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[Licence| Download | New Version Template] adwe_v5_0.tar.gz(1914 Kbytes)
Manuscript Title: Simulation of n-qubit quantum systems V. Quantum measurements
Authors: T. Radtke, S. Fritzsche
Program title: FEYNMAN
Catalogue identifier: ADWE_v5_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 181(2010)440
Programming language: Maple 12.
Computer: Any computer with Maple software installed.
Operating system: Any system that supports Maple; the program has been tested under Microsoft Windows XP and Linux.
Keywords: qubit, quantum register, entanglement, separability, decoherence, parametrization, measurement.
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 decade, the field of quantum information science has largely contributed to our understanding of quantum mechanics, and has provided also new and efficient protocols that are used on quantum entanglement. To further analyze the amount and transfer of entanglement in n-qubit quantum protocols, symbolic and numerical simulations need to be handled efficiently.

Solution method:
Using the computer algebra system Maple, we developed a set of procedures in order to 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 and measurements that act upon the quantum registers. All commands are organized in an hierarchical order and 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:
Until the present, the FEYNMAN program supported the basic data structures and operations of n-qubit quantum registers [1], a good number of separability and entanglement measures [2], quantum operations (noisy channels) [3] as well as the parametrizations of various frequently applied objects, such as (pure and mixed) quantum states, hermitian and unitary matrices or classical probability distributions [4]. With the current extension, we here add all necessary features to simulate quantum measurements, including the projective measurements in various single-qubit and the two-qubit Bell basis, and POVM measurements. Together with the previously implemented functionality, this greatly enhances the possibilities of analyzing quantum information protocols in which measurements play a central role, e.g., one-way computation.

Running time:
Most commands require ≤ 10 seconds of processor time on a Pentium 4 processor with ≥ 2GHz RAM or newer, if they work with quantum registers with five or less qubits. Moreover, about 5 - 20 MB of working memory is typically needed (in addition to the memory for the Maple environment itself). However, especially when working with symbolic expressions, the requirements on the 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 Kraus operators, may result 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 than not only a numerical evaluation is feasible. Since the various commands can be applied to quite different scenarios, no general scaling rule can be given for the CPU time or the request of memory.

[1] T. Radtke, S. Fritzsche, Comput. Phys. Commun. 173 (2005) 91.
[2] T. Radtke, S. Fritzsche, Comput. Phys. Commun. 175 (2006) 145.
[3] T. Radtke, S. Fritzsche, Comput. Phys. Commun. 176 (2007) 617.
[4] T. Radtke, S. Fritzsche, Comput. Phys. Commun. 179 (2008) 647.