Event Title
Linear Algebra in Quantum Computing
Location
Diamond 323
Start Date
1-5-2014 11:00 AM
End Date
1-5-2014 12:00 PM
Project Type
Presentation- Restricted to Campus Access
Description
The immense power of computing has been continually growing, yet we still want more speed and computing capacity. If, as Moores Law states, the number of transistors on a microprocessor continues to double every other year, we will find the circuits on a microprocessor measured on an atomic scale in a couple of decades. Then, we would start to consider quantum computers, which will make use of the power of atoms to perform memory and processing tasks. The mathematics behind quantum computers will be the focus of my presentation. The information contained in qubits (quantum bits), which are analogues of classical bits, can be represented in a matrix form, namely a density matrix. It has been found that a density matrix is positive semi-definite and of trace 1. The operators acting on density matrices need to preserve the trace and positivity so that the resulting output after processing the information is still a density matrix. Therefore, these operators can be thought of as a trace-preserving positive map. In this presentation, the definitions of such maps and properties will be introduced along with the theorems that are related to completely positive maps.
Faculty Sponsor
Leo Livshits
Sponsoring Department
Colby College. Mathematics and Statistics Dept.
CLAS Field of Study
Natural Sciences
Event Website
http://www.colby.edu/clas
ID
807
Linear Algebra in Quantum Computing
Diamond 323
The immense power of computing has been continually growing, yet we still want more speed and computing capacity. If, as Moores Law states, the number of transistors on a microprocessor continues to double every other year, we will find the circuits on a microprocessor measured on an atomic scale in a couple of decades. Then, we would start to consider quantum computers, which will make use of the power of atoms to perform memory and processing tasks. The mathematics behind quantum computers will be the focus of my presentation. The information contained in qubits (quantum bits), which are analogues of classical bits, can be represented in a matrix form, namely a density matrix. It has been found that a density matrix is positive semi-definite and of trace 1. The operators acting on density matrices need to preserve the trace and positivity so that the resulting output after processing the information is still a density matrix. Therefore, these operators can be thought of as a trace-preserving positive map. In this presentation, the definitions of such maps and properties will be introduced along with the theorems that are related to completely positive maps.
https://digitalcommons.colby.edu/clas/2014/program/64