The Entanglement Level and the Detection of Quantum Data Transfer Correctness in Short Qutrit Spin Chains

The quantum entanglement is an important feature of many protocols in the field of quantum computing. In this paper we evaluate a level of entanglement in short qutrit chains. This evaluation is carried out with use of the CCNR criterion and the concurrence measure. We also present some explicit formulae describing the values of CCNR criterion and concurrence for exemplary short spin chains. Utilizing the obtained results, we indicate that analyzing the level of entanglement allows to detect the noise or deviation in the transfer process, in comparison to the perfect transfer where only operation realizing transfer is present.Comment: 15 pages, 9 figures, small typos fi

QTM: computational package using MPI protocol for quantum trajectories method

The Quantum Trajectories Method (QTM) is one of {the} frequently used methods for studying open quantum systems. { The main idea of this method is {the} evolution of wave functions which {describe the system (as functions of time). Then,} so-called quantum jumps are applied at {a} randomly selected point in time. {The} obtained system state is called as a trajectory. After averaging many single trajectories{,} we obtain the approximation of the behavior of {a} quantum system.} {This fact also allows} us to use parallel computation methods. In the article{,} we discuss the QTM package which is supported by the MPI technology. Using MPI allowed {utilizing} the parallel computing for calculating the trajectories and averaging them -- as the effect of these actions{,} the time {taken by} calculations is shorter. In spite of using the C++ programming language, the presented solution is easy to utilize and does not need any advanced programming techniques. At the same time{,} it offers a higher performance than other packages realizing the QTM. It is especially important in the case of harder computational tasks{,} and the use of MPI allows {improving the} performance of particular problems which can be solved in the field of open quantum systems.Comment: 28 pages, 9 figure

Recommendation systems with quantum k-NN and Grover's algorithms for data processing

In this article, we discuss the implementation of a quantum recommendation system that uses a quantum variant of the k-nearest neighbours algorithm and the Grover algorithm to search for a specific element in unstructured database. In addition to the presentation of the recommendation system as an algorithm, the article also shows a main steps in construction of a suitable quantum circuit for realisation of a given recommendation system. The computational complexity of individual calculation steps during recommendation system was also indicated. The verification correctness of a proposed recommendation system was also analysed, indicating an algebraic equation describing the probability of success of the recommendation. The article also shows numerical examples presenting the behaviour of the recommendation system for two selected cases.Comment: 17 pages, 5 figure

FPGA-Based Bandwidth Selection for Kernel Density Estimation Using High Level Synthesis Approach

FPGA technology can offer significantly hi\-gher performance at much lower power consumption than is available from CPUs and GPUs in many computational problems. Unfortunately, programming for FPGA (using ha\-rdware description languages, HDL) is a difficult and not-trivial task and is not intuitive for C/C++/Java programmers. To bring the gap between programming effectiveness and difficulty the High Level Synthesis (HLS) approach is promoting by main FPGA vendors. Nowadays, time-intensive calculations are mainly performed on GPU/CPU architectures, but can also be successfully performed using HLS approach. In the paper we implement a bandwidth selection algorithm for kernel density estimation (KDE) using HLS and show techniques which were used to optimize the final FPGA implementation. We are also going to show that FPGA speedups, comparing to highly optimized CPU and GPU implementations, are quite substantial. Moreover, power consumption for FPGA devices is usually much less than typical power consumption of the present CPUs and GPUs.Comment: 23 pages, 6 figures, extended version of initial pape