Abstract A while loop tests a termination condition on every iteration. On a quantum computer, such measurements perturb the evolution of the algorithm. We define a while loop primitive using weak measurements, offering a trade-off between the perturbation caused and the amount of information gained per iteration. This trade-off is adjusted with a parameter set by the programmer. We provide sufficient conditions that let us determine, with arbitrarily high probability, a worst-case estimate of the number of iterations the loop will run for. As an example, we solve Grover’s search problem using a while loop and prove the quadratic quantum speed-up is maintained.

中文翻译：

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弱测量的while循环：窥探量子态

摘要 一个while循环在每次迭代时测试一个终止条件。在量子计算机上，这样的测量会扰乱算法的发展。我们使用弱测量定义了一个while循环原语，在引起的扰动和每次迭代获得的信息量之间进行权衡。这种权衡是通过程序员设置的参数来调整的。我们提供了充分的条件，让我们以任意高的概率确定循环将运行的迭代次数的最坏情况估计。例如，我们使用 while 循环解决 Grover 的搜索问题，并证明保持了二次量子加速。