Code:

1.0

Project Title:

Quantum Information Theory

0082222

Name:

Mladen

Family name:

Pavičić

Scientific vocation:

Professor

3.1 Code of the

Instituon:

3.0

Institution:

University of Zagreb, Faculty of Civil Engineering

0082

3.2

Department:

Department of Mathematics

Ministry

Other sources

4.1

Expenses in the 1st year:

8

t. of US$

0

t. of US$

4.2

Total expenses:

24

t. of US$

0

t. of US$

4.3

Duration of the project:

3

years

5.0

Summary:

The proposed project would use quantum logic (algebra of quantum logic gates) to give theoretical extrapolations of major experimental implementation of qubits (QED, NMR, ENDOR, etc) so as to verify their suitability for quantum registers, gates, processors, buses, repeaters, storage devices, etc. of the would-be quantum computers and decide on the most promising physical implementation. The ability of physical systems to carry out massive quantum calculation, keep coherence, stand error correction procedure, etc., will be estimated. New requests on coherence, error correction procedure, etc., are expected to emerge from the study and enable new experiments for a final decision on suitability of existing physical implementation of qubits. On the other hand, the project would consider a generalization of existing quantum logic so as to obtain an n-dimensional Hilbert space theory with the help of quantum state equations which emerged from a previous project. To this aim algorithms for constructing new quantum state equations will be made. The algorithms will use the hypergraph theory as well as an isomorph-free exhaustive hypergraph generation. The obtained equations will in the end be used be used to give an n-dimensional Hilbert lattice theory possibly not as an approximation of the standard infinite dimensional Hilbert space but as a genuine quantum theory for quantum computers. Algorithms for constructing quantum state equations are first expected to give four and five atom in a block state which no one has succeed to obtain so far. Then, new classes of equations are expected to be found which would define an n dimensional Hilbert lattice theory. An immediate test for such a construct would be a generation of minimal and arbitrary Kochen-Specker vectors which might then be experimentally verified. Also, the elaboration of laser control of qubits might give significant new effects in the field of quantum optical resonance.

Principal investigator:

President of the Scientific Council

Dean or the Director of the Institution:

Mladen Pavičić

Prof. Željko Korlaet

Prof. Željko Korlaet

6.1

Major field:

Natural sciences

6.2

Field:

Physics

6.3

Branch:

Quantum Mechanics

6.4

Research type:

Oriented basic research

6.5

Institution of emplyment:

University of Zagreb, Faculty of Civil Engineering

6.6

Department:

Department of Mathematics

7.0 Keywords:

quantum information theory, quantum entanglement, quantum computing, quantum logic, quantum logic gates, quantum communication, quantum computers, Hilbert lattices, Hilbert space, hypergraphs, quantum algorithms

Name:

Mladen

Family name:

Pavičić

ZIP code:

10000

City:

Zagreb

Fax:

+385-1-4828050

E-mail:

pavicic@grad.hr

Web-address

http://m3k.grad.hr/pavicic

Code

JMBG:

Name:

Family name:

ID code:

Scientific vocation

Status:

0082

Mladen

Pavičić

077362

PR.INV.

16.1 General goal :

The goal of this project which deals with quantum information theory (quantum computation, communication, and cryptography) and its experimental verifications is twofold. On the one hand, it would make theoretical extrapolations of major experimental implementations of qubits (quantum bits) (QED, NMR, ENDOR, Josephson-junctions, dipole-dipole, silicon nuclear spin, Bose-Einstein condensation, quantum dots, SQUID, etc) so as to verify their suitability for quantum registers, gates, processors, buses, repeaters, storage devices, etc. of the would-be quantum computers. On the other hand, the project would develop a general quantum algebra for universal quantum computation and communication and a general finite dimensional theory of quantum systems suitable for simulating states and processes of these systems. Also, the project should give new results in the theory of Hilbert space and the theory of Hilbert lattices.

16.2 Purpose:

The theory of quantum computation, quantum communication, and quantum cryptography, recently generally called quantum information theory, developed tremendously in the last few years. Still, the most suitable hardware for the devices (e.g., quantum computers) has not been singled out yet. Also, a general quantum algebra underlying quantum computers (as Boolean algebra underlies classical computers) has not been formulated so far. Of the present project is expected first, to give a theoretical blueprint for handling greater number of qubits and more massive calculations for major current experimental implementations. Such theoretical evaluation of the implementations should dispense with particular algorithms (Deutsch-Jozsa, Simon, Shor, Grover, Boghosian, Bernstein-Vazirani, etc.) which might be hardware dependent and rely on possibly general algorithms instead. The general quantum computer language and algebra which the project develop should serve should do the job.

16.3 Application of the research:

The research will have its application in selecting physical effects and processes that are most suitable to serve as hardware of quantum computers, quantum communication, and ultimately quantum network. For, at the moment there are more than fifteen different physical implementations of quantum gates that handle qubits. An essential role in putting together main parts of quantum computers (quantum gate, register, processor, bus, storage devices, etc.) will play the quantum entanglement which will find its application not only in further development of theory and experiments of quantum computers and of quantum mechanics itself but also in quantum teleportation and in quantum communication theory and devices and in particular in quantum networks and cryptography. On the other hand, the development of the general algebra underlying quantum computation, which is often called quantum logic, will find its application not only in the quantum computation theory but also in the theory of Hilbert space, lattice theory, theory of Hilbert lattices, as well as in graph and hypergraph theory. In the end, elaboration of the interaction-free preparation of quantum qubits will find its application in handling and controlling quantum systems that must not be kicked out from their positions (trapped ions, Bose-Einstein condensates).

17.1 Background:

Previous results of the researcher are integrated in the current trends in the field which is best reviewed in three recent books: Gruska, J.: Quantum Computing, Osborne McGraw-Hill, London (1999), Preskill, J: Quantum Information and Computation, http://theory.caltech.edu/~preskill/ph229/#lecture and Bouwmeester, D., Ekert, A., and Zeilinger, A. (Eds): The Physics of Quantum Information, Springer Verlag, Berlin (2000). The proposal stresses three main aspects of the quantum information theory: entanglement (1), communication (2), and algorithms (3). Below, these points are illustrated by some previous contributions of the researcher:// (1) In (1.1) Pavicic, M. and J. Summhammer, Phys. Rev. Lett., 73, 3191 (1994) the researcher developed an entanglement and teleportation scheme based on four-photon spin intensity interferometry independently of and at the same time with C. Bennett (IBM, USA) and A. Zeilinger (Innsbruck, Austria). For example, the scheme presented in (1.2) Pavicic, M., J. Opt. Soc. Am. B, 12, 821 (1995) is the scheme which was later on used in the famous teleportation experiment carried out in Innsbruck in 1998. The scheme was further elaborated in (1.3) Pavicic, M., Optics Comm., 142, 308 (1997). The entanglement elaborated in these paper serves as a basis for theoretical approach of entanglement of qubits in quantum computer schemes to be developed in the project; // (2) Quantum communication, quantum cryptography, quantum network, and partly controlling quantum computer gates are all mostly based on quantum optical devices (see e.g., Quantum Communication, Computing, and Measurement 2, Kumar, P, D'Ariano, and Hirota, O. (Eds.), Kluwer Academic, New York, 2000) and the researcher took an active part in the development of this fields. In (2.1) Pavicic, M., Phys. Rev. A 50, 3486-3491 (1994) it was discovered that there is a 100 percent correlation in polarization between two unpolarized photons subjected to simultaneous detection at a beam splitter. In (2.2) Paul, H. and Pavicic, M., Int. J. Theor. Phys., 35, 2085 (1996) the researcher combined the idea he put forward in his PhD in 1986 (alas, in Croatian - later it was independently elaborated by Elitzur, A. and Vaidman, L, Found. Phys., 23, 987 (1993)) with the detection scheme of H. Paul. In (2.3) Pavicic, M., Phys. Lett., A 223, 241 (1996) the researcher gave the first proposal of erasing interference fringes without transferring a single quant of energy to the system. This was soon afterwards experimentally verified by A. Karlsson and G. Bjoerk's group in the Royal Institute of Technology in Kista, Sweden. Further elaborations are presented in (2.4) Pavicic, M., Phys. Lett., A 224, 220 (1997), (2.5) Paul, H. and Pavicic, M., J. Opt. Soc. Am. B, 14, 1273-1277 (1997);// (3) All experiments leading towards quantum computing (Bouwmeester, D., Ekert, A., and Zeilinger, A. (Eds): The Physics of Quantum Information, Springer Verlag, Berlin, 2000) and implicitly all existing algorithms (Pittenger, A. O.: An Introduction to Quantum Computing Algorithms, Birkhauser, Basel, 1999) rely on a recent result (Lloyd, S., Phys. Rev. Lett.,75, 346 (1995) - rigorously proved by Weaver, N., J. Math. Phys., 41, 240, (2000)) which shows that any quantum gate can be used to approximate any unitary transformation of a chosen Hamiltonian. Now, an open problem is how to formulate a general Hamiltonian which will eventually simulate any quantum system or process. Such a quantum simulator would require a general quantum algebra and the researcher paved the road towards it in a series of papers: (3.1) Pavicic, M. and Megill, N.D., Helv. Phys. Acta, 72, 189 (1999), (3.2) Pavicic, M., Int. J. Theor. Phys., 39, 813 (2000), (3.3) Pavicic, M., Fortschr. Physik--Progr. Physics, 48, 497 (2000), (3.4) McKay, B.D., Megill, N.D., and Pavicic, M., Int. J. Theor. Phys., 39, 2393 (2000), (3.5) Megill, N.D. and Pavicic, M., Int.J. Theor. Phys., 39, 2349 (2000).

17.2 Contination of the previous research:

The researcher was the principal investigator of the previous project Quantum Computation and Quantum Communication (0082006). The proposed project would use the following results from the previous project: (1) the entanglement between two subsystems of a quantum systems that had no common past and that nowhere interacted with each other (1 in 17.1); (2) a loophole-free pre-selected Bell systems can be obtained by using nonmaximal singlet states (1 in 17.1); (3) an interaction-free control of quantum gates is possible (2 in 17.1); (4) new classes of quantum state equations (3 in 17.1).

17.3: Citations, current application, patents:

Number of citations in Science Citation Index (1996-March 2001): 109 (101 journal papers, 8 proceedings papers). // D. R. Vij, ed. of Progress in Lasers Series at Kluwer Publishers, New York, offered the researcher to write a book on quantum information theory and experiments mid 2001; Contract for the book entitled Quantum Computation and Quantum Communication: Theory and Experiments signed Sept. 2001; // A. Karlsson and G. Bjoerk's group in the Royal Institute of Technology in Kista, Sweden carried out interaction-free experiments according to the researcher's schemes from references (see subsection 17.1 above): (2.2) - (2.5): Inoue, A.U., J. Optics B, 2, 338 (2000), Karlsson, A.U., Phys. Rev. Lett. 80, 1198 (1998), etc.;// A. Zeilinger's group in 1998 carried entanglement swapping and in effect the teleportation experiment using the same scheme as presented in Pavicic, M.,J. Opt.Soc.Am. B, 12, 821 (1995); Reviewed by Hariharan and Sanders, Progr. Optics XXXVI, p.106-8 (1996).

18.1: Hypothesis

It is possible to use quantum logic (algebra of quantum logic gates) to give theoretical extrapolations of major experimental implementation of qubits (QED, NMR, ENDOR, etc) so as to verify their suitability for quantum registers, gates, processors, buses, repeaters, storage devices, etc. of the would-be quantum computers and decide on the most promising implementation. Quantum logic itself can be generalized (as an n dimensional Hilbert theory) so as to enable a construction of quantum simulator whose qubits would simulate a given quantum system.

18.2 Meaning of the proposed research:

The fact that one of the leading scientific publisher in the World (Kluwer, see 17.3 above) commissioned the book on some results of the proposed research in advance indicates its importance and meaning as well the researcher's merit for carrying it out. Billions of dollars which have recently been poured into the field as well the exponentially growing number of papers are other signs of its importance. It should be stressed here that not only the field of quantum computing and communication would benefit from the research. The new classes of quantum state equations will be a significant contribution to the Hilbert space theory as well as the theory of Hilbert lattices and hypergraph theory. On the other hand the quantum information theory especially through its elaboration of quantum entanglement offers a new insight into quantum mechanics and quantum optics and leads to many new applicable discoveries as has been well shown in the past ten years.

18.3 Methods:

To extrapolate experimental implementations of quibts the research will use Gruska, J.: Quantum Computing, Osborne McGraw-Hill, London (1999), Preskill, J: Quantum Information and Computation, http://theory.caltech.edu/~preskill/ph229/#lecture and Bouwmeester, D., Ekert, A., and Zeilinger, A. (Eds): The Physics of Quantum Information, Springer Verlag, Berlin (2000) and the researcher's own elaboration of entanglement as given in Pavicic, M., J. Opt. Soc. Am. B, 12, 821 (1995) and his other papers. Elaboration of quantum communication, quantum cryptography, quantum network, and partly controlling quantum computer gates will start with mostly quantum optical methods as presented in Quantum Communication, Computing, and Measurement 2, Kumar, P, D'Ariano, and Hirota, O. (Eds.), Kluwer Academic, New York, 2000 and Bouwmeester, D., Ekert, A., and Zeilinger, A. (Eds): The Physics of Quantum Information, Springer Verlag, Berlin (2000) and the researcher's own contributions (1.3),(2.1)-(2.5) as cited in subsection 17.1 above. To arrive at a generalized n dimensional quantum logic the research will start with Gruska, J.: Quantum Computing, Osborne McGraw-Hill, London (1999) and combine it with methods and algorithms developed in : Pavicic, M. and Megill, N.D., Helv. Phys. Acta, 72, 189 (1999), Pavicic, M., Int. J. Theor. Phys., 39, 813 (2000), Pavicic, M., Fortschr. Physik--Progr. Physics, 48, 497 (2000), McKay, B.D., Megill, N.D., and Pavicic, M., Int. J. Theor. Phys., 39, 2393 (2000), Megill, N.D. and Pavicic, M., Int.J. Theor. Phys., 39, 2349 (2000), Megill, N.D. and Pavicic, M., Int.J. Theor. Phys., 40, 1387 (2001) as well as with isomorph-free exhaustive generation of hypergraphs developed in McKay, B.D., J. Algorithms, 26, 306 (1998).

18.4 Protocol and program plan:

First, the elaboration of a theoretical extrapolation of particular experimental implementations of quantum logic gates will be made. The ability of particular physical systems to carry out massive quantum calculation, keep coherence, stand error correction procedure, etc., will be estimated. Then the preliminary algorithms for constructing quantum state equations will be made. The algorithms will use the hypergraph theory as well as an isomorph-free exhaustive hypergraph generation. The obtained equations will in the end be used be used to give an n dimensional Hilbert lattice theory possibly not only as an approximation of the standard infinite dimensional Hilbert space but also a genuine quantum theory for quantum computers

18.5 Expected results:

Of the proposed theoretical extrapolation of particular experimental implementations of quantum logic gates is expected to decide on the most suitable physical implementations of quantum computers. New requests on coherence, error correction procedure, etc., are expected to emerge from the study and enable new experiments. Algorithms for constructing quantum state equations are first expected to give four and five atom in a block state which no one has succeed to obtain so far. Then, new classes of equations are expected to be found which would define an n dimensional Hilbert lattice theory. An immediate test for such a construct would be a generation of minimal and arbitrary Kochen-Specker vectors which might then be experimentally verified. Also, the elaboration of laser control of qubits might give significant new effects in the field of quantum optical resonance.

18.6 Ethical norms and conformance to the Croatian legislation and international conventions:

19.0 Notes:

I am aware that it would be more proper to form a group of investigators. The reason why I am the only investigator is twofold. First, I am the only physicist at my faculty. Secondly, I am the only researcher in Croatia who is engaged in the field of quantum information theory, quantum computing, and quantum communication which are all rapidly growing fields in the world.

20.0 List of 10 major scientific references of all researchers in the period between 1997 and 2001

Pavicic, M., Loophole-Free Four Photon EPR Experiment, Physics Letters, A 224, 220-226 (1997).

Paul, H. and Pavicic, M., Nonclassical Interaction-Free Detection of Objects in a Monolithic Total-Internal-Reflection Resonator, Journal of the Optical Society of America, B 14, 1273-1277 (1997).

Pavicic, M., A Method for Reaching Detection Efficiencies Necessary for Optical Loophole-Free Bell Experiments, Optics Communications, 142, 308-314 (1997).

Paul, H. and Pavicic, M., Realistic Interaction-Free Detection of Objects in a Resonator, Foundations of Physics, 28, 959-970 (1998).

Pavicic, M. and Megill, N.D., Non-Orthomodular Models for Both Standard Quantum Logic and Standard Classical Logic: Repercussions for Quantum Computers, Helvetica Physica Acta, 72, 189-210 (1999).

Pavicic, M., Quantum Logic for Quantum Computers, International Journal of Theoretical Physics, 39, 813-825 (2000).

Pavicic, M., Quantum Simulators and Quantum Repeaters, Fortschritte der Physik-Progress of Physics, 48, 497-503 (2000).

Megill, N. D. and Pavicic, M., Equations, States, and Lattices of Infinite-Dimensional Hilbert Spaces, International Journal of Theoretical Physics, 39, 2349-2391 (2000).

McKay, B.D., Megill, N.D., and Pavicic, M., Algorithms for Greechie Diagrams, International Journal of Theoretical Physics, 39, 2393-2417 (2000).

Pavicic, M., Quantum Logic for Genuine Quantum Simulators, in Donkor, E. and Pirich, A.R. (eds.), Quantum Computing, Proceedings of SPIE Vol. 4047 (2000); pp. 90-96.

JMBG:

Name:

Family name:

ID code:

Scientific vocation:

Last appointment

into vocation

Mladen

Pavičić

Full Professor

14.11.2001

Year

Institution

Major field

Field

Branch

Ph.D.:

1986

Physics Dept., Belgrade Univ.

Natural sciences

Physics

Quant.Mech.

Principal investigator role on the project:

To conceive and carry out the research

Employment and duties

1979-1982 Assistant in Math. and Phys., Faculty of Civil Engineering, Department of Mathematics

1982-1990, Scientific Assistant in Math. and Phys., University of Zagreb, Faculty of Civil Engineering, Dept. of Math.

1990-1996, Assistant Professor in Physics, University of Zagreb, Faculty of Civil Engineering, Dept. of Mathematics

1996-2001, Associate Professor in Physics, University of Zagreb, Faculty of Civil Engineering, Dept. of Mathematics

1999-2000, Visiting Professor in Physics, University of Maryland Baltimore County, Baltimore, USA, Dept. of Phys.

2001-, Full Professor in Physics, University of Zagreb, Faculty of Civil Engineering, Department of Mathematics

Education and specialisation

1988-1990, University of Cologne, Germany, Institute for Theoretical Physics

1993, June, Atomic Institute of the Austrian Universites, Vienna, Austria.

1993, July-September, Technical University of Berlin, Germany, Institute for Theoretical Physics.

1994, August-September, Atomic Institute of the Austrian Universites, Vienna, Austria.

1995, June-October, Humboldt-University of Berlin, Germany, Department of Non-Classical Radiation

1999-2000, University of Maryland Baltimore County, Baltimore, USA, Dept. of Phys.

Membership

International Quantum Structure Association, Inc., Atlanta, Georgia, USA.; Member Founder

Humboldt-Club of Croatia, Zagreb, Croatia; President.

European Physical Society

Optical Society of America

Awards

Alexander von Humboldt Foundation Award: 1988-1990, University of Cologne, Germany, Institute for Theoretical Physics

Alexander von Humboldt Foundation Award: 1993, Technical University of Berlin, Germany, Instit. for Theoretical Physics

Alexander von Humboldt Foundation Award: 1995, Humboldt-University of Berlin, Germany, Dept.of Non-Class.Radiation

Senior Fulbright Teaching/Research Award:1999-2000, University of Maryland Baltimore County, USA, Dept. of Physics