Marek Sawerwain

University of Zielona Góra | UZ · Institute of Control and Computational Engineering

Quantum entanglement is an extremely important phenomenon in the field of quantum computing. It is the basis of many communication protocols, cryptography and other quantum algorithms. On the other hand, however, it is still an unresolved problem, especially in the area of entanglement detection methods. In this article, we present a computational...

Information switching and swapping seem to be fundamental elements of quantum communication protocols. Another crucial issue is the presence of entanglement and its level in inspected quantum systems. In this article, a formal definition of the operation of the swapping local quantum information and its existence proof, together with some elementar...

It has been observed that the reduced density matrices of bipartite qudit pure states possess a Gram matrix structure. This observation has opened a possibility of analysing the entanglement in such systems from the purely geometrical point of view. In particular, a new quantitative measure of an entanglement of the geometrical nature, has been pro...

Networks of quantum circuits or, more generally, networks transmitting quantum information will need, just like classical networks (e.g. internet), a mechanism for directing data to adequate nodes. Routing, understood as packet switching, is one of the most important processes in classical networks. The issue of routing is also present in quantum n...

The paper is dedicated to the problem of supervised learning in quantum circuits. We present two solutions: SWAP-test and Simple Quantum Circuits (SQCs) based on the tree tensor networks which are able to properly classify samples from Moons, Circles, Blobs and Iris sets. Moreover, the mentioned circuits were constructed not only for qubits, but al...

Gram matrix approach to an entanglement analysis of pure states describing $(d,\infty)$ -- quantum systems is being introduced. In particular, maximally entangled states are described as those having a special forms of the corresponding Gram matrices.

It is observed that the reduced density matrices corresponding to pure states of bipartite qudits systems possess the Gram matrix structure. This observation has opened a possibility to analyse the entanglement in such systems from the purely geometrical point of view. In particular a new, of the geometrical nature quantitative measure of an entang...

The quantum Lyapunov control is one of the methods presently used in the quantum state engineering. The mentioned approach allows not only generating specified quantum states but also controlling the dynamics of the operators defining the computational process in a quantum register. In this work, we present the quantum Lyapunov control scheme which...

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 an unstructured database. In addition to the presentation of the recommendation system as an algorithm, the article also shows the main steps...

The growing size of modern databases and recommendation systems make it necessary to use a more efficient hardware and also software solutions that will meet the requirements of users of such systems. These requirements apply to both the size of databases and the speed of response, quality of recommendation. The evolving techniques of the quantum c...

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 c...

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 traj...

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 call...

The article contains a description of two quantum circuits for pattern recognition. The first approach is realized with use of k nearest neighbors algorithm and the second with support vector machine. The task is to distinguish between Hermitian and non-Hermitian matrices. The quantum circuits are constructed to accumulate elements of a learning se...

We suppose that a structure working as a quantum switch will be a significant element of future networks realizing transmissions of quantum information. In this chapter we analyze a process of switch's operating -- especially in systems with a noise presence. The noise is caused by a phenomenon of quantum decoherence, i.e. distorting of quantum sta...

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 computable cross norm and realignment criterion and the concurrence measure. We also present some explicit formulae describing...

The quantum entanglement is considered as one of the most important notions of quantum computing. The entanglement is a feature of quantum systems and it is used as a basis for many quantum algorithms and protocols. In this paper we analyze the level of entanglement for the quantum switch, during its work. The level of entanglement during the corre...

The chapter contains information about a construction of quantum switch for qutrits. It is an expansion of the idea of quantum switch for qubits. For the networks based on quantum effects the switch could realize an operation of changing the direction of transferred information. A presented definition of quantum switch may be easily generalized to...

The chapter contains a description of quantum circuit for pattern recognition. The task is to distinguish Hermitian and Non-Hermitian matrices. The quantum circuit is constructed to accumulate the elements of a learning set and with use of Hamming distance and some Hamiltonian designed for so-called quantum summing operation it is able to distingui...

In this paper a quantum communication protocol with use of repeaters is presented. The protocol is constructed for qudits i.e. the generalized quantum information units. One-dit teleportation is based on the generalized Pauli-Z (phase-flip) gate’s correction. This approach avoids using Pauli-X and Hadamard gates unlike in other known protocols base...

In this chapter a quantum communication protocol with use of repeaters is presented. The protocol is constructed for qudits i.e. the generalized quantum information units. One-dit teleportation is based on the generalized Pauli-Z (phase-flip) gate's correction. This approach avoids using Pauli-X and Hadamard gates unlike in other known protocols ba...

FPGA technology can offer significantly higher performance at much lower power than is available from CPUs and GPUs in many computational problems. Unfortunately, programming for FPGA (using hardware 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...

The entanglement is an extremely important property of quantum computations. However, detecting the entanglement is a difficult problem – even if models of quantum systems are simulated with use of classical computers. It is caused by the exponential complexity of quantum systems which implies overloading the computational resources. This problem a...

The phenomenon of quantum entanglement is an important component of many protocols in the field of quantum computing. In this chapter a level of entanglement in short qudit chains is evaluated. The evaluation is carried out with use of the CCNR criterion and the concurrence measure. There are also some explicit formulae describing the values of CCN...

Nowadays, a dynamic progress in computational techniques allows for development of various methods, which offer significant speed-up of computations, especially those related to the problems of quantum optics and quantum computing. In this work, we propose computational solutions which re-implement the quantum trajectory method (QTM) algorithm in m...

At present, the spin chains are discussed as the solution which may be used in future to construct quantum communication networks. In this paper the definition of XY-type Hamiltonian is presented. The Hamiltonian realizes the transfer of information in a one-dimensional spin chain, which is built of generalised units of quantum information - so-cal...

The chapter describes a Monte Carlo method’s implementation for analyzing the dynamics of open quantum systems—so-called quantum trajectories method. The discussed implementation is realized with use of the CUDA technology. It should be pointed out that using GPU in this approach allows to increase the performance of the quantum trajectories method...

Recently, it has been presented some algorithms and physical models which give prospects for construction of quantum computers capable to solve systems of linear equations. The common feature which is shared in these works is the use of qubits which allow to solve systems with $2^n$ variables. In this work we propose a quantum circuit based on qutr...

The issue of quantum states' transfer -- in particular, for so-called Perfect State Transfer (PST) -- in the networks represented by the spin chains seems to be one of the major concerns in quantum computing. Especially, in the context of future communication methods that can be used in broadly defined computer science. The chapter presents a defin...

The Bose lattice quantum gas based protocols for perfect coherent states transfer are discussed. Additionally, the perfect transfer of qudit states protocol based on Heisenberg-like interactions and in 1D-chains is discussed together with its computer implementation within Zielona Góra Quantum Computer Simulator.

In this paper the parallel algorithms to simulate measurements and unitary operations in the quantum computing model are presented. The proposed solutions are implemented using the CUDA technology. Moreover, a more effective routine for processing density matrices is presented. The main advantages of this approach are the reduced memory requirement...

A coordinate-wise description of the multi-local operations performed on multi-partite quantum systems is presented. A particular application of the result presented to the maximally-entangled cluster decomposition of a general multi-partite quantum states is given together with their ZG QCS environment implementations as well. Keywordsquantum ent...

A general concept of quantum communication networks and some fundamental properties of them are discussed. In particular case of unitary dynamics based protocols some general results were formulated. A particular case of transferring pure states in spin chains, due to XY-like unitary dynamics, has been numerically explored within the ZG QCS simulat...

Simulations of standard 1D and 2D quantum walks have been performed within Quantum Computer Simulator (QCS system) environment and with the use of GPGPU (General Purpose Graphics Processor Unit) supported by CUDA (Compute Unified Device Architecture) technology. In particular, simulations of quantum walks may be seen as an appropriate benchmarks fo...

We describe a general methods to localize any sort of k-separability and therefore also the corresponding partial entanglement in genuinely multipartite mixed quantum states. Our methods are based exclusively on the known twopartite methods and some systematic procedures of combinatorial nature. Our methods are formalized in an algorithmic-like fas...

The canonical Schmidt decomposition of quantum states is discussed and its implementation to the Quantum Computation Simulator is outlined. In particular, the semiorder relation in the space of quantum states induced by the lexicographic semiorder of the space of the Schmidt coefficients is discussed. The appropriate sorting algorithms on the corre...

Natural Quantum Operational Semantics with Predicates A general definition of a quantum predicate and quantum labelled transition systems for finite quantum computation systems is presented. The notion of a quantum predicate as a positive operator-valued measure is developed. The main results of this paper are a theorem about the existence of gener...

Generalisation of the quantum weakest precondition result of D'Hondt and Panangaden is presented. In particular the most general notion of quantum predicate as positive operator valued measure (POVM) is introduced. The previously known quantum weakest precondition result has been extended to cover the case of POVM playing the role of a quantum pred...

In this paper we present the software to simulate circuits and one-way quantum computation models in parallel environments build from PC workstations connected by the standard Ethernet network. We describe the main vector state transformation and its application to one and multi-qubit gate application process. We also show the realisation of the me...

A notion of partial entanglement in multipartite systems is discussed. Some algorithms for detecting and localizing the introduced partial entanglement in general multipartite quantum states are presented. The main feature of the methods presented is that they are exclusively based on two-partite methods.

Streszczenie: Informatyka kwantowa to z pewnoci przyszo informatyki. Na obecnym etapie z braku rozwiza sprz towych, szczególnie istotne s symulatory oblicze kwantowych. Przeprowadzanie eksperymentów jest bardzo trudne oraz niewtpliwe drogie. Tote stosowanie programowych symulatorów jest jedynym dost pnym aktualnie rozwizaniem istotnym dla szeroko p...