by Samuel J. Lomonaco, Jr., Louis H. Kauffman
http://www2.math.uic.edu/~kauffman/ContShor.pdf
Add To MetaCart
Abstract:
Abstract. In this paper, we use the methods found in [12] to create a continuous variable analogue of Shor’s quantum factoring algorithm. By this we mean a quantum hidden subgroup algorithm that finds the period P of a function Φ: R − → C from the reals R to the complex numbers C, where Φ belongs to a very general class of functions, called the class of admissible functions. This algorithm gives some insight into the inner workings of Shor’s quantum factoring algorithm.
Citations
|
413
|
An introduction to the Theory of Numbers
– Hardy, Wright
- 1980
|
|
399
|
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
– Shor
- 1996
|
|
115
|
The Principles of Quantum Mechanics
– Dirac
- 1947
|
|
34
|
Polynomial-time quantum algorithms for Pell’s equation and the principal ideal problem
– Hallgren
- 2002
|
|
7
|
The rigged Hilbert space and quantum mechanics
– Bohm
- 1978
|
|
6
|
Introduction to Quantum Algorithms
– Shor
- 1999
|
|
2
|
The Art of Computer Programming,” (second edition
– Knuth
- 1981
|
|
2
|
Quantum hidden subgroup problems: A mathematical perspective
– Lomonaco, Kauman
- 2002
|
|
1
|
Quantum searching with continuous variables
– Pati, Braustein, et al.
|
|
1
|
Smauel Braustein, Deutsch-Jozsa algorithm for continuous variables
– Pati
|
|
1
|
Correspondence between continuous variable and discrete quantum systems of arbitrary dimensions
– Brukner, Kim, et al.
|
|
1
|
A unified mathematical formalism for the Dirac formulation of quantum mechanics
– Gadella, Gomez
- 2002
|
|
1
|
Shor’s quantum factoring algorithm
– Lomonaco
|
|
1
|
Théorie des Distributions,” vols. I et II, Herman et Cie
– Schwartz
- 1950
|