Weakly measured while loops: peeking at quantum states

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