Simulation of Quantum Time-Frequency Transform Algorithms
Abstract
The demand for exact computation in scientific fields related to quantum physics is not met by the Symbolic Math Toolbox developed in MATLAB. In particular, exact evaluation rational multiples of 2 square is at the heart of efficient implementation of quantum time-frequency transforms. Computations performed using this Toolbox generate erroneous results when used with numbers with more than twenty digits in length. Furthermore, the results of our investigation lead us to believe that floating-point operations may be used during the computing process of this Toolbox. The Exact Computing system introduced in this report yields significant decreases in computation times, as well as providing an exact method of storing and computing data. In this system, exact values are obtained by storing numbers as numerator and denominator of rational numbers'. Integers can be of any length. We define a data structure of rational matrices using rational numbers and a set of related operators. We also started to use alternative approach to represent all integers and rational numbers in terms of a set of residues with respect to a prime number and its powers, called a p-adic number system. The p-adic arithmetic has many attractive features.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 20, 2005
- Accession Number
- ADA435027
Entities
People
- Chao Lu
Organizations
- Towson University