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Lecture notes in computer science

The Circuit Model of Quantum Computation and Its Simulation with Mathematica

Vladimir P. Gerdt, Alexander N. Prokopenya

Published Jan 1, 2012• 9 citations
Publisher
DOI
10.1007/978-3-642-28212-6_4

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In this paper we briefly describe a Mathematica program for simulation of quantum circuits and illustrate some of its facilities by simple examples. Unlike other Mathematica-based quantum simulators, our program provides a user-friendly graphical interface for generating quantum circuits and computing the circuit unitary matrices. In addition to standard linear algebra-based tools, our program implements special computer-algebra technique for constructing the multivariate polynomial system that, for a circuit composed from the Toffoli and Hadamard gates, uniquely defines the circuit matrix.
A correct simulation of a quantum circuit on a classical computer is more important because of their future use.The main purpose of this work is to illustrate a full adder circuit by using a standard Mathematica add-on package.The circuit can be constructed by using CNOT-based quantum gates.The program provides a curriculum unit, to generate the basic elements that make up quantum circuit.This paper shows effective computational design by using analogy of classical circuits.We presented an explicit example to show efficiency of the 4 qubit full adder circuit on classical computer.The method given in this paper can be used to design various quantum circuits.
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.