Universality of entanglement and quantum-computation complexity

Román Orús and José I. Latorre
Phys. Rev. A 69, 052308 – Published 12 May 2004

Abstract

We study the universality of scaling of entanglement in Shor’s factoring algorithm and in adiabatic quantum algorithms across a quantum phase transition for both the NP-complete exact cover problem as well as Grover’s problem. The analytic result for Shor’s algorithm shows a linear scaling of the entropy in terms of the number of qubits, therefore making it hard to generate an efficient classical simulation protocol. A similar result is obtained numerically for the quantum adiabatic evolution exact cover algorithm, which also shows universality of the quantum phase transition near which the system evolves. On the other hand, entanglement in Grover’s adiabatic algorithm remains a bounded quantity even at the critical point. The classification of scaling of entanglement appears as a natural grading of the computational complexity of simulating quantum phase transitions.

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  • Received 14 November 2003

DOI:https://doi.org/10.1103/PhysRevA.69.052308

©2004 American Physical Society

Authors & Affiliations

Román Orús and José I. Latorre

  • Departament d’Estructura i Constituents de la Matèria, Universidad Barcelona, 08028, Barcelona, Spain

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Issue

Vol. 69, Iss. 5 — May 2004

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