Weakly measured while loops: peeking at quantum states
arXiv:2009.08832 · doi:10.1088/2058-9565/ac47f1
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.
arXiv commentAccepted in Quantum Sci. Technol. 17 pages (+refs & one appendix), 4 figures
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