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Manuscript Title: Simulation of n-qubit quantum systems IV. Parametrizations of quantum states, matrices and probability distributions. | ||

Authors: T. Radtke, S. Fritzsche | ||

Program title: FEYNMAN | ||

Catalogue identifier: ADWE_v4_0Distribution format: tar.gz | ||

Journal reference: Comput. Phys. Commun. 179(2008)647 | ||

Programming language: Maple 11. | ||

Computer: Any computer with Maple software installed. | ||

Operating system: Any system that supports Maple; program has been tested under Microsoft Windows XP, Linux. | ||

Keywords: qubit, quantum register, separable states, parametrization. | ||

PACS: 03.67.Ac, 03.67.Mn, 03.65.Ud. | ||

Classification: 4.15. | ||

Does the new version supersede the previous version?: Yes | ||

Nature of problem:During the last decades, quantum information science has contributed to our understanding of quantum mechanics and has provided also new and efficient protocols, based on the use of entangled quantum states. To determine the behaviour and entanglement of n-qubit quantum registers, symbolic and numerical simulations need to be applied in order to analyze how these quantum information protocols work and which role the entanglement plays hereby. | ||

Solution method:Using the computer algebra system Maple, we have developed a set of procedures that support the definition, manipulation and analysis of n-qubit quantum registers. These procedures also help to deal with (unitary) logic gates and (nonunitary) quantum operations that act upon the quantum registers. With the parameterization of various frequently-applied objects, that are implemented in the present version, the program now facilitates a wider range of symbolic and numerical studies. All commands can be used interactively in order to simulate and analyze the evolution of n-qubit quantum systems, both in ideal and noisy quantum circuits. | ||

Reasons for new version:In the first version of the FEYNMAN program [1], we implemented the data structures and tools that are necessary to create, manipulate and to analyze the state of quantum registers. Later [2,3], support was added to deal with quantum operations (noisy channels) as an ingredient which is essential for studying the effects of decoherence. With the present extension, we add a number of parametrizations of objects frequently utilized in decoherence and entanglement studies, such that as hermitian and unitary matrices, probability distributions, or various kinds of quantum states. This extension therefore provides the basis, for example, for the optimization of a given function over the set of pure states or the simple generation of random objects. | ||

Running time:Most commands that act upon quantum registers with five or less qubits take ≤ 10 seconds of processor time on a Pentium 4 processor with ≥ 2GHz or newer, and about 5-20 MB of working memory (in addition to the memory for the Maple environment). Especially when working with symbolic expressions, however, the requirements on CPU time and memory critically depend on the size of the quantum registers, owing to the exponential growth of the dimension of the associated Hilbert space. For example, complex (symbolic) noise models, i.e. with several symbolic Kraus operators, result for multi-qubit systems often in very large expressions that dramatically slow down the evaluation of e.g. distance measures or the final-state entropy etc. In these cases, Maple's assume facility sometimes helps to reduce the complexity of the symbolic expressions, but more often only a numerical evaluation is possible eventually. Since the complexity of the various commands of the FEYNMAN program and the possible usage scenarios can be very different, no general scaling law for CPU time or the memory requirements can be given. | ||

References: | ||

[1] | T. Radtke, S. Fritzsche, Comp. Phys. Comm. 173 (2005) 91. | |

[2] | T. Radtke, S. Fritzsche, Comp. Phys. Comm. 175 (2006) 145. | |

[3] | T. Radtke, S. Fritzsche, Comp. Phys. Comm. 176 (2007) 617. |

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