Short Introduction to Quantum Computation
Abstract
This paper presents a quantum lattice gas method useful for nano-scale computing and quantum computing. There are several important issues that arise when one considers fabricating nano-scale computing devices, and these issues are different depending on the type of computing one expects to do at this scale. The first type of computing, introduced by Ed Fredkin, Tom Toffoli, and Norm Margolus would be classical computing where Boolean bits that have a definite value of either 0 or 1 are still employed and where all logical gate operations are represented by unitary permutation operators causing neither any quantum mechanical superposition nor any quantum entanglement. This kind of computing may best be termed nano-scale computing. A second type of computing, introduced by Richard Feynman has been termed quantum computing where two-level quantum objects, such as spin-1/2 particles, are used to represent quantum bits or "qubits" and where quantum superposition and entanglement are integral to the logical gate operations and are required for computational efficiency. The characteristic nature of a qubit is that it can be in a superposition of the Boolean states 0 and 1, prototypically the ground state and excited state of a two-level quantum system. In nano-scale computing, one tries to implement reversible classical algorithms whose logical gate operations are represented by orthogonal permutation matrices, which are a special class of unitary matrices. The author discusses various reasons why one is driven to develop reversible algorithms for nano-scale computing. He then discusses how quantum computing relies on quantum interference and entanglement over a system of qubits occurring in a controlled fashion. These qubits will likely be spin-1/2 objects. To date, only one important algorithm is known whose efficiency is based on quantum interference and entanglement: Shors' prime number factoring algorithm.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 26, 1996
- Accession Number
- ADA434366
Entities
People
- Jeffrey Yepez
Organizations
- Phillips Laboratory