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/ √ N for total error and 1/( √ N log 2 N ) for the local case, correction is not needed.
The performance of today's quantum computers are affected by noise. This effect can be analyzed in the result of simple quantum algorithms in real quantum computers. The noise can be characterized as a decoherence error or a systematic error, the last could be corrected by a unitary rotation. In this article we propose two methods to model a systematic error, in the Quantum Fourier Transform algorithm (QFT). The first method uses the isotropic index presented in `` [1] and needs to reconstruct the density matrix of the experimental state, while the second method, although less general, only needs to reconstruct the reduced density matrices for each qubit. In both methods, a unitary transformation is proposed, which approximates the experimental result to the expected theoretical state. As an example, the QFT algorithm is analyzed for two qubit states, in quantum IBM Q computer ibmq\_santiago.
Quantum error correcting codes can be cast in a way which is strikingly similar to a quantum heat engine undergoing an Otto cycle. In this paper we strengthen this connection further by carrying out a complete assessment of the thermodynamic properties of 4-strokes operator-based error correcting codes. This includes an expression for the entropy production in the cycle which, as we show, contains clear contributions stemming from the different sources of irreversibility. To illustrate our results, we study a classical 3-qubit error correcting code, well suited for incoherent states, and the 9-qubit Shor code capable of handling fully quantum states. We show that the work cost associated with the correction gate is directly associated with the heat introduced by the error. Moreover, the work cost associated with encoding/decoding quantum information is always positive, a fact which is related to the intrinsic irreversibility introduced by the noise. Finally, we find that correcting the coherent (and thus genuinely quantum) part of a quantum state introduces substantial modifications related to the Hadamard gates required to encode and decode coherences.
The present article proposes a measure of correlation for multiqubit mixed states. The measure is defined recursively, accumulating the correlation of the subspaces, making it simple to calculate without the use of regression. Unlike usual measures, the proposed measure is continuous additive and reflects the dimensionality of the state space, allowing to compare states with different dimensions. Examples show that the measure can signal critical points (CP) in the analysis of Quantum Phase Transitions in Heisenberg models.
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.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
customersupport@researchsolutions.com
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.