Work

Complete characterization of mixing time for the continuous quantum walk on the hypercube with Markovian decoherence model

Year: 2009

Type: article

Abstract: The n-dimensional hypercube quantum random walk (QRW) is a particularily appealing example of a quantum walk because it has a natural implementation on a register on n qubits. However, any real implementation will encounter decoherence effects due to interactions with uncontrollable degrees of freedom. We present a complete characterization of the mixing properties of the hypercube QRW under a physically relevant Markovian decoherence model. In the local decoherence model considered the non-unitary dynamics are modeled as a sum of projections on individual qubits to an arbitrary direction on the Bloch sphere. We prove that there is always classical (asymptotic) mixing in this model and specify the conditions under which instantaneous mixing always exists. And we show that the latter mixing property, as well as the classical mixing time, depend heavily on the exact environmental interaction and its strength. Therefore, algorithmic applications of the QRW on the hypercube, if they intend to employ mixing properties, need to consider both the walk dynamics and the precise decoherence model.

Source: Quantum Information and Computation

DOI: 10.26421/qic9.9-10-8

Authors: M. Drezgich, A.P. Hines, M. Sarovar, S. Sastry

Institutions: University of California, Berkeley, University of British Columbia

Language: English

Topic: Quantum Computing Algorithms and Architecture

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Award: ITR: Exploration and Control of Condensed Matter Qubits