论文标题
度量意识变异量子算法的测量成本
Measurement cost of metric-aware variational quantum algorithms
论文作者
论文摘要
变异量子算法是近期量子计算机的有前途的工具，因为它们的浅电路对实验瑕疵是可靠的。但是，它们的实际适用性在很大程度上取决于其电路需要执行多少次，以充分减少射击。我们考虑度量感知的量子算法：使用量子计算机有效估计矩阵和向量对象的变异算法。例如，最近引入的量子自然梯度方法使用量子渔民信息矩阵作为度量张量，以校正电路参数的共依赖性梯度向量。我们严格地表征和上限，将迭代步骤确定为固定精度所需的测量数量，并提出了一种最佳分配样品在矩阵和向量入口之间的一般方法。最后，我们确定估计量子Fisher信息矩阵所需的电路重复次数在越来越多的迭代和Qubits上渐近可以忽略不计。
Variational quantum algorithms are promising tools for near-term quantum computers as their shallow circuits are robust to experimental imperfections. Their practical applicability, however, strongly depends on how many times their circuits need to be executed for sufficiently reducing shot-noise. We consider metric-aware quantum algorithms: variational algorithms that use a quantum computer to efficiently estimate both a matrix and a vector object. For example, the recently introduced quantum natural gradient approach uses the quantum Fisher information matrix as a metric tensor to correct the gradient vector for the co-dependence of the circuit parameters. We rigorously characterise and upper bound the number of measurements required to determine an iteration step to a fixed precision, and propose a general approach for optimally distributing samples between matrix and vector entries. Finally, we establish that the number of circuit repetitions needed for estimating the quantum Fisher information matrix is asymptotically negligible for an increasing number of iterations and qubits.
