Matrix Product Operator Simulations of Quantum Algorithms

Abstract

We develop simulation methods for matrix product operators, and perform simulations of the Quantum Fourier Transform, Shor's algorithm and Grover's algorithm using matrix product states and matrix product operators. By doing so, we provide numerical evidence that a constant number of QFTs can be efficiently classically simulated on any state whose Schmidt rank grows only polynomially with the number of qubits, and quantify the amount of entanglement present in Shor's algorithm. The efficiency of the matrix product state and operator representation allows us to perform moderately large simulations of both Shor's algorithm with Z errors and Grover's algorithm with up to 15 X, Y and Z errors. While larger simulations have been performed, our results have been computed with little computational power and provide new methods to perform large-scale quantum algorithm simulations.

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 2015
Accession Number
AD1014258

Entities

People

  • Kieran Woolfe

Organizations

  • University of Melbourne

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Coding
  • Computers
  • Databases
  • Error Correction Codes
  • Ion Traps
  • Logic Gates
  • Probability Distributions
  • Quantum Algorithms
  • Quantum Bits
  • Quantum Circuits
  • Quantum Computing
  • Quantum Information
  • Quantum Information Science
  • Quantum Mechanics
  • Shor'S Algorithm
  • Two Dimensional

Readers

  • Computational Modeling and Simulation
  • Graph Algorithms and Convex Optimization.
  • Quantum Dot Semiconductor Device Photonics and Graphene Optoelectronic Materials and THz Physics.

Technology Areas

  • Quantum Computing