Title

On The Quantum Hardness Of Solving Isomorphism Problems As Nonabelian Hidden Shift Problems

Keywords

Hidden shift problem; Hidden subgroup problem; Quantum algorithms

Abstract

We consider an approach to deciding isomorphism of rigid n-vertex graphs (and related isomorphism problems) by solving a nonabelian hidden shift problem on a quantum computer using the standard method. Such an approach is arguably more natural than viewing the problem as a hidden subgroup problem. We prove that the hidden shift approach to rigid graph isomorphism is hard in two senses. First, we prove that Ω(n) copies of the hidden shift states are necessary to solve the problem (whereas O(n log n) copies are sufficient). Second, we prove that if one is restricted to single-register measurements, an exponential number of hidden shift states are required. © Rinton Press.

Publication Date

1-1-2007

Publication Title

Quantum Information and Computation

Volume

7

Issue

5-6

Number of Pages

504-521

Document Type

Article

Personal Identifier

scopus

Socpus ID

34547539405 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/34547539405

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