arXiv 1901.074812019-01-22quant-ph

利用少量经典随机比特有效估计量子逻辑门的平均保真度

Efficiently estimating average fidelity of a quantum logic gate using few classical random bits

Aditya Nema, Pranab Sen

备注：: 16 pages

摘要：

我们给出了三个新的算法，有效的就地估计，而不使用辅助量子比特，量子逻辑门的平均保真度的d维系统上使用的随机比特比已知的要少得多。以前的方法，有效地估计平均门保真度取代Haar随机酉在朴素估计算法的近似酉2-设计，并均匀和独立地采样。相比之下，在我们的第一个算法中，我们使用有限独立的伪随机发生器，一个强大的工具，从去随机化理论的近似酉2-设计均匀采样的酉。该算法使用的基本操作数与以前的有效算法相同，但随机位数要少得多。减少对经典随机比特的要求增加了估计的可靠性，因为高质量随机比特通常是昂贵的计算资源。我们的第二个有效的算法，基于一个4量子张量积扩展器，工程，如果门尺寸d是大的。它使用比第一算法更少的随机比特，并且具有额外的优点，即它只需要实现一个酉，而不是第一算法中近似2-设计的所有酉。我们的第三个有效的算法，基于一个l-量子张量积扩展适度大的值l，工程的所有值的参数。它使用比其他算法稍微多的随机位，但具有的优点是，它只需要实现少量的酉，而不是第一算法中的近似2-设计的所有酉。这一优势对于不久的将来的实验性实现具有重要意义。

英文摘要：

We give three new algorithms for efficient in-place estimation, without using ancilla qubits, of average fidelity of a quantum logic gate acting on a d-dimensional system using much fewer random bits than what was known so far. Previous approaches for efficient estimation of average gate fidelity replaced Haar random unitaries in the naive estimation algorithm by approximate unitary 2-designs, and sampled them uniformly and independently. In contrast, in our first algorithm we sample the unitaries of the approximate unitary 2-design uniformly using a limited independence pseudorandom generator, a powerful tool from derandomisation theory. This algorithm uses the same number of basic operations as previous efficient algorithms but much fewer number of random bits. Reducing the requirement of classical random bits increases the reliability of estimation as often, high quality random bits are an expensive computational resource. Our second efficient algorithm, based on a 4-quantum tensor product expander, works if the gate dimension d is large. It uses even lesser random bits than the first algorithm, and has the added advantage that it needs to implement only one unitary versus potentially all the unitaries of an approximate 2-design in the first algorithm. Our third efficient algorithm, based on an l-quantum tensor product expander for moderately large values of l, works for all values of the parameters. It uses slightly more random bits than the other algorithms but has the advantage that it needs to implement only a small number of unitaries versus potentially all the unitaries of an approximate 2-design in the first algorithm. This advantage is of great importance to experimental implementations in the near future.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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英文摘要：

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