Work

On the quantum hardness of solving isomorphism problems as nonabelian hidden shift problems

Year: 2007

Type: paratext

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 Omega(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.

Source: Quantum Information and Computation

DOI: 10.26421/qic7.5-6

Authors: Childs, Andrew M., Wocjan, Pawel

Institution: California Institute of Technology

Language: English

Topic: Quantum Computing Algorithms and Architecture

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, National Security Agency, Army Research Office

Award: Institute for Quantum Information

OpenAlex ID: W2949935208

Cites: 38

Cited by: 5

Related to: 10