Ilan Cohn | Searcharxiv

arXiv2016

Characterizing error propagation in quantum circuits: the Isotropic Index

This paper presents a novel index in order to characterize error propagation in quantum circuits by separating the resultant mixed error state in two components: an isotropic component, that quantifies the lack of information, and a dis-alignment component, that represents the shift between the current state and the original pure quantum state. The Isotropic Triangle, a graphical representation that fits naturally with the proposed index, is also introduced. Finally, some examples with the analysis of well-known quantum algorithms degradation are given.

quant-ph↗

arXiv2016

Grover's search with local and total depolarizing channel errors

In this article the effect of noise on Grover's algorithm is analyzed, modeled as a total depolarizing channel (TDCh) and a local depolarizing channel in each qubit (LDCh). The focus was not in error correction (e.g. by the fault-tolerant method), but to provide an insight to the kind of error, or degradation, that needs to be corrected. In the last years analytical results regarding mainly the TDCh model have been obtained. In this paper we extend these previous results to the local case, concluding that the degradation of Grover's algorithm with the latter is worse than the former. It has been shown that for both cases with an $N$-dependent small enough error-width, smaller than $1/\sqrt{N}$ for total error and $1/(\sqrt{N}\log_2{N})$ for the local case, correction is not needed.

quant-ph↗