Abstract
This paper introduces QUANTUM, a free library of commands of Wolfram Mathematica that can be used to perform calculations directly in Dirac braket and operator notation. Its development started several years ago, in order to study quantum random walks. Later, many other features were included, like operator and commutator algebra, simulation and graphing of quantum computing circuits, generation and solution of Heisenberg equations of motion, among others. To the best of our knowledge, QUANTUM remains a unique tool in its use of Dirac notation, because it is used both in the input and output of the calculations. This work depicts its usage and features in Quantum Computing and Quantum Hamilton Dynamics.
Highlights
QUANTUM is an add-on of Mathematica implementing calculations in Dirac notation [1], and allowing the end user to enter that notation using keyboard and palettes toolbars
This paper introduces QUANTUM, a free library of commands of Wolfram Mathematica that can be used to perform calculations directly in Dirac braket and operator notation
The core of QUANTUM was constructed based on quantum information and quantum computing applications, several of the advanced commands in the current version are restricted to discrete Hilbert spaces
Summary
QUANTUM is an add-on of Mathematica (versions 8 to 10) implementing calculations in Dirac notation [1], and allowing the end user to enter that notation using keyboard and palettes toolbars. The fourth section describes the second module, Quantum’Computing’, including qubits and quantum gates for the simulation of algorithms and the automated drawing of quantum computing circuits. The third module, Quantum’QHD’, implements the Quantized Hamilton Dynamics (QHD) approximation to the Heisenberg equations of motion. It can be used for the simulation of physical systems such as molecules.
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