Applications of the Schur Basis to Quantum Algorithms

Abstract

Quantum computation offers a promising avenue to high performance computing, for certain applications, but depends on development of new quantum algorithms. Thus far, all major quantum algorithms which are exponentially fast compared with classical counterparts are based on the quantum Fourier transform. This project seeks to develop new quantum algorithms, based on a different mathematical transform known as the Schur transform. The Schur transform (or Schur-Weyl duality) arises naturally in many areas of mathematics, chemistry, and physics, and many applications of it have now been found in quantum coding and information theory. This project has also led to the efficient quantum circuits for the Schur transform, and a new quantum algorithm for superpolynomial speedups based on quantum circuits.

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Document Details

Document Type
Technical Report
Publication Date
Jan 10, 2011
Accession Number
ADA544920

Entities

People

  • Aram Harrow
  • Isaac L. Chuang

Organizations

  • Massachusetts Institute of Technology

Tags

Communities of Interest

  • C4I
  • Energy and Power Technologies
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Coding
  • Computer Programming
  • Computer Science
  • Computers
  • Data Compression
  • Data Science
  • Information Processing
  • Information Theory
  • Ion Traps
  • Probability Distributions
  • Quantum Algorithms
  • Quantum Computing
  • Quantum Information
  • Quantum Information Science
  • Quantum Mechanics
  • Random Variables
  • Three Dimensional

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Image Processing and Computer Vision.
  • Quantum spin resonance or Electron Paramagnetic Resonance spectroscopy.

Technology Areas

  • Quantum Computing