Quantum Computer Circuit Analysis and Design

Abstract

Recent developments in the Riemannian geometry of quantum computation offer a new approach to the analysis of quantum computation. A geodesic equation defined on the SU(2n) group manifold, representing quantum gate operations on n qubits, may be used to determine optimal quantum evolutions and minimum-complexity quantum circuits. The geodesic equation is a first order nonlinear differential matrix equation of the Lax type. This report gives derivations of the Levi-Civita connection, Riemann curvature, sectional curvature, and geodesic equation on the SU(2n) Riemannian manifold.

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 2009
Accession Number
ADA494934

Entities

People

  • Howard E. Brandt

Organizations

  • United States Army Research Laboratory

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Circuit Analysis
  • Circuits
  • Computations
  • Computers
  • Curvature
  • Equations
  • Geometry
  • Mathematical Analysis
  • Military Research
  • Networks
  • Quantum Algorithms
  • Quantum Circuits
  • Quantum Computers
  • Quantum Computing
  • Quantum Information
  • Quantum Information Science

Readers

  • Calculus or Mathematical Analysis
  • Graph Algorithms and Convex Optimization.
  • Quantum spin resonance or Electron Paramagnetic Resonance spectroscopy.

Technology Areas

  • Quantum Computing