的量子错误缓解的通用成本限制
Universal cost bound of quantum error mitigation based on quantum estimation theory
论文作者
论文摘要
我们提出了一种根据量子估计理论来分析各种量子错误缓解方法成本的统一方法。通过分析有效代表量子误差缓解方法的操作的虚拟量子电路的量子渔民信息矩阵，我们在一类宽类的马尔可夫噪声下为通用分层的量子电路提供了得出，该噪声是对可观察到的可观察到的指数增长的无偏见的估计，该估计是指数级的质量增长，并在测量成本下的下限。在整体的去极化噪声下，我们特别发现，仅通过重新缩放测量结果就可以渐近地饱和。此外，我们证明了带有局部噪声的随机电路，这些成本也随量子计数而成倍增长。我们的数值模拟支持这样的观察结果，即即使电路只有线性连接，例如砖墙结构，每个噪声通道也会随着量子计数的指数增长而收敛到全局去极化通道。这不仅意味着通过深度和Qubit计数的成本呈指数增长，而且还验证了恢复技术是否有足够深的量子电路。我们的结果有助于理解缓解量子错误的物理局限性，并提供了评估量子误差缓解技术性能的新标准。
We present a unified approach to analyzing the cost of various quantum error mitigation methods on the basis of quantum estimation theory. By analyzing the quantum Fisher information matrix of a virtual quantum circuit that effectively represents the operations of quantum error mitigation methods, we derive for a generic layered quantum circuit under a wide class of Markovian noise that, unbiased estimation of an observable encounters an exponential growth with the circuit depth in the lower bound on the measurement cost. Under the global depolarizing noise, we in particular find that the bound can be asymptotically saturated by merely rescaling the measurement results. Moreover, we prove for random circuits with local noise that the cost grows exponentially also with the qubit count. Our numerical simulations support the observation that, even if the circuit has only linear connectivity, such as the brick-wall structure, each noise channel converges to the global depolarizing channel with its strength growing exponentially with the qubit count. This not only implies the exponential growth of cost both with the depth and qubit count, but also validates the rescaling technique for sufficiently deep quantum circuits. Our results contribute to the understanding of the physical limitations of quantum error mitigation and offer a new criterion for evaluating the performance of quantum error mitigation techniques.
