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Abstract: The Feynman program has been developed during the last years to support case studies on the dynamics and entanglement of n-qubit quantum registers. Apart from basic transformations and (gate) operations, it currently supports a good number of separability criteria and entanglement measures, quantum channels as well as the parametrizations of various frequently applied objects in quantum information theory, such as (pure and mixed) quantum states, hermitian and unitary matrices or classical probability distributions. With the present update of the Feynman program, we provide a simple access to (the simulation of) quantum measurements. This includes not only the widely-applied projective measurements upon the eigenspaces of some given operator but also single-qubit measurements in various pre- and user-defined bases as well as the support for two-qubit Bell measurements. In addition, we help perform generalized and POVM measurements. Knowing the importance of measurements for many quantum information protocols, e.g., one-way computing, we hope that this update makes the Feynman code an attractive and versatile tool for both, research and education. New version program summary: Program title: FEYNMAN Catalogue identifier: ADWE_v5_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADWE_v5_0.html Program obtainable from: CPC Program Library, Queen''s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 27 210 No. of bytes in distributed program, including test data, etc.: 1 960 471 Distribution format: tar.gz 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 Classification: 4.15 Catalogue identifier of previous version: ADWE_v4_0 Journal reference of previous version: Comput. Phys. Commun. 179 (2008) 647 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 a 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 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. References: [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. [Copyright &y& Elsevier]

Entanglement is known today as a key resource in many protocols from quantum computation and quantum information theory. However, despite the successful demonstration of several protocols, such as teleportation or quantum key distribution, there are still many open questions of how entanglement affects the efficiency of quantum algorithms or how it can be protected against noisy environments. The investigation of these and related questions often requires a search or optimization over the set of quantum states and, hence, a parametrization of them and various other objects. To facilitate this kind of studies in quantum information theory, here we present an extension of the Feynman program that was developed during recent years as a toolbox for the simulation and analysis of quantum registers. In particular, we implement parameterizations of hermitian and unitary matrices (of arbitrary order), pure and mixed quantum states as well as separable states. In addition to being a prerequisite for the study of many optimization problems, these parameterizations also provide the necessary basis for heuristic studies which make use of random states, unitary matrices and other objects. Program summary: Program title: FEYNMAN Catalogue identifier: ADWE_v4_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADWE_v4_0.html Program obtainable from: CPC Program Library, Queen''s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 24 231 No. of bytes in distributed program, including test data, etc.: 1 416 085 Distribution format: tar.gz 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 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 behavior 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 secon [Copyright &y& Elsevier]

During the last decade, several quantum information protocols, such as quantum key distribution, teleportation or quantum computation, have attracted a lot of interest. Despite the recent success and research efforts in quantum information processing, however, we are just at the beginning of understanding the role of entanglement and the behavior of quantum systems in noisy environments, i.e. for nonideal implementations. Therefore, in order to facilitate the investigation of entanglement and decoherence in n-qubit quantum registers, here we present a revised version of the Feynman program for working with quantum operations and their associated (Jamiołkowski) dual states. Based on the implementation of several popular decoherence models, we provide tools especially for the quantitative analysis of quantum operations. Apart from the implementation of different noise models, the current program extension may help investigate the fragility of many quantum states, one of the main obstacles in realizing quantum information protocols today. [Copyright &y& Elsevier]

Abstract: Studies on the entanglement of n-qubit quantum systems have attracted a lot of interest during recent years. Despite the central role of entanglement in quantum information theory, however, there are still a number of open problems in the theoretical characterization of entangled systems that make symbolic and numerical simulation on n-qubit quantum registers indispensable for present-day research. To facilitate the investigation of the separability and entanglement properties of n-qubit quantum registers, here we present a revised version of the Feynman program in the framework of the computer algebra system Maple. In addition to all previous capabilities of this Maple code for defining and manipulating quantum registers, the program now provides various tools which are necessary for the qualitative and quantitative analysis of entanglement in n-qubit quantum registers. A simple access, in particular, is given to several algebraic separability criteria as well as a number of entanglement measures and related quantities. As in the previous version, symbolic and numeric computations are equally supported. Program summary: Title of program: Feynman Catalogue identifier:ADWE_v2_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADWE_v2_0 Program obtainable from: CPC Program Library, Queen''s University of Belfast, N. Ireland Licensing provisions:None Computers for which the program is designed: All computers with a license of the computer algebra system Maple [Maple is a registered trademark of Waterloo Maple Inc.] Operating systems under which the program has been tested: Linux, MS Windows XP Programming language used: Maple 10 Typical time and memory requirements:Most commands acting on quantum registers with five or less qubits take ⩽10 seconds of processor time (on a Pentium 4 with or equivalent) and 5–20 MB of memory. However, storage and time requirements critically depend on the number of qubits, n, in the quantum registers due to the exponential increase of the associated Hilbert space. No. of lines in distributed program, including test data, etc.:3107 No. of bytes in distributed program, including test data, etc.:13 859 Distribution format:tar.gz 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. Does this version supersede the previous version: Yes Nature of the physical 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. Method of solution: 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 [T. Radtke, S. Fritzsche, Comput. Phys. Comm. 173 (2005) 91]. The provided hierarchy of commands can be used interactively in order to simulate the behavior of n-qubit quantum systems (by applying a number of unitary or non-unitary operations) and to analyze their separability and entanglement properties. Restrictions onto the complexity of the problem: 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 or equivalent) machine with of memory. Unusual features of the program: 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. [Copyright &y& Elsevier]

Abstract: During recent years, quantum computations and the study of n-qubit quantum systems have attracted a lot of interest, both in theory and experiment. Apart from the promise of performing quantum computations, however, these investigations also revealed a great deal of difficulties which still need to be solved in practice. In quantum computing, unitary and non-unitary quantum operations act on a given set of qubits to form (entangled) states, in which the information is encoded by the overall system often referred to as quantum registers. To facilitate the simulation of such n-qubit quantum systems, we present the Feynman program to provide all necessary tools in order to define and to deal with quantum registers and quantum operations. Although the present version of the program is restricted to unitary transformations, it equally supports—whenever possible—the representation of the quantum registers both, in terms of their state vectors and density matrices. In addition to the composition of two or more quantum registers, moreover, the program also supports their decomposition into various parts by applying the partial trace operation and the concept of the reduced density matrix. Using an interactive design within the framework of Maple, therefore, we expect the Feynman program to be helpful not only for teaching the basic elements of quantum computing but also for studying their physical realization in the future. Program summary: Title of program: Feynman Catalogue number:ADWE Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADWE Program obtainable from:CPC Program Library, Queen''s University of Belfast, N. Ireland Licensing provisions:None Computers for which the program is designed:All computers with a license of the computer algebra system Maple [Maple is a registered trademark of Waterlo Maple Inc.] Operating systems or monitors under which the program has been tested:Linux, MS Windows XP Programming language used: Maple 9.5 (but should be compatible with 9.0 and 8.0, too) Memory and time required to execute with typical data:Storage and time requirements critically depend on the number of qubits, n, in the quantum registers due to the exponential increase of the associated Hilbert space. In particular, complex algebraic operations may require large amounts of memory even for small qubit numbers. However, most of the standard commands (see Section 4 for simple examples) react promptly for up to five qubits on a normal single-processor machine ( with 512 MB memory) and use less than 10 MB memory. No. of lines in distributed program, including test data, etc.: 8864 No. of bytes in distributed program, including test data, etc.: 493 182 Distribution format: tar.gz Nature of the physical problem:During the last decade, quantum computing has been found to provide a revolutionary new form of computation. The algorithms by Shor [P.W. Shor, SIAM J. Sci. Statist. Comput. 26 (1997) 1484] and Grover [L.K. Grover, Phys. Rev. Lett. 79 (1997) 325. ], for example, gave a first impression how one could solve problems in the future, that are intractable otherwise with all classical computers. Broadly speaking, quantum computing applies quantum logic gates (unitary transformations) on a given set of qubits, often referred to a quantum registers. Although, the theoretical foundation of quantum computing is now well understood, there are still many practical difficulties to be overcome for which (classical) simulations on n-qubit systems may help understand how quantum algorithms work in detail and what kind of physical systems and environments are most suitable for their realization. Method of solution:Using the computer algebra system Maple, a set of procedures has been developed to define and to deal with n-qubit quantum registers and quantum logic gates. It provides a hierarchy of commands which can be applied interactively and which is flexible enough to incorporate non-unitary quantum operations and quantum error corrections models in the future. Restrictions on the complexity of the problem:The present version of the program facilitates the set-up and manipulation of quantum registers by a large number of (predefined) quantum logic gates. In contrast to such idealized unitary transformations, however, less attention has been paid so far to non-unitary quantum operations or to the modeling of decoherence phenomena, although various suitable data structures are already designed and implemented in the code. A further restriction concerns the number of qubits, n, due to the exponentially growing time and memory requirements. Up to now, most of the complex commands are restricted to quantum registers with about 6 to 8 qubits, if use has to be made of a standard single-processor machine. Unusual features of the program:The Feynman program has been designed for interactive simulations on n-qubit quantum registers with no other restriction than given by the size and time resources of the computer. Apart from the standard quantum gates, as discussed in the literature [M.A. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, Cambridge, 2000], it provides all the necessary tools to generalize these gates for n-qubits (in any given order of the individual qubits). Both common representations of the quantum registers in terms of their state vectors and/or density matrices are equally supported by the program whenever possible. In addition, the program also facilitates the composition of two or more quantum registers into a combined one as well as their decomposition into subsystems by using the partial trace and the use of the reduced density matrix for the individual parts. [Copyright &y& Elsevier]