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Manuscript Title: Simulation of n-qubit quantum systems II. Separability and entanglement
Authors: T. Radtke, S. Fritzsche
Program title: FEYNMAN
Catalogue identifier: ADWE_v2_0 Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 175(2006)145
Programming language: Maple 10.
Computer: All computers with a license for the computer algebra system Maple [1].
Operating system: Linux, MS Windows XP.
RAM: Most commands acting on quantum registers with five or less qubits take 5 - 20 MB of memory. However, storage requirements critically depend on the number of qubits, n, in the quantum registers due to the exponential increase of the associated Hilbert space.
Keywords: quantum register, qubit, entanglement, separability.
PACS: 03.67.-a, 03.67.Lx, 03.65.Ud.
Classification: 4.15.
Does the new version supersede the previous version?: Yes
Nature of problem: Entanglement has been identified as an essential resource in virtually all aspects of quantum information theory. Therefore, the detection and quantification of entanglement is a necessary prerequisite for many applications, such as quantum computation, communications or quantum cryptography. Up to the present, however, the multipartite entanglement of n-qubit systems has remained largely unexplored owing to the exponential growth of complexity with the number of qubits involved.
Solution method: Using the computer algebra system Maple, a set of procedures has been developed which supports the definition and manipulation of n-qubit quantum registers and quantum logic gates [2]. The provided hierarchy of commands can be used interactively in order to simulate the behaviour of n-qubit quantum systems (by applying a number of unitary or non-unitary operations) and to analyze their separability and entanglement properties.
Reasons for new version: The first program version established the data structures and commands which are needed to build and manipulate quantum registers. Since the (evolution of) entanglement is a central aspect in quantum information processing the current version adds the capability to analyze separability and entanglement of quantum registers by implementing algebraic separability criteria and entanglement measures and related quantities.
Restrictions: The present version of the program facilitates the setup and the manipulation of quantum registers by means of (predefined) quantum logic gates; it now also provides the tools for performing a symbolic and/or numeric analysis of the entanglement for the quantum states of such registers. Owing to the rapid increase in the computational complexity of multi-qubit systems, however, the time and memory requirements often grow rapidly, especially for symbolic computations. This increase of complexity limits the application of the program to about 6 or 7 qubits on a standard single processor (Pentium 4 with ≥ 2 GHz or equivalent) machine with ≤ 1GB of memory .
Unusual features: The Feynman program has been designed within the framework of Maple for interactive (symbolic or numerical) simulations on n-qubit quantum registers with no other restriction than given by the memory and processor resources of the computer. Whenever possible, both representations of quantum registers in terms of their state vectors and/or density matrices are equally supported by the program. Apart from simulating quantum gates and quantum operations, the program now facilitates also investigations on the separability and the entanglement properties of quantum registers
Running time: Most commands acting on quantum registers with five or less qubits take ≤ 10 seconds of processor time (on a Pentium 4 with ≥ 2 GHz or equivalent). However, time requirements critically depend on the number of qubits, n, in the quantum registers due to the exponential increase of the associated Hilbert space.
References:
[1]	Maple is a registered trademark of Waterloo Maple Inc.
[2]	T. Radtke, S. Fritzsche, Comp. Phys. Commun. 173 (2005) 91.