We study the functional relationship between quantum control pulses in the idealized case and the pulses in the presence of an unwanted drift. We show that a class of artificial neural networks called LSTM is able to model this functional relationship with high efficiency, and hence the correction scheme required to counterbalance the effect of the drift. Our solution allows studying the mapping from quantum control pulses to system dynamics and then analysing the robustness of the latter against local variations in the control profile.

}, doi = {10.1007/s11128-019-2240-7}, author = {Mateusz Ostaszewski and J.A. Miszczak and Przemys{\l}aw Sadowski and L. Banchi} } @article {2650, title = {QSWalk. jl: Julia package for quantum stochastic walks analysis}, journal = {Computer Physics Communications}, volume = {235}, year = {2019}, month = {2019}, chapter = {414}, doi = {doi.org/10.1016/j.cpc.2018.09.001}, author = {Adam Glos and J.A. Miszczak and Mateusz Ostaszewski} } @article {2668, title = {The role of quantum correlations in Cop and Robber game}, journal = {Quantum Studies: Mathematics and Foundations}, volume = {6}, year = {2019}, chapter = {15}, abstract = {We introduce and study quantized versions of Cop and Robber game. We achieve this by using graph-preserving quantum operations, which are the quantum analogues of stochastic operations preserving the graph. We provide the tight bound for the number of operations required to reach the given state. By extending them to the controlled operations, we define a quantum-controlled Cop and Robber game, which expands the classical Cop and Robber game, as well as the classically controlled quantum Cop and Robber game. In contrast to the typical scheme for introducing quantum games, we assume that both parties can utilise full information about the opponent{\textquoteright}s strategy. We show that the utilisation of the full knowledge about the opponent{\textquoteright}s state does not provide the advantage. Moreover, the chances of catching the Robber decrease for classical cop-win graphs. This result does not depend on the chosen model of evolution. On the other hand, the possibility to execute controlled quantum operations allows catching the Robber on almost all classical cop-win graphs. By this, we demonstrate that it is necessary to enrich the structure of correlations between the players{\textquoteright} systems to provide a non-trivial quantized Cop and Robber game. Thus the quantum controlled operations offer a significant advantage over the classically controlled quantum operations.

}, issn = {2196-5617}, doi = {10.1007/s40509-017-0148-4}, url = {https://doi.org/10.1007/s40509-017-0148-4}, author = {Adam Glos and J.A. Miszczak} } @article {2841, title = {Geometrical versus time-series representation of data in learning quantum control}, journal = {arXiv preprint arXiv:1803.05169}, year = {2018}, author = {Mateusz Ostaszewski and J.A. Miszczak and Sadowski, P} } @article {2666, title = {Impact of the malicious input data modification on the efficiency of quantum algorithms}, journal = {arXiv:1802.10041}, year = {2018}, abstract = {In this paper we demonstrate that the efficiency of quantum algorithms can be significantly altered by malicious manipulation of the input data. We exemplify the possibility of attacks on quantum spatial search based on Szegedy walk. We achieve this by proposing a framework suitable for analysing efficiency of attacks on quantum search algorithms. We provide the analysis of proposed attacks for different models of random graphs.

}, url = {https://arxiv.org/abs/1802.10041}, author = {Adam Glos and J.A. Miszczak} } @article {2613, title = {Limiting properties of stochastic quantum walks on directed graphs}, journal = {Journal of Physics A: Mathematical and Theoretical}, volume = {51}, year = {2018}, chapter = {035304}, doi = {https://doi.org/10.1088/1751-8121/aa9a4a}, url = {https://arxiv.org/abs/1703.01792}, author = {Adam Glos and J.A. Miszczak and Mateusz Ostaszewski} } @article {2665, title = {A quantum-inspired version of the nearest mean classifier}, journal = {Soft Computing}, year = {2017}, doi = {10.1007/s00500-016-2478-2}, author = {Sergioli, G. and Santucci, E. and Didaci, L. and J.A. Miszczak and Giuntini, R.} } @article {iitisid_0518, title = {Symbolic integration with respect to the Haar measure on the unitary groups}, journal = {Bulletin of the Polish Academy of Sciences: Technical Sciences}, volume = {65}, year = {2017}, note = {arXiv:1109.4244}, month = {02/2017}, chapter = {21}, abstract = {We present IntU package for Mathematica computer algebra system. The presented package performs a symbolic integration of polynomial functions over the unitary group with respect to unique normalized Haar measure. We describe a number of special cases which can be used to optimize the calculation speed for some classes of integrals. We also provide some examples of usage of the presented package.

}, doi = {10.1515/bpasts-2017-0003}, url = {https://doi.org/10.1515/bpasts-2017-0003}, author = {Zbigniew Pucha{\l}a and J.A. Miszczak} } @article {2501, title = {A general scheme for information interception in the ping pong protocol}, journal = {Advances in Mathematical Physics,}, volume = {2016}, year = {2016}, pages = {3162012}, doi = {10.1155/2016/3162012}, author = {P. Zawadzki and J.A. Miszczak} } @article {2502, title = {Lively quantum walks on cycles}, journal = {J. Phys. A: Math. Theor.}, volume = {49}, year = {2016}, pages = {375302}, doi = {10.1088/1751-8113/49/37/375302}, author = {Przemys{\l}aw Sadowski and J.A. Miszczak and Mateusz Ostaszewski} } @article {iitisid_0681, title = {Generalized open quantum walks on Apollonian networks}, journal = {PLoS ONE}, volume = {10}, number = {7}, year = {2015}, note = {arXiv:1407.1184}, pages = {e0130967}, author = {{\L}ukasz Pawela and Piotr Gawron and J.A. Miszczak and Przemys{\l}aw Sadowski} } @article {iitisid_0620, title = {General model for a entanglement-enhanced composed quantum game on a two-dimensional lattice}, journal = {Fluctuation and Noise Letters}, volume = {13}, number = {2}, year = {2014}, note = {arXiv:1306.4506}, author = {J.A. Miszczak and {\L}ukasz Pawela and Jan S{\l}adkowski} } @article {iitisid_0637, title = {Quantum network exploration with a faulty sense of direction}, journal = {Quantum Information \& Computation}, volume = {14}, number = {13\&14}, year = {2014}, pages = {1238{\textendash}1250}, abstract = {We develop a model which can be used to analyse the scenario of exploring quantum network with a distracted sense of direction. Using this model we analyse the behaviour of quantum mobile agents operating with non-adaptive and adaptive strategies which can be employed in this scenario. We introduce the notion of node visiting suitable for analysing quantum superpositions of states by distinguishing between visiting and attaining a position. We show that without a proper model of adaptiveness, it is not possible for the party representing the distraction in the sense of direction, to obtain the results analogous to the classical case. Moreover, with additional control resources the total number of attained positions is maintained if the number of visited positions is strictly limited.}, author = {J.A. Miszczak and Przemys{\l}aw Sadowski} } @article {iitisid_0678, title = {Quantum walks with memory on cycles}, journal = {Physica A}, volume = {399}, year = {2014}, pages = {163{\textendash}170}, author = {Michael Mc Gettrick and J.A. Miszczak} } @article {iitisid_0595, title = {Analysis of patent activity in the field of quantum information processing}, journal = {International Journal of Quantum Information}, volume = {11}, number = {1}, year = {2013}, note = {arXiv:1212.2439}, pages = {1350007}, issn = {0219-7499}, author = {Ryszard Winiarczyk and Piotr Gawron and J.A. Miszczak and {\L}ukasz Pawela and Zbigniew Pucha{\l}a} } @article {iitisid_0565, title = {Employing online quantum random number generators for generating truly random quantum states in Mathematica}, journal = {Comput. Phys. Commun.}, volume = {184}, year = {2013}, pages = {127{\textendash}128}, author = {J.A. Miszczak} } @article {iitisid_0537, title = {Increasing the security of the ping-pong protocol by using many mutually unbiased bases}, journal = {Quantum Information Processing}, volume = {12}, number = {1}, year = {2013}, note = {arXiv:1201.3230}, pages = {569{\textendash}576}, abstract = {In this paper we propose an extended version of the ping-pong protocol and study its security. The proposed protocol incorporates the usage of mutually unbiased bases in the control mode. We show that, by increasing the number of bases, it is possible to improve the security of this protocol. We also provide the upper bounds on eavesdropping average non-detection probability and propose a control mode modification that increases the attack detection probability.}, author = {P. Zawadzki and Zbigniew Pucha{\l}a and J.A. Miszczak} } @article {iitisid_0510, title = {Generating and using truly random quantum states in Mathematica}, journal = {Computer Physics Communications}, volume = {183}, number = {1}, year = {2012}, pages = {118{\textendash}124}, abstract = {The problem of generating random quantum states is of a great interest from the quantum information theory point of view. In this paper we present a package for Mathematica computing system harnessing a specific piece of hardware, namely Quantis quantum random number generator (QRNG), for investigating statistical properties of quantum states. The described package implements a number of functions for generating random states, which use Quantis QRNG as a source of randomness. It also provides procedures which can be used in simulations not related directly to quantum information processing.}, issn = {0010-4655}, author = {J.A. Miszczak} } @book {iitisid_0566, title = {High-level Structures for Quantum Computing}, series = {Synthesis Lectures on Quantum Computing}, volume = {6}, year = {2012}, publisher = {Morgan \& Claypool Publishers}, organization = {Morgan \& Claypool Publishers}, isbn = {1608458512}, author = {J.A. Miszczak} } @article {iitisid_0513, title = {Qubit flip game on a Heisenberg spin chain}, journal = {Quantum Information Processing}, volume = {11}, number = {6}, year = {2012}, note = {arXiv:1108.0642}, pages = {1571{\textendash}1583}, abstract = {We study a quantum version of a penny flip game played using control parameters of the Hamiltonian in the Heisenberg model. Moreover, we extend this game by introducing auxiliary spins which can be used to alter the behaviour of the system. We show that a player aware of the complex structure of the system used to implement the game can use this knowledge to gain higher mean payoff.}, author = {J.A. Miszczak and Piotr Gawron and Zbigniew Pucha{\l}a} } @article {iitisid_0536, title = {Restricted numerical shadow and geometry of quantum entanglement}, journal = {J. Phys. A: Math. Theor.}, volume = {45}, year = {2012}, note = {arXiv:1201.2524}, pages = {415309}, abstract = {The restricted numerical range W\_R(A) of an operator A acting on a D-dimensional Hilbert space is defined as a set of all possible expectation values of this operator among pure states which belong to a certain subset R of the of set of pure quantum states of dimension D. One considers for instance the set of real states, or in the case of composite spaces, the set of product states and the set of maximally entangled states. Combining the operator theory with a probabilistic approach we introduce the restricted numerical shadow of A {\textendash} a normalized probability distribution on the complex plane supported in W\_R(A). Its value at point z in C is equal to the probability that the expectation value is equal to z, where |psi> represents a random quantum state in subset R distributed according to the natural measure on this set, induced by the unitarily invariant Fubini{\textendash}Study measure. Studying restricted shadows of operators of a fixed size D=N\_A N\_B we analyse the geometry of sets of separable and maximally entangled states of the N\_A x N\_B composite quantum system. Investigating trajectories formed by evolving quantum states projected into the plane of the shadow we study the dynamics of quantum entanglement. A similar analysis extended for operators on D=2^3 dimensional Hilbert space allows us to investigate the structure of the orbits of GHZ and W quantum states of a three{\textendash}qubit system.}, author = {Zbigniew Pucha{\l}a and J.A. Miszczak and Piotr Gawron and Charles F. Dunkl and J.A. Holbrook and Karol {\.Z}yczkowski} } @inbook {iitisid_0512, title = {Eigengestures for natural human computer interface}, booktitle = {Man-Machine Interactions 2}, year = {2011}, note = {arXiv:1105.1293}, pages = {49{\textendash}56}, publisher = {Springer}, organization = {Springer}, address = {Berlin / Heidelberg}, abstract = {We present the application of Principal Component Analysis for data acquired during the design of a natural gesture interface. We investigate the concept of an eigengesture for motion capture hand gesture data and present the visualisation of principal components obtained in the course of conducted experiments. We also show the influence of dimensionality reduction on reconstructed gesture data quality.}, isbn = {978-3-642-23168-1}, author = {Piotr Gawron and Przemys{\l}aw G{\l}omb and J.A. Miszczak and Zbigniew Pucha{\l}a}, editor = {Tadeusz Czach{\'o}rski and Stanis{\l}aw Kozielski and Urszula Sta{\'n}czyk} } @article {iitisid_0466, title = {Experimentally feasible measures of distance between quantum operations}, journal = {Quantum Information Processing}, volume = {10}, number = {1}, year = {2011}, note = {arXiv:0911.0567 IF=2.085(2010);}, pages = {1{\textendash}12}, abstract = {We present two measures of distance between quantum processes which can be measured directly in laboratory without resorting to process tomography. The measures are based on the superfidelity, introduced recently to provide an upper bound for quantum fidelity. We show that the introduced measures partially fulfill the requirements for distance measure between quantum processes. We also argue that they can be especially useful as diagnostic measures to get preliminary knowledge about imperfections in an experimental setup. In particular we provide quantum circuit which can be used to measure the superfidelity between quantum processes. We also provide a physical interpretation of the introduced metrics based on the continuity of channel capacity.}, issn = {1570-0755}, author = {Zbigniew Pucha{\l}a and J.A. Miszczak and Piotr Gawron and B. Gardas} } @article {iitisid_0478, title = {Models of quantum computation and quantum programming languages}, journal = {Bulletin of the Polish Academy of Sciences - Technical Sciences}, volume = {59}, number = {3}, year = {2011}, pages = {305{\textendash}324}, abstract = {The goal of this report is to provide an introduction to the basic computational models used in quantum information theory. We various review models of quantum Turing machine, quantum circuits and quantum random access machine (QRAM) along with their classical counterparts. We also provide an introduction to quantum programming languages, which are developed using the QRAM model. We review the syntax of several existing quantum programming languages and discuss their features and limitations.}, author = {J.A. Miszczak} } @article {iitisid_0509, title = {Numerical shadow and geometry of quantum states}, journal = {J. Phys. A: Math. Theor.}, volume = {44}, number = {33}, year = {2011}, note = {arXiv:1104.2760 IF=1.641(2010);}, pages = {335301}, abstract = {The totality of normalised density matrices of order N forms a convex set Q\_N in R^(N^2-1). Working with the flat geometry induced by the Hilbert-Schmidt distance we consider images of orthogonal projections of Q\_N onto a two-plane and show that they are similar to the numerical ranges of matrices of order N. For a matrix A of a order N one defines its numerical shadow as a probability distribution supported on its numerical range W(A), induced by the unitarily invariant Fubini-Study measure on the complex projective manifold CP^(N-1). We define generalized, mixed-states shadows of A and demonstrate their usefulness to analyse the structure of the set of quantum states and unitary dynamics therein.}, issn = {1751-8113}, author = {Charles F. Dunkl and Piotr Gawron and J.A. Holbrook and J.A. Miszczak and Zbigniew Pucha{\l}a and Karol {\.Z}yczkowski} } @article {iitisid_0514, title = {Probability measure generated by the superfidelity}, journal = {J. Phys. A: Math. Theor.}, volume = {44}, year = {2011}, note = {arXiv:1107.2792 IF=1.641(2010);}, pages = {405301}, abstract = {We study the probability measure on the space of density matrices induced by the metric defined by using superfidelity. We give the formula for the probability density of eigenvalues. We also study some statistical properties of the set of density matrices equipped with the introduced measure and provide a method for generating density matrices according to the introduced measure.}, author = {Zbigniew Pucha{\l}a and J.A. Miszczak} } @article {iitisid_0473, title = {Product numerical range in a space with tensor product structure}, journal = {Linear Algebra Appl.}, volume = {434}, number = {1}, year = {2011}, note = {arXiv:1008.3482 IF=1.005(2010);}, pages = {327{\textendash}342}, abstract = {We study operators acting on a tensor product Hilbert space and investigate their product numerical range, product numerical radius and separable numerical range. Concrete bounds for the product numerical range for Hermitian operators are derived. Product numerical range of a non-Hermitian operator forms a subset of the standard numerical range containing the barycenter of the spectrum. While the latter set is convex, the product range needs not to be convex nor simply connected. The product numerical range of a tensor product is equal to the Minkowski product of numerical ranges of individual factors.}, issn = {0024-3795}, author = {Zbigniew Pucha{\l}a and Piotr Gawron and J.A. Miszczak and {\L}. Skowronek and Man-Duen Choi and Karol {\.Z}yczkowski} } @article {iitisid_0511, title = {Singular value decomposition and matrix reorderings in quantum information theory}, journal = {J. Mod. Phys. C}, volume = {22}, number = {9}, year = {2011}, month = {9}, pages = {897{\textendash}918}, abstract = {We review Schmidt and Kraus decompositions in the form of singular value decomposition using operations of reshaping, vectorization and reshuffling. We use the introduced notation to analyze the correspondence between quantum states and operations with the help of Jamio{\l}kowski isomorphism. The presented matrix reorderings allow us to obtain simple formulae for the composition of quantum channels and partial operations used in quantum information theory. To provide examples of the discussed operations, we utilize a package for the Mathematica computing system implementing basic functions used in the calculations related to quantum information theory.}, issn = {0129-1831}, author = {J.A. Miszczak} } @article {iitisid_0477, title = {Design-on-demand or how to create a target-oriented social web-site}, journal = {arXiv:1010.4934}, year = {2010}, author = {J.A. Miszczak and I. Sobota-Miszczak} } @article {iitisid_0458, title = {Extending scientific computing system with structural quantum programming capabilities}, journal = {Bulletin of the Polish Academy of Sciences - Technical Sciences}, volume = {58}, number = {1}, year = {2010}, note = {arXiv:1006.1549}, pages = {77{\textendash}88}, issn = {0239-7528}, author = {Piotr Gawron and Jerzy Klamka and J.A. Miszczak and Ryszard Winiarczyk} } @article {iitisid_0476, title = {Restricted numerical range: A versatile tool in the theory of quantum information}, journal = {J. Math. Phys.}, volume = {51}, number = {10}, year = {2010}, note = {arXiv:0905.3646 IF=1.291(2010);}, pages = {102204}, issn = {00222488}, author = {Piotr Gawron and Zbigniew Pucha{\l}a and J.A. Miszczak and {\L}. Skowronek and Karol {\.Z}yczkowski} } @article {iitisid_0431, title = {Bound on trace distance based on superfidelity}, journal = {Phys. Rev. A}, volume = {79}, year = {2009}, note = {arXiv:0811.2323 IF=2.866(2009);}, pages = {024302}, abstract = {We provide a bound for the trace distance between two quantum states. The lower bound is based on the superfidelity, which provides the upper bound on quantum fidelity. One of the advantages of the presented bound is that it can be estimated using a simple measurement procedure. We also compare this bound with the one provided in terms of fidelity.}, author = {Zbigniew Pucha{\l}a and J.A. Miszczak} } @article {iitisid_0421, title = {Sub- and super-fidelity as bounds for quantum fidelity}, journal = {Quantum Information \& Computation}, volume = {9}, number = {1\&2}, year = {2009}, note = {arXiv:0805.2037 IF=2.980(209); IF5=2.402(2010);}, month = {1}, pages = {0103{\textendash}0130}, abstract = {We derive several bounds on fidelity between quantum states. In particular we show that fidelity is bounded from above by a simple to compute quantity we call super{\textendash}fidelity. It is analogous to another quantity called sub{\textendash}fidelity. For any two states of a two{\textendash}dimensional quantum system ($N=2$) all three quantities coincide. We demonstrate that sub{\textendash} and super{\textendash}fidelity are concave functions. We also show that super{\textendash}fidelity is super{\textendash}multiplicative while sub{\textendash}fidelity is sub{\textendash}multiplicative and design feasible schemes to measure these quantities in an experiment. Super{\textendash}fidelity can be used to define a distance between quantum states. With respect to this metric the set of quantum states forms a part of a $N^2-1$ dimensional hypersphere.}, issn = {1533-7146}, author = {J.A. Miszczak and Zbigniew Pucha{\l}a and Pawe{\l} Horodecki and A. Uhlmann and Karol {\.Z}yczkowski} } @article {iitisid_0401, title = {Noise Effects in Quantum Magic Squares Game}, journal = {International Journal of Quantum Information}, volume = {06}, number = {Supp}, year = {2008}, note = {arXiv:0801.4848}, pages = {667}, issn = {0219-7499}, author = {Piotr Gawron and J.A. Miszczak and Jan S{\l}adkowski} } @article {iitisid_0402, title = {Quantum state discrimination: A geometric approach}, journal = {Phys. Rev. A}, volume = {77}, number = {4}, year = {2008}, note = {arXiv:0711.4286 IF=2.908(2008);}, pages = {042111}, abstract = {We analyze the problem of finding sets of quantum states that can be deterministically discriminated. From a geometric point of view, this problem is equivalent to that of embedding a simplex of points whose distances are maximal with respect to the Bures distance (or trace distance). We derive upper and lower bounds for the trace distance and for the fidelity between two quantum states, which imply bounds for the Bures distance between the unitary orbits of both states. We thus show that, when analyzing minimal and maximal distances between states of fixed spectra, it is sufficient to consider diagonal states only. Hence when optimal discrimination is considered, given freedom up to unitary orbits, it is sufficient to consider diagonal states. This is illustrated geometrically in terms of Weyl chambers.}, issn = {1094-1622}, author = {D. Markham and J.A. Miszczak and Zbigniew Pucha{\l}a and Karol {\.Z}yczkowski} } @article {iitisid_0395, title = {Kompilator j{\k e}zyka QCL QCL2QML}, journal = {Studia Informatica}, volume = {28}, number = {4}, year = {2007}, pages = {5{\textendash}18}, author = {Ryszard Winiarczyk and Piotr Gawron and J.A. Miszczak} } @article {iitisid_0389, title = {Quantum Parrondo{\textquoteright}s game with random strategies}, journal = {Journal of Modern Optics}, volume = {54}, number = {13-15}, year = {2007}, month = {9}, pages = {2275{\textendash}228}, abstract = {We present a quantum implementation of Parrondo{\textquoteright}s game with randomly switched strategies using (1) a quantum walk as a source of {\textquoteright}randomness{\textquoteright} and (2) a completely positive (CP) map as a randomized evolution. The game exhibits the same paradox as in the classical setting where a combination of two losing strategies might result in a winning strategy. We show that the CP-map scheme leads to significantly lower net gain than the quantum-walk scheme.}, author = {J. Kosik and J.A. Miszczak and V. Buzek} } @article {iitisid_0119, title = {Description and visualisation of quantum circuits with XML}, journal = {Archiwum Informatyki Teoretycznej i Stosowanej}, volume = {17}, number = {4}, year = {2005}, author = {J.A. Miszczak} } @article {iitisid_0036, title = {Numerical simulations of mixed state quantum computation}, journal = {International Journal of Quantum Information}, volume = {3}, number = {1}, year = {2005}, author = {Piotr Gawron and J.A. Miszczak} } @article {iitisid_0049, title = {Quantum Implementation of Parrondo Paradox}, journal = {Fluctuation and Noise Letters}, volume = {5}, number = {4}, year = {2005}, note = {arXiv:quant-ph/0502185}, pages = {L471{\textendash}L478}, abstract = {We propose a quantum implementation of a capital-dependent Parrondo{\textquoteright}s paradox that uses O(log2(n)) qubits, where n is the number of Parrondo games. We present its implementation in the quantum computer language (QCL) and show simulation results.}, author = {Piotr Gawron and J.A. Miszczak} } @inbook {iitisid_0162, title = {Wysokowydajne sieci komputerowe}, year = {2005}, publisher = {WK{\L}}, organization = {WK{\L}}, chapter = {Symulacje gier kwantowych}, author = {Piotr Gawron and J.A. Miszczak}, editor = {Andrzej Grzywak and Andrzej Kwiecie{\'n}} } @book {iitisid_0071, title = {Nano i kwantowe systemy informatyki. Wyd.Drugie}, year = {2004}, publisher = {Wydawnictwo Politechniki {\'S}l{\k a}skiej}, organization = {Wydawnictwo Politechniki {\'S}l{\k a}skiej}, address = {Gliwice}, author = {Stefan W{\k e}grzyn and Jerzy Klamka and S{\l}awomir Bugajski and M. Gibas and Ryszard Winiarczyk and Lech Znamirowski and J.A. Miszczak and S{\l}awomir Nowak} } @book {iitisid_0260, title = {Kwantowe systemy informatyki}, year = {2003}, publisher = {Wydawnictwo Pracowni Komputerowej Jacka Skalmierskiego}, organization = {Wydawnictwo Pracowni Komputerowej Jacka Skalmierskiego}, edition = {2}, isbn = {83-89105-46-2}, author = {Stefan W{\k e}grzyn and Jerzy Klamka and J.A. Miszczak}, editor = {Tadeusz Czach{\'o}rski} } @book {iitisid_0060, title = {Nano i Kwantowe Systemy Informatyki}, year = {2003}, publisher = {Wydawnictwo Politechniki {\'S}l{\k a}skiej}, organization = {Wydawnictwo Politechniki {\'S}l{\k a}skiej}, address = {Gliwice}, author = {Stefan W{\k e}grzyn and Jerzy Klamka and S{\l}awomir Bugajski and M. Gibas and Ryszard Winiarczyk and Lech Znamirowski and J.A. Miszczak and S{\l}awomir Nowak} } @article {iitisid_0121, title = {Quantum algorithm for factorization}, journal = {Archiwum Informatyki Teoretycznej i Stosowanej}, volume = {14}, number = {2}, year = {2002}, author = {J.A. Miszczak} }