Fast quantum algorithms for approximating some irreducible representations of groups - Quantum PhysicsReport as inadecuate




Fast quantum algorithms for approximating some irreducible representations of groups - Quantum Physics - Download this document for free, or read online. Document in PDF available to download.

Abstract: We consider the quantum complexity of estimating matrix elements of unitaryirreducible representations of groups. For several finite groups including thesymmetric group, quantum Fourier transforms yield efficient solutions to thisproblem. Furthermore, quantum Schur transforms yield efficient solutions forcertain irreducible representations of the unitary group. Beyond this, weobtain polyn-time quantum algorithms for approximating matrix elements fromall the irreducible representations of the alternating group A n, and all theirreducible representations of polynomial highest weight of Un, SUn, andSOn. These quantum algorithms offer exponential speedup in worst casecomplexity over the fastest known classical algorithms. On the other hand, weshow that average case instances are classically easy, and that the techniquesanalyzed here do not offer a speedup over classical computation for theestimation of group characters.



Author: Stephen P. Jordan

Source: https://arxiv.org/







Related documents