Computer Physics Communications Program Library

Programs in Physics & Physical Chemistry



Manuscript Title: Simulation of n-qubit quantum systems III. Quantum operations
Authors: T. Radtke, S. Fritzsche
Program title: FEYNMAN
Catalogue identifier: ADWE_v3_0 Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 176(2007)617
Programming language: MAPLE 10.
Computer: Any system that supports Maple.
Operating system: Any system that supports Maple; tested under Microsoft Windows XP, SuSe Linux 10.
RAM: see "Running time " below.
Keywords: quantum register, quantum operation, channel, decoherence.
PACS: 03.67.Lx, 03.65.Ud, 03.75.Gg.
Classification: 4.15.
Does the new version supersede the previous version?: Yes
Nature of problem: Today, entanglement is identified as the essential resource in virtually all aspects of quantum information theory. In most practical implementations of quantum information protocols, however, decoherence typically limits the lifetime of entanglement. It is therefore necessary and highly desirable to understand the evolution of entanglement in noisy environments.
Solution method: Using the computer algebra system MAPLE, we have developed a set of procedures that support the definition and manipulation of n-qubit quantum registers as well as (unitary) logic gates and (nonunitary) quantum operations that act on quantum registers. The provided hierarchy of commands can be used interactively in order to simulate and analyze the evolution of n-qubit quantum systems in ideal and nonideal quantum circuits.
Reasons for new version: While the previous program versions were designed mainly to create and manipulate the state of quantum registers, the present extension aims to support quantum operations as the essential ingredient for studying the effects of noisy environments.
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 ≥ 2 GHz or equivalent) and 5 - 20 MB of memory. Especially when working with symbolic expressions, however, the memory and time requirements critically depend on the number of qubits in the quantum registers, owing to the exponential dimension growth of the associated Hilbert space. For example, complex (symbolic) noise models (with several Kraus operators) for multi-qubit systems often result in very large symbolic expressions that dramatically slow down the evaluation of measures or other quantities. In these cases, MAPLE's assume facility sometimes helps to reduce the complexity of symbolic expressions, but often only numerical evaluation is possible. Since the complexity of the FEYNMAN commands is very different, no general scaling law for the CPU time and memory usage can be given.