Multi-scale tensor networks offer a way to efficiently represent ground states of critical systems and may be adapted for state-preparation on a quantum computer. The tensor network for a single scale specifies a quantum channel whose fixed-point is a subregion of the approximate critical ground state. The fixed-point of a noisy channel is perturbed linearly in the noise parameter from the ideal state, making local observables stable against errors for these iterative algorithms. We consider the wavelet-designed circuit for the 1+1D critical Ising ground state as a concrete example to numerically test the noise robustness against our error models and compare the smallest instance case with an implementation on a present-day ion-trap quantum computer.


Talk Number 20110054
Speaker Profile Troy Sewell
Perimeter Institute Recorded Seminar Archive