A Mathematica Package for Simulation of Quantum Computation

Gerdt, Vladimir P.; Kragler, R.; Prokopenya, Alexander N.

doi:10.1007/978-3-642-04103-7_11

Cited by 9 publications

(1 citation statement)

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“…During the last few years Mathematica computing system has become very popular in the area of quantum information theory and the foundations of quantum mechanics. The main reason for this is its ability to merge the symbolic and numerical capabilities [4], both of which are often necessary to understand the theoretical and practical aspects of quantum systems [5,6,7,8].…”

Section: Introductionmentioning

confidence: 99%

States and Channels in Quantum Mechanics Without Complex Numbers

Miszczak

2017

Applications of Computer Algebra

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In the presented note we aim at exploring the possibility of abandoning complex numbers in the representation of quantum states and operations. We demonstrate a simplified version of quantum mechanics in which the states are represented using real numbers only. The main advantage of this approach is that the simulation of the n-dimensional quantum system requires n 2 real numbers, in contrast to the standard case where n 4 real numbers are required. The main disadvantage is the lack of hermicity in the representation of quantum states. Using Mathematica computer algebra system we develop a set of functions for manipulating real-only quantum states. With the help of this tool we study the properties of the introduced representation and the induced representation of quantum channels.

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Section: Introductionmentioning

confidence: 99%