AU2020103849A4 - QCIU- Education Environment System: Quantum Computing Integrated Development Education Environment Using IoT-Based System - Google Patents

Abstract

Our Invention "QCIU- Education Environment System" is a computer-implemented, quantum computer method provides an educational environment in a virtual reality setting and individuals navigate a virtual reality campus by using an avatar to interact with other users and to engage in learning experiences in the virtual setting. The invented technology also individual's complete projects in virtual reality by accessing educational materials in electronic format and communicating with one another via text-based chats and real time audio. The invented technology also includes virtual reality campus emulates a physical campus by providing meeting spaces and work areas where students spontaneously share information and complete pre-planned tasks. An electronic database tracks biographical and educational information about each user that users progress in achieving study goals and the deliverables that the student produces to fulfil requirements of virtual instruction. The database also links to other systems such as a registration database so that the student's entire learning experience on both a physical campus and in virtual reality can be conveniently accessed electronically. 23 11 Q1 = A o -12 ~ ~ 13 Q2-=A2[nalna) A2[no18Z| A2 A3 A2[silno] A2[3ijii .14 AQnia Aalnolsil Asinal Asailsil Q4 = A[nolna,no] Almno,,sil Al[nojsi,noj Al[nolsi,si) Al[ino,nol Al[sino,sil Alasilsi,nol AleiaSi,Sij Smart Aqa Senso....... Analymarrepona Srennsors J: cleanwaatr FI.1:SOW LBLLDGRP NDTE OR OE ARIE ASCATDWIHTH OU ODSO THE GRAPH. A QB NET CONSISTS OF 2PS:lBlLERPHADAtOLCToFnOEMARCS ONEu~enr MARIeOREAHNOE

Description

Q1 = A o

-12 ~ ~ 13 Q2-=A2[nalna) A2[no18Z| A2 A3 A2[silno] A2[3ijii

.14 AQnia Aalnolsil Asinal Asailsil

Q4 = A[nolna,no] Almno,,sil Al[nojsi,noj Al[nolsi,si) Al[ino,nol Al[sino,sil Alasilsi,nol AleiaSi,Sij

Smart Aqa Senso.......

Analymarrepona Srennsors J: cleanwaatr

FI.1:SOW LBLLDGRP NDTE OR OE ARIE ASCATDWIHTH OU ODSO A QB THE GRAPH. NET CONSISTS OF 2PS:lBlLERPHADAtOLCToFnOEMARCS ONEu~enr MARIeOREAHNOE

QCIU- Education Environment System: Quantum Computing Integrated Development Education Environment Using loT-Based System

FIELD OF THE INVENTION

Our invention "QCIU- Education Environment System "is related to quantum computing integrated development education environment using IOT-based system and also relates to an array of quantum bits known as a quantum computer.

BACKGROUND OF THE INVENTION

This invention deals with quantum computers. A quantum computer is an array of quantum bits (qubits) together with sonic hardware for manipulating these qubits. Quantum computers with only a few bits have already been built. For a review of quantum computers, see DiV95: D. P. Di-Vincenzo. Science 270, 255 (1995). See also Ste97: A. M. Steane, Los Alamos eprint http://xxx.lanl.gov/abs/quant-ph/9708022. This invention also deals with Quantum Bayesian (QB) nets. QB Nets are a method of modeling quantum systems graphically in terms of network diagrams. For more information, see Tuc95: R. R. Tucci. Int. Jour. of Mod. Physics B9, 295 (1995). See also Tuc98: U.S. Pat. No. ,787,236.

In classical computation and digital electronics, one deals with sequences of elementary instructions (instructions such as AND, NOT and OR). These sequences are used to manipulate an array of classical bits. The instructions are elementary in the sense that they act on only a few bits (usually 1, 2 or 3) at a time. Henceforth, we will sometimes refer to sequences as products and to instructions as operations, operators, steps or gates. Furthermore, we will abbreviate the phrase "sequence of elementary operations" by "SEO". In quantum computation, one also deals with SEOs, but for manipulating qubits instead of classical bits. This invention comprises a classical computer running a computer program that expresses the information contained in a QB net as a SEO. One can then run these SEOs on a quantum computer. Of course, QB nets can and have been run entirely on a classical computer. (See the software program called "Quantum Fog", produced by the Artiste company (www.ar-tiste.com)). However, because of the higher speeds promised by quantum parallelism, one expects QB nets to run much faster on a quantum computer.

With classical computers, one usually writes a computer program in a high level language (like Fortran, C or C++). A compiler then expresses this as a SEO for manipulating bits. In the case of quantum computers, a QB net may be thought of as a program in a high level language. This invention is like a "quantum compiler" in the sense that it can take a QB net input, and re-express it as a SEO that can then be used to manipulate qubits. This invention shows how to reduce a QB net into a SEO by a twostep process. First, express the information contained in the QB net as a sequence of unitary operators. Second, express each of those unitary operators as a SEO. An appendix to this document contains the C++ source code of a computer program called "Qubiter.1.0". In its current version (1.0), Qu biter can decompose into a SEO only the simplest non-trivial kind of QB net: a single unitary matrix, or, equivalently. 2 connected nodes. Future versions of Qubiter are planned that will take an arbitrary QB net as input, and return as output a SEO for running a quantum computer. QB nets are to quantum physics what Classical Bayesian (CB) nets are to classical physics. For a review of CB nets, see Nea90: Richard E. Neapolitan, Probabilistic Reasoning in Expert Systems: Theory and Algorithms (Wiley, 1990). See also Pea88: Judea Pearl, Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference (Morgan Kaufmann, Palo Alto, 1988). CB nets have been used very successfully in the field of artificial intelligence (AI). Thus, we hope and expect that someday QB nets, running on quantum computers, will be used for Al applications. In fact, we believe that quantum computers are ideally suited for such applications.

First, because Al tasks often require tremendous power, and quantum computers seem to promise this. Second, because (quantum computers are plagued by quantum noise, which makes their coherence times short. There are palliatives to this, such as quantum error correction (See the review Ste97). But such palliatives come at a price: a large increase in the number of steps. The current literature often mentions factoring a large number into primes as a future use of quantum computers (See the review Ste97). However, due to noise, quantum computers may ultimately prove to be impractical for doing long precise calculations such as this. On the other hand, short coherence times appear to be a less serious problem for the types of calculations involved in Al. The human brain has coherence times too short to factor a 100-digit number into primes, and yet long enough to conceive the frescoes in the Sistine Chapel. We do not mean to imply that the human brain is a quantum computer. An airplane is not a bird, but it makes a good flyer. Perhaps a quantum computer, although not a human brain, can make a good thinker.

To our knowledge, nobody else has invented a method of reducing an arbitrary QB net to a SEO for running a quantum computer. It's true that previous workers (See Bar95: A. Barrenco, C. H. Bennett, R. Cleve, D. P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. H. Smolin, H. Weinfurter, Physical Review A 52, 3457 (1995)) have described a method for reducing a single unitary operator into a SEO. But our method for doing this is significantly different from theirs. Their method is based on a mathematical technique described in Rec94: M. Reck and A. Zeilinger, Physical Review Letters 73, 58 (1994). Our method is based on a mathematical technique called the CS Decomposition, to be described later. For a review of the CS decomposition, see Pai94: C. C. Paige, M. Wei, Linear Algebra. and Its Applications 208, 303 (1994). Our CS method for reducing unitary matrices has inherent binary symmetries that make it easy to apply to qubit systems, which also possess binary symmetries. The method of Bar95 possesses no such symmetries. For this reason, we believe our method to be superior to theirs.

The invention is a computer product that implements a virtual education system and a peer-based method of instructing students. The educational system utilizes a three dimensional ("3-D") social environment in which students, instructors, and administrators interact within a virtual campus over a computer network. The students achieve preplanned educational goals by participating in online learning experiences within the virtual campus. The faculty tracks and evaluates students' activities and required interactions to guide students toward realization of the educational goals. The system administrators provide the computer functionality, especially database services, to monitor the effectiveness of the virtual learning environment. Society has evolved to a point where individuals are equally comfortable communicating via computer or in person. The demands of the busier and more mobile culture in which individuals interact today require familiarity with electronic systems and platforms. As such, educational systems increasingly rely upon electronic communications to complete certain tasks within a course of study. There have been numerous opportunities for students to complete distance-based and online courses in an electronic environment for a number of years. Computer products such as the Blackboard Academic Suite@ and WebCT@ have historically provided electronic educational services in web-based applications.

Previous electronic educational services, however, have continued to rely upon a top down structure in which educators placed content in an electronic space that students could access. Even the advent of email and text-based chatting did not change the traditional format of these prior electronic systems in which the educational content was basically a substitute for sitting in a classroom listening to a lecture. None of the available web-based educational experiences allowed students to form small groups for sharing workspaces and assignments. Also, there were few opportunities for real-time, simultaneous discussions among all participants or subsets of participants using the system at any given time. The prior programs offered threaded discussion boards in which users listed comments one after the other. These threads were available for anyone to see and were often cumbersome when one tried to glean useful information from the thread. Blackboard@ and WebCT@, along with similar programs Moodle@ and Sakai@, have included text chat functions, but they offered only limited opportunities for unplanned synchronous interaction. Students and teachers had to set up a time to meet in the chat area. In this environment, it has been difficult for electronic classrooms to provide an educational experience that is anywhere close to an actual experience on a physical campus.

One of the most dramatic influences on the structure of electronic education systems has been the proliferation of gaming devices that have captured so much attention of late. Modern electronic games give the players a sense of "presence" in a world that is different from their own reality. The game participants take on an identity within the game and operate inside a virtual 3D environment. This type of stimulation has led to numerous individuals participating in virtual settings at every opportunity. As a result, there are multiple resources available for individuals to learn more about virtual reality settings and even create their own virtual reality programs. One company that offers in-depth access to virtual reality programs is known as Activeworlds@, Inc. According to their website, "the Active Worlds Universe is a community of hundreds of thousands of users that chat and build 3D virtual reality environments in millions of square kilometers of virtual territory." Obviously, a large segment of the population has come to expect access to virtual reality settings as part of their everyday life. This explains the success of virtual reality programs like Second Life@ and Sims Online@, which offer users the ability to take on a persona within a virtual reality world to play games, interact with other players, or even buy property in a virtual geography. The proliferation of virtual reality systems has actually accomplished little to correct limitations in communication structures among students in an electronic educational setting, however. These prior electronic, or virtual reality, systems allowed users to talk to all users or just one other user, but the systems lacked any ability to facilitate groups or communities within the overall population on the system.

Small group experiences and learning opportunities among selected peers are the hallmarks of true-to-life student experiences in a campus setting. One other feature of a physical campus that has been lacking in electronic education is that of learning by merely being around other students and engaging in impromptu discourse. Students tend to stroll about a physical campus, and even when engaging in a casual period of "hanging out" with friends, opportunities arise to discuss each other's course work, their readings, and other meaningful topics. Just being present on a campus leads to serendipitous learning opportunities. Without these types of small group interactions, the electronic educational systems (e.g., web-based or online courses) could not fully emulate a real world campus setting. As a result, the quality of the education available in electronic classrooms or online suffered. The inventors herein, then, have identified a need to promote these impromptu or serendipitous learning opportunities within a virtual campus so that electronic or online experiences are better simulations of a physical campus.

Prior efforts to provide virtual reality educational systems have been shown in patent literature. For example, U.S. Pat. No. 6,226,669 (Huang, 2001) et al. discloses a multi-user virtual reality interaction system that is accessible via the world-wide web. Huang mentions (col. 11, line 57) that one example of a multiple-participant 3D virtual reality environment has been used at Tamkang University in Taiwan. Huang shows that all users can enter a virtual reality version of the Tamkang campus and interact with one another by chatting at will. Huang, therefore, focuses mainly upon allowing simultaneous, real time communications instead of providing a higher quality educational experience in the virtual campus.

Along the same lines as the Huang patent, European Patent Application No. EP1689143 (Nez, 2006) shows another improvement in communications within a virtual reality setting. The Nez '143 publication provides a system of communications between virtual reality participants, referred to therein as automats or smart agents. The Nez system allows these participants to interact in groups via public or private conversations over the internet. An agent can send a message to its group or to any number of other agents via text, voice, or video data. The Nez system formats the message for faster and more accurate reception by the intended user on the other end. Although Nez mentions that the communications system may be used in any number of settings, Nez offers no details on how such communication systems would benefit an educational experience. The invention herein meets a need in the educational arena for electronics-based instruction that still provides a social context for learning by allowing more flexible communications among students, educators, and administrators.

PRIOR ART SEARCH

S6219045B1*1995-11-132001-04-17Worlds, Inc. Scalable virtual world chat client server system US6226669B1*1997-12-192001-05-01Jiung-Yao Huang Muti-user 3D virtual reality interaction system utilizing protocol data units for data communication among WWW server and clients US20010044833A1 *1999-01-152001-11-22Edwin Eisen-drath Online virtual campus US20020113809A1*2000-12-272002-08-22Yoshiko Akazawa Apparatus and method for providing virtual world customized for user US6628287B1*2000-01-122003-09-30There, Inc. Method and apparatus for consistent, responsive, and secure distributed simulation in a computer network environment US7036128B1*1999-01-052006-04-25Sri International Offices Using a community of distributed electronic agents to support a highly mobile, ambient computing environment US20060238381A1*2005-04-212006-10-26Microsoft Corporation Virtual earth community based recommendations US20080215994A1*2007-03-012008-09-04Phil Harrison Virtual world avatar control, interactivity and communication interactive messaging US20030028387A1*2001-07-112003-02-06Daniel Kilbank System and method for compressing data US20030121028A1*2001-12-222003-06-26Michael Coury Quantum computing integrated development environment US20030164490A1*2001-02-132003-09-04Alexandre Blais Optimization method for quantum computing process US20040000666A1*2002-04-042004-01-01Daniel Lidar Encoding and error suppression for superconducting quantum computers US20040086038A1*2002-04-232004-05-06Daniel Kilbank System and method for using microlets in communications US20040207548A1*2003-04-212004-10-21Daniel Kilbank System and method for using a microlets-based modem US20040238813A1 *2003-03-032004-12-02D-Wave Systems, Inc. Dressed qubits US20050059020A1*2003-09-112005-03-17Franco Italian Quantum information processing elements and quantum information processing platforms using such elements US20050059138A1*2003-09-112005-03-17Franco Vitaliano Quantum information processing elements and quantum information processing platforms using such elements

OBJECTIVES OF THE INVENTION

1) The objective of the invention is to a computer-implemented, quantum computer method provides an educational environment in a virtual reality setting and individuals navigate a virtual reality campus by using an avatar to interact with other users and to engage in learning experiences in the virtual setting. 2) The other objective of the invention is to a individual's complete projects in virtual reality by accessing educational materials in electronic format and communicating with one another via text-based chats and real time audio.

3) The other objective of the invention is to a virtual reality campus emulates a physical campus by providing meeting spaces and work areas where students spontaneously share information and complete pre-planned tasks. 4) The other objective of the invention is to a electronic database tracks biographical and educational information about each user that users progress in achieving study goals and the deliverables that the student produces to fulfil requirements of virtual instruction. 5) The other objective of the invention is to a links to other systems such as a registration database so that the student's entire learning experience on both a physical campus and in virtual reality can be conveniently accessed electronically.

SUMMARY OF THE INVENTION

A quantum computer is an array of quantum bits (qubits) together with some method for manipulating these qubits. Quantum Bayesian (QB) nets are a method of modeling quantum systems graphically in terms of network diagrams. This invention comprises a classical computer that runs a computer program. The program takes a QB net and decomposes it into a sequence of elementary operations (SEO). Such a sequence can be used to manipulate a quantum computer. This invention shows how to reduce a QB net into a SEO by performing four steps: (1) Find eras. (2) Insert delta functions. (3) Find unitary extensions of era matrices. (4) Decompose each unitary matrix into a SEO.

In step (1), we partition the set of nodes of the QB net into subsets called eras. All nodes in a given era "occur at roughly the same time". We also assign a matrix to each era. In step (2), we pad the era matrices of step (1) with delta functions so that the resultant era matrices can be multiplied by each other. In step (3), we extend the era matrices of step (2) (by adding rows and columns) so that the resultant era matrices are all unitary and of the same size. In step (4), we reduce into a SEO each of the unitary era matrices of step (3). Step (4) is based on the CS Decomposition Theorem. This theorem asserts that: given a unitary matrix U, if we partition it into 4 blocks Uo, U 1 , U 2 , U 3 of the same size, then one can express each Uk, k where kE{0, 1, 2, 3}, as a product LkDkRI such that Lkand Rkare unitary matrices and Dkis diagonal. Since the matrices Lk and Rkare unitary one can apply the CS Decomposition Theorem to them next. One can continue to apply the CS Decomposition Theorem to the unitary matrices generated in previous steps. In this way, one can express the original matrix U as a product of matrices of a type that we call "central matrices". We show how to express any central matrix as a SEO.

An appendix to this document contains the C++ source code of a computer program called "Qubiterl.O". In its current version (1.0), Qubiter can decompose into a SEO only the simplest non-trivial kind of QB net: a single unitary matrix, or, equivalently, 2 connected nodes. Future versions of Qubiter are planned that will take an arbitrary QB net as input, and return as output a SEO for running a quantum computer. The invention is a computer program product, computerized system, and computer-implemented method of providing an educational environment in a virtual reality setting. Individuals, including students, faculty, and administrators navigate the campus by using a graphical representation of themselves, known as an avatar, to interact with other users and to engage in learning experiences available in the virtual setting. Individuals complete pre-planned projects and assignments in virtual reality by accessing educational materials in electronic format and communicating with one another via text-based chats and real time audio.

The system and method described herein also encourages serendipitous learning by encouraging users to explore the virtual campus at will and make the most of opportunities to engage other system users. In this way, the virtual reality campus emulates a physical campus by providing meeting spaces and work areas where students spontaneously share information whether assigned to do so or not. System users' progress within the campus is tracked and maintained in electronic format, most preferably by linking the virtual reality campus to a database. The database includes biographical and educational information about each user, that user's progress in achieving goals of a course of study, and the deliverables that the student produces to fulfill requirements of virtual instruction. The database may also link to other systems, such as a registration database so that the student's entire learning experience on a physical campus and in virtual reality can be conveniently accessed electronically.

The method of teaching in a virtual campus allows for more in-depth experiences in an electronic education by giving students and faculty more freedom in designing and completing assignments. The virtual campus is accessible by any number of students in multiple physical locations, yet the navigation in virtual reality brings all the users together to achieve common goals. Accordingly, the method herein encourages cross collaboration among students from different walks of life, different courses of study, and different peer groups on campus.

BRIEF DESCRIPTION OF THE DIAGRAM

FIG. 1: shows a labelled graph and the four node matrices associated with the four nodes of the graph. A QB net consists of 2 parts: a labelled graph and a collection of node matrices, one matrix for each node. FIG. 2: shows a QB Net for Teleportation. This figure also shows the number of quantum or classical bits carried by each arrow. FIG. 3: shows the root node eras for the Teleportation net. FIG. 4: shows the external node eras for the Teleportation net. FIG. 5: shows an example of a QB net in which an external node is not in the final era. FIG. 6: shows a binary tree. Each node p has a single parent. If the parent is to p's right (ditto, left), then p contains the names of the matrices produced by applying the CS Decomposition Theorem to the L matrices (ditto. R matrices) of p's parent. FIG. 7: is a flowchart of the overall teaching method implemented within the virtual campus of this invention. FIG. 8: is an illustration of a student database record linked to the virtual campus of this invention. FIG. 9: is an illustration of a course database record linked to the virtual campus of this invention.

DESCRIPTION OF THE INVENTION

We call a graph (or a diagram) a collection of nodes with arrows connecting some pairs of these nodes. The arrows of the graph must satisfy certain constraints. We call a labelled graph a graph whose nodes are labelled. A QB net consists of two parts: a labelled graph with each node labelled by a random variable, and a collection of node matrices, one matrix for each node. These two parts must satisfy certain constraints. An internal arrow is an arrow that has a starting (source) node and a different ending (destination) one. We will use only internal arrows. We define two types of nodes: an internal node is a node that has one or more internal arrows leaving it, and an external node is a node that has no internal arrows leaving it. It is also common to use the terms root node or prior probability node for a node which has no incoming arrows (if any arrows touch it, they are outgoing ones).

We restrict our attention to acyclic graphs: that is, graphs that do not contain cycles. (A cycle is a closed path of arrows with the arrows all pointing in the same sense.) We assign a random variable to each node of the QB net. (Henceforth, we will underline or put a caret over random variables. For example, we might write P({circumflex over (x)}=x) for the probability that the random variable {circumflex over (x)} assumes the particular value x.) Suppose the random variables assigned to the N nodes are{circumflex over (x)}, {circumflex over (x)}2, . . . , {circumflex over (x)}N. For each jEZ1,N, the random variable {circumflex over (x)}jwill be assumed to take on values within a finite set Ej called the set of possible states of{circumflex over (x)}j.

For example, consider the net of FIG. 1. Nodes 11, 12 and 13 are internal and node 14 is external. Node 11 is a root node. There are four nodes so N=4. We will assume that the four nodes must lie in one of two states: either no or si. Thus, E1=E2=E3=E4={no,si}. If S={k,k2, . . . ,kisi}CZ1,N, and k1 <k2 <. . . <Kisi, define (x.)s=(xk1,xk 2, . . . , xk isi) and ({circumflex over (x)}.)s=(xk1, {circumflex over (x)}k2, . . . , {circumflex over (x)}kisi). Sometimes, we also abbreviate (x.)Z 1,N (i.e., the vector that includes all the possible x components) by just x., and ({circumflexover (x)}.)Z1,Nby just (circumflex over (x)}.. For example, suppose N=4. One has Z 1,4 ={1,2,3,4}. If S={1,3}, then |S|=2. Furthermore, (x.)s=(x1,x3) and ({circumflex over (x)}.)s=({circumflex over (x)},{circumflex over (x)}3). One defines x.=(x.)Z1,4 =(x1,x2,x3,x4) and {circumflex over (x)}.=({circumflex over (x)}.)Z1,4 =({circumflex over (x)},{circumflex over (x)}2,{circumflex over (x)}3,{circumflex over (x)}4).

Let Zext be the set of all jEZ1,N such that {circumflex over (x)}jis an external node, and let Zintbe the set of all jEZ1.Nsuch that {circumflex over (x)}jis an internal node. Clearly, Zextand Zintare disjoint and their union is Z1,N. For example, for FIG. 1, Zext={ 4 } and Zint={1,2,3}. Each possible value x. of {circumflex over (x)}. defines a different net story. For any net story x., we call (x.)Zintthe internal state of the story and (x.)Zext its external state. For example, a possible story for the net of FIG. 1 is the case when{circumflex over (x)}1={circumflex over (x)}2=si and {circumflex over (x)}3 ={circumflex over (x)}4=no. This net story may also be represented by{circumflex over (x)}.=(si, si, no, no). Since we are assuming that each of the four nodes of FIG. 1 can assume two states, there are total of

24=16 stories possible for the net of FIG. 1. For story {circumflex over (x)}.=(si,si,no,no), the internal state is (x1,x2,x3)=(si,si,no) and the external state isx4=no.

For each net story, we may assign an amplitude to each node. Define Sito be the set of all k such that an arrow labelled xk (i.e., an arrow whose source node is{circumflex over (x)}k) enters node {circumflex over (x)};. We assign a complex number Aj[xji(x.)sj] to node {circumflex over (x)}. We call Aj[xi|(x.)sj] the amplitude of node {circumflex over (x)}jwithin net story x.. For example, consider a particular net story, call it (x1,x2,x3,x4),of FIG.1. No arrow enters node {circumflex over (x)}so both Siand (x.)s 1are empty. Node {circumflex over (x)}2is entered by an arrow from node{circumflex over (x)}so S2={1} and (x.)s 2=(xi). Likewise, S3={1} and (x.)s 3=(xi). Finally, S4={2,3} and (x.)s 4=(x2,x3). We assign the complex number Ai[xi] to node {circumflex over (x)}, A2[x2lx] to node {circumflex over (x)}2, A 3 [x3lx] to node {circumflex over (x)}3, and A4[x 4 |x 2 ,x3 ] to node {circumflex over (x)}4.

The amplitude of net story x., call it A(x.), is defined to be the product of all the node amplitudes Aj[xI(x.)s j] for jEZ1,N. Thus,A.(x.)=]HjEZ1, N AjI[xj](x.)Isj](1)

For example, consider a particular net story, call it (x1,x2,x3,x4),of FIG. 1. One has that A(x1,x 2 ,x3,x 4 )=A1[x1]A 2 [x 2 |x1]A3[x 3 x1]A 4 [x 4 x 2 ,x 3] (2) The function Ajwith values Aj[x|(x.)s j] determines a matrix that we will call the node matrix of node {circumflex over (x)}, and denote by Qj. Thus, xj is the matrix's row index and (x.)s jis its column index. For example, FIG. 1 gives the four node matrices Q1, Q2, Q3, Q4 associated with the four nodes of the graph shown there.

One can translate a QB net into a SEO by performing 4 steps: (1) Find eras. (2) Insert delta functions. (3) Find unitary extensions of era matrices. (4) Decompose each unitary matrix into a SEO. Next we will discuss these 4 steps in detail. We will illustrate our discussion by using Teleportation as an example. Teleportation was first discussed in Te193: C. H. Bennett, G. Brassard, C. Cr6peau, R. Jozsa, A. Peres, W. K. Wootters, Physical Review Letters 70, 1895 (1993). FIG. 2 shows a QB net for Teleportation. Reference Bra96: G. Brassard, Los Alamos eprint http://xxx.lanl.gov/abs/quant-ph/9605035, gives a SEO, expressed graphically as a qubit circuit, for Teleportation. It appears that the author of Bra96 obtained his circuit mostly by hand, based on information very similar to that contained in a QB net. The present invention gives a general method whereby such circuits can be obtained from a QB net in a completely mechanical way by means of a classical computer.

Step 1: Find Eras The root node eras of a graph are defined as follows. Call the original graph Graph (1). The first era Tiis defined as the set of all root nodes of Graph (1). Call Graph (2) the graph obtained by erasing from Graph(1) all the T 1 nodes and any arrows connected to these nodes. Then T 2 is defined as the set of all root nodes of Graph(2). One can continue this process until one defines an era T1i1 such that Graph(|T|+1) is empty. (One can show that if Graph (1) is acyclic, then one always arrives at a Graph(ITI+1) that is empty.) For example, FIG. 3 shows the root node eras of the Teleportation net FIG. 2. Let T represent the set of eras: T={Tl,T2, . . . ,Tli}. Note that TaCZ1,Nfor all aEZ1, 1 and the union of all Ta equals Z1,N. In mathematical parlance, the collection of eras is a partitionof Z1,N Suppose that aEZ1, 1. The arrows exiting the a'th era are labelled by (X.)T a. Those entering it are labelled by (x.)Fa, where[a is defined byFa=UjET a Sj.Note that the a'th era node is only entered by arrows from nodes that belong to previous (not subsequent) eras so FaCTa-1U. . . UT 2 UT 1. The amplitude Baof the a'th era is defined asBam[(x.)T a M(x.)Fa]=jE TaMAj [xj (x.)Msj].(3)

Ba (x.)r(x.)F ]= 71 j[i 3.)].

The amplitude A(x.) of story x. is given by A M (x.)=H a =1 M B a. (4) 11-1 (4

) A(x. )=17 Ba a=1 For example, for Teleportation we get from FIG. 3 B 1(x 1,x 4 )=A i(x 1)A 4(X4), (5a) B 2 (x2 ,xsx 1)=A 2 (x2|x 1)A 3(x 3 x 1), (5b) B 3 (xsx 2,x 4)=A s(x s X2,X 4), (5c) B 4 (x6 |xs,xs)=A6(x6X3,X5), (5d) and A(x.)=B 4 B s B 2 B 1. (6) Step 2: Insert Delta Functions The Feynman Integral FI for a QB net is defined byFI M[(x.) M zext]= (x.)Zint M A M(x.). (7) FI[(x.) ] = A(x.).(7)

Note that we are summing over all stories x. that have (x.)zext as their external state. We want to express the right side of Eq. (7) as a product of matrices. Consider how to do this for Teleportation. In that case one has FI (x 6)= x 1, x 2, M .. M x5MB4MB3MB2MB1,(8)

FI(x6)= B4B3B-B 1. (8)

where the Ba are given by Eqs. (5). The right side of Eq. (8) is not ready to be expressed as a product of matrices because the column indices of Ba+1 and the row indices of Ba are not the same for all aZ1,i-1. Furthermore, the variable x3 occurs in B 4 and B 2 but not in B3 .

Likewise, the variable x4 occurs in B 3 and B 1 but not in B 2 . Suppose we define{overscore (B)}a for aZ1,ii by {overscore(B)}1(x11,X41)=B1(x11,x41), (9a) {overscore (B)} 2(x 22 ,x 2 ,x4 2 /x1 1 ,x4 1 )=B 2(x 2 2,x 3 2 Ix1 1)6(x 4 2,x 4 1 ), (9b)

{overscore (B) 3(x 3 3 ,x 5 3 /x 2 2,x 3 2,x 4 2)=B 3 (x 5 3,x 2 2,x 4 2)6(x 3 3,x 3 2), (9c) {overscore (B)} 4 (x 6/x 3 3 X s 3 )=B 4(x 6/X 3 3,X 3). (9d)

initerml where we sum over all intermediate indices; i.e., allx; a except X6. Contrary to Eq. (8), the right side of Eq. (10) can be expressed immediately as a product of matrices since now Ba-column indices and Ba row indices are the same. The purpose of inserting a delta function of x3 into B 3 is to allow the system to "remember" the value of X 3 between non consecutive eras T 4 and T 2 . Inserting a delta function of x4 into B 2 serves a similar purpose. In the Teleportation net of FIG. 2, the last era contains all the external nodes. However, for some QB nets like the one in FIG. 5. this is not the case. For the net of FIG. 5. B 1(x 1)=A 1(x 1), (11a) B 2(X 2,X 3 /x 1 )=A 3(X 3 /x 1 )A 2(X 2 Ix 1), (11b) B3(x 4 /x 3)=A 4(X 4 Ix 3), (11c) B 4(X 5 /x 4 )=A 5(X s Ix 4). (11d) Even though node {circumflex over (x)}2 is external, the variable x2 does not appear as a row index in B 4 . Suppose we set {overscore (B)] (x 1 )=Bi&1 1), (12a) {overscore (B)} 2(x2 2 ,x 3 2 Ix 1)=B 2(x2 2 ,x 32x 11), (12b) {overscore (B)} 3(x 2 3 ,x 4 3 /x 2 2 ,x 3 2 ,)=B (x 4 3/x 3 2 )6(x 2 3 ,x 2 2 ), (12c) 3 3 {overscore (B)} 4(x 2,x s/X 2 3,x 4 )=B 4 (x s /x 4 )6(x 2,x 2 3). (12d)

FiPX-.xi) = E 4B 3 3B 1 PI(3 interim where we sum over all intermediate indices; i.e., allxj a except x2 and x5. Contrary to B 4 , the rows of {overscore (B)} 4 are labelled by the indices of both external nodes{circumflex over (x)}2 and {circumflex over (x)}5. This technique of inserting delta functions can be generalized as follows to deal with arbitrary QB nets. For jEZ1,N, let amin(j) be the smallest aEZ1,ii such that xj appears in Ba. Hence, amin(j) is the first era in which xjappears. If {circumflex over (x)}jis an internal node, let amax(j) be the largest a such that xjappears in Ba(i.e., the last era in which xjappears). If {circumflex over (x)}jis an external node, letaax(j)=|TI+1. ForaEZ1,II, let A a ={jZ 1,N lamin()<a<max()}, (14) a= B0 [(xj a-1 yv 1 (15)

InEq.(15),xjMT M

ii should be identified with x; and xj 0with no variable at all. Equation (7) for FI can be written in terms of the {overscore FI((x. l B- B 1 ZB)z (16) where the sum is over all intermediate indices (i.e., all Xj a for which a #1i). For all a, define matrix Maso that the x,y entry of Mais {overscore (B)}a(XJy). Define M to be a column vector whose components are the values of FI for each external state. Then Eq. (16)canbe expressedas: M=M ii ...M 2M1. (17) The rows of the column vector M1 are labelled by the possible valuesof (x.)Zext.The rows of the column vector M 1 are labelled by the possible values of (x.)T 1, where Ti is the set of root nodes.

Step 3: Find Unitary Extensions of Era Matrices So far, we have succeeded in expressing FI as a product of matrices Ma, but these matrices are not necessarily unitary. In this step, we will show how to extend each Mamatrix (by adding rows and columns) into a unitary matrix Ua. By combining adjacent Ma's, one can produce a new, smaller set of matrices Ma. Suppose the union of two consecutive eras is also defined to be an era. Then combining adjacent Ma's is equivalent to combining consecutive eras to produce a new, smaller set of eras. We define a breakpoint as any position aEZtii-1between two adjacent matrices Ma.iand Ma. Combining two adjacent Ma' eliminates a breakpoint. Breakpoints are only necessary at positions where internal measurements are made. For example, in Teleportation experiments, one measures node {circumflex over (x)}s. The subscript was mistyped which is in era T 3 . Hence, a breakpoint between M 4 and M 3 is necessary. If that is the only internal measurement to be made, all other breakpoints can be dispensed with. Then we will have M=M 2 'M1 ' where M '=M 2 4

, M 1'=M 3 M 2 M. If no internal measurements are made, then we can combine all matrices Ma into a single one, and eliminate all breakpoints.

We will henceforth assume that for all aZ1,T, the columns of Maare orthonormal. If for some aoEZII,Ma o does not satisfy this condition, it may be possible to "repair" Ma0, SO that it does. First: If a row Pof Ma 0-1is zero, then eliminate the column p of ma o, and the row p of Ma -1. Next: If a row P of the column vector Ma 0-1 ...M 2 M1is zero, then flag the column p of Ma o. The flagged columns of Ma o can be changed without affecting the value of M. If the non-flagged columns of Ma o are orthonormal, and the number of columns in Ma o does not exceed the number of rows, then the Gram Schmidt method, to be discussed later, can be used to replace the flagged columns by new columns such that all the columns of the new matrix Ma o are orthonormal. If it is not possible to repair Ma o in any of the above ways (or in some other way that might become clear once we program this), one can always remove the breakpoint between Ma o1and Ma o .

where v is just the column vector M with{overscore (d)}|Ti zeros attached to the end. To determine suitable values for the gray entries of the Ua matrices, one call use the Gram Schmidt (G.S.) method. (See Nob88: B. Noble and J. W. Daniels, Applied Linear Algebra, Third Edition (Prentice Hall, 1988)). This method takes as input an ordered set S=(v1,v2, . . .,vN) of vectors, not necessarily independent ones. It yields as output another ordered set of vectors S'=(ui,u2,. . . ,uN), such that S' spans the same vector space as S. Some vectors in S' may be zero. Those vectors of S' which aren't zero will be orthonormal. For rEZN, if the first r vectors of S are already orthonormal, then the first r vectors of S' will be the same as the first r vectors of S. Let ej for jZ,N sbe the j'th standard unit vector

(i.e., the vector whose j'th entry is one and all other entries are zero). For each aZl,1, to determine the gray entries of Ua one can use the G.S. method on the set S consisting of the non-gray columns of Ua together with the vectors eie2,... eN S.

Step 4: Decompose Each Unitary Matrix Into a SEO In this section we present a CS method for decomposing an arbitrary unitary matrix into a SEO. By following the previous 3 steps, one can reduce a QB net to a product of unitary operators Ua. By applying the CS method of this section to each of the matrices Ua, one can reduce the QB net to a SEO. We will use the symbol NB for the number ( 1) of bits and Ns=2N Bfor the number of states with NBbits. We define Bool={O,1}. We will use lower case Latin letters a,bc ... EBool to represent bit values and lower case Greek lettersa,p,y,. EZO,N b -1 to represent bit positions. NB-1 (21 d(L}= ( 2y,.

p=0 For pEZO,N B-1, we will use {right arrow over (u)}(P) to denote the s'th standard unit vector, i.e, the vector with bit value of 1 at bit position p and bit value of zero at all other bit positions.

Ir will represent the r dimensional unit matrix. Suppose pEZO,N B- and M is any 2x2 matrix. Ve define M(p) by M(P )=I2 (x) ... (x)1 2 (x)M(x) 1 2 (x) ... (x)1 2, (22) where the matrix M on the right side is located at bit position p in the tensor product of NB2x2 matrices. The numbers that label bit positions in the tensor product increase from right to left (<--), and the rightmost bit is taken to be at position 0. For any two square matrices A and B of the same dimension, we define the (.) product by A(.)B=ABAt, where At is the Hermitian conjugate of A. {right arrow over (a)}=(ax,ay,az) will represent the vector of Pauli matrices, whereax=(0110),ay=(0-ii0),az=(100- 1). (23) 0 1 0 -i 1 0(3 1 10-0 0 11 -11.

The Sylvester-Hadamard matrices Hrare 2rx2r matrices whose entry at row {right arrow over (a)} and column {right arrow over (b)} is given by (H r){right arrow over(a)},{right arrow over (b)} {right arrow over (a)}.{right arrow over (b)}, (24) r-1 (25

h=0~

The qubit's basis states 10> and |1> will be represented byMO) =[10],M1) =[01].(26)

The number operator n of the qubit is defined by n =[0 0 0 1 1 - a z 2. (27)

0 0 I T- (27) () 12 Note that n|O>=,n/1>=|1>. (28) We will often use {overscore (n)} as shorthand for n =1 - n =[10 0 0 ]=1 + z 2. (29)

[1 ( ) 1 +r(2 0 02 WedefinePoandPibyP0=n=[1000],P1=n=[0001].(30)

PO = T1=['-1() ]r==[1'= -1 -() (1 1. 3

) ForrpEZO,N B-1,we define Po(@),Pi(3), n(3) and {overscore (n)}() by means of Eq. (22). For {right arrow over (a)}EBoolN B,et P a -> = P a N B - 1 M( x ) . .

. _X). (X)P X)P X)PyN As mentioned earlier, we utilize a mathematical technique called CS Decomposition. In this name, the letters C and S stand for "cosine" and "sine". Next we will state the special case of the CS Decomposition Theorem that arises in a preferred embodiment of the invention. Consider FIG. 6. We start at 61 with a unitary matrix U. Without loss of generality, we can assume that the dimension of U is 2N Bfor some NB 1. (If initially U's dimension is not a power of 2, we replace it by a direct sum U(+)Irwhose dimension is a power of two.) We apply the CS Decomposition method to U. This yields node 62 comprising matrix D(0,U) of singular values, two unitary matrices L(0,U) and L(1,U) on the left and two unitary matrices R(0,U) and R(1,U) on the right. Then we apply the CS Decomposition method to each of the 4 matrices L(0.U),L(1.U),R(0,U) and R(1,U) and obtain nodes 63 and 64. Then we apply the CS Decomposition method to each of the 16 R and L matrices in nodes 63 and 64. And so on. This process ends when the current row of nodes in the pyramid of FIG. 6 has L's and R's that are 1x1 dimensional, i.e., just complex numbers. Call a central matrix either (1) a single D matrix, or (2) a direct sum D1 (+)D 2 (+) ... (+)DrOf D matrices, or (3) a diagonal unitary matrix. From FIG. 6 it is clear that the initial matrix U can be expressed as a product of central matrices, with each node of the tree providing one of the central matrices in the product. Next, we show how to decompose each of the 3 possible kinds of central matrices into a SEO.

Case 1: Central Matrix is a Single D Matrix Consider how to decompose a central matrix when it is a single D matrix. Before dealing with arbitrary NBconsider NB=3. Then the central matrix D can be expressed as:

.11= eXp(N4alTy (AX)?(AX) l abe1ool

Suppose {right arrow over (W)} (ditto, {right arrow over (0)}) is a column vector whose components are the numbers {right arrow over (a)} (ditto, O{right arrow over (a)}) arranged in order of increasing {right arrow over (a)}. We define new angles {right arrow over (6)} in terms

Then one can show that D=A oo A 0 1 A 1 0 Ain, (37) where A oo=exp(iBooOy)((X)I 2(x)I 2, (38a) A o1=ax(2)n()(-)[exp(iOO1ay)(x)I 2(x)I 2], (38b) A io=ax(2)"(1)(-)[exp(iOlOy)(X)I 2(x)I 2], (38c) A i=[ax(2)n(1)x(2)n(0](.)[exp(iO nacy)(x)I 2(x)I 2]. (38d) Eqs. (37)-(38) achieve our goal of decomposing D into a SEO. Now consider an arbitrary

Case 2: Central Matrix is Direct Sum of D Matrices

The computer program product of this invention implements the learning model of FIG. 7 by providing certain educational tools over a distributed network to allow students an opportunity to complete pre-planned educational experiences in a virtual setting. The computer program product includes a computer readable storage medium having campus navigator commands thereon, preferably in the form of a drop-down menu or a tool bar (13). The navigator commands are executable by processors on servers and personal computers and generate a virtual reality campus (10) in which students, educators, and administrators interact. The software includes an avatar (20) generation sequence for creating an avatar (20) in the form of an animated representation of at least one student. Of course, multiple students can access the computer program at the same time. The software further includes a campus generation sequence for creating a mapped virtual campus (10) in which the avatar (20) moves and engages in educational experiences within the campus.

The virtual campus (10) of this invention is a 3-D representation of the campus that includes the traditional structures that a student would expect the physical campus. The virtual campus (10) houses an electronic library, student center, meeting spaces, bulletin boards for announcements, and even allows for vendors to offer products and services on campus. In one particularly useful embodiment, the system includes a movie theater in which multiple individuals are able to view the same or different presentations on their respective computers at the same time. So User No. 1 may watch a first presentation, and User No. 2 may start another presentation a few minutes later with both users viewing their preferred content.

To get started, a user selects the attributes of the representative avatar (20) from a drop down menu (12). The avatars (20) are available for customization depending on the student's level of skill in manipulating the graphics of the virtual campus. The user can access keys on the traditional keyboard to move the avatar (20) from one location to another and to communicate with other avatars in the virtual campus. In a preferred embodiment, the avatars (20) communicate via audio links and text-based messaging links. Both audio and text based messaging may be implemented in "whisper" mode to control the extent to which comments are published to the group, i.e., small groups may communicate without others being involved. The communication abilities within this system allow for real-time and asynchronous messaging. The shared audio and presentation work spaces enable the system to offer speakers and seminars to address large groups ofstudents atonce.

Most of the options for controlling an avatar (20) on the virtual campus (10) are available from a drop-down menu also known as the dashboard. As noted above, the dashboard (12) allows students to move within the virtual campus (10). The virtual campus (10) may be set up to include different "worlds" that have various functions. Certain worlds may be more student-activity based while others provide significant amounts of school administration opportunities. One particularly useful world in a preferred embodiment of this invention gives a student access to the courses that are offered at the physical university. This student can complete the requirements of a real course by using the avatar appropriately to fulfill course requirements in the virtual campus. By linking the virtual campus (10) to real courses that would be offered in a physical campus, the method and system of this invention offer new teaching styles that do not rely on purely traditional relationships between faculty and students. The course requirements in a virtual course must be evaluated in the same manner by which a student would be graded in a normal classroom. To accomplish this evaluation process, the computer program product of this invention connects to a database for tracking each student's progress in regard to objectives of the course.

In applying these new teaching techniques available in a virtual world to courses of study that are practical and useful in a physical world, the administrators of the system herein create an assessment process that is student focused. Course requirements to be fulfilled in a virtual reality experience are based on the same standards that a teacher would apply in the physical classroom. In this way, the teacher can map activities for the students to engage and link these activities to the artifacts, or course deliverables, that the students must complete to get credit for the course. As in traditional classroom experiences, the virtual reality program allows for the generation of student achievement reports, course the effectiveness reports, and overall program accountability reports.

A database link to the virtual reality campus is extraordinarily useful to ensure that the students are participating, completing assignments, and learning the material at hand. Within the database, each student has a matrix based on the standards of the program. The students can access this matrix by navigating their respective avatar to the appropriate administrative area on the virtual campus. In one preferred embodiment, the students can assess the standards for a course and propose deliverables that would meet the appropriate objectives. The computer program product and system described herein give a student wide latitude in determining how to complete the course in a virtual reality setting in a way that is most suitable to that student. By accessing the same area in a virtual campus, teachers and administrators can guide students' progress by analyzing the students' proposed deliverables and suggesting means for completing those. By no means is a student left to complete a course of study unassisted. The teaching method used in the virtual reality campus allows the students to communicate electronically and interact in a virtual setting with as much freedom as possible and as much guidance as necessary.

By linking database services to the virtual reality campus, the computer system described herein allows the school faculty and administration opportunities to guide students much as they would in a physical campus. For example, FIG. 8 shows a representative student achievement report for a course of study. This screen would serve as a starting point for students to manage their respective matrix. The deliverables section (60) links to the respective student's matrix. The goals section lets users plan their achievements for the course. The students maintain their own matrices by adding or editing deliverables within the database. Students select types of deliverables that will fulfill course objectives and provide a title, a brief description, and either the Web address or the geographical location (65) where this student will leave the deliverable on the virtual campus (10).

If the student chooses to leave the deliverable (60) at a specified location in the virtual campus, the system may allow certain other users access to that deliverable. Typically, at least a professor or faculty member will have access to the deliverable, and the deliverable will be listed as "under review" until approved by that reviewing faculty member. The system is sufficiently flexible to allow multiple faculty members to review and comment on the same deliverable, depending on the nature of the project.

The system may be configured to allow multiple levels of review by various system users. In a preferred embodiment of this system, deliverables that have been submitted are listed in the student's matrix. The database connected to the virtual reality campus (10) provides details on the deliverable, including a record of previous reviews and a listing of comments submitted by other users. Once the deliverable moves from "under review" to ''approved," the background color of that cell is changed to green for visual indication of completion.

The database functionality of the system herein may be connected to traditional computer programs used by a campus registrar on a physical campus. The database, therefore, can track student records including, but not limited to, student biographical information, course transcripts, and completion dates for various activities within the course of study. The database may be searched to show the academic results of individual students, a course group or section, or the history of any course that has been taught using the virtual reality campus.

In a most preferred embodiment, the database actually maintains records of deliverables that the students have submitted in completing a course. As shown in FIG. 9, a course effectiveness report (70) lists the standards, the goals, and the submitted products associated with that course. This detailed review displays the course activities and a list of recently submitted artifacts addressing the activity. The title links to the product, or course deliverable, and the student name links to the matrix. The course effectiveness report also gives the coordinates of the location in the virtual reality geography at which the course deliverable may be found. In a different embodiment, the course effectiveness report lists the aggregate results from online course evaluation forms. Those with access to the forms may add reflection statements to accompany the evaluation results, thereby communicating more information to students who are interested in taking that course.

The database functionality of this system also allows for a program accountability report. The program accountability report provides data on the performance, alignment, and progress of program participants, courses, and activities. The various views within the database provide snapshot information of important data within that course, such as demographics and graduation rates. The database also provides a convenient means of collecting data from interviews and surveys that users may encounter in the virtual campus world.

The computerized method and system of this invention allow for new teaching methods because of the nature of electronic communications and the virtual reality campus. One method used herein is that of dividing students into groups known as "cohorts." Cohorts may include certain segments of the virtual population that will proceed through the same course of study within the campus. Cohorts may be assigned by some objective criteria; such as date of matriculation or geographic proximity.

As the faculty creates assignments for a program within the campus, the assignments may include requirements that students form teams within a cohort, or the assignments might require the teams to include members from more than one cohort. Forming the teams becomes an exercise requiring interaction among citizens of the virtual world and promotes educational discourse among a diverse population.

Cohort activity is tracked within the database so that an individual student's matrix includes results of that student's participation in a small group. The idea behind using small group activity within a virtual community campus is to flatten relationships between teachers and students and have students interact as part of the learning experience. Of course, the cohorts can interact with one another using the text-based and audio communication functions of the product described herein. One of the first assignments within the virtual reality classroom could be that of establishing a team having certain demographic qualities. In this way, the students have to navigate the campus and meet other students that are in the same course. The students get to know each other in the virtual setting, i.e., their avatars interact, and the students select peers in the virtual campus to be part of their group. The virtual reality campus, therefore, takes advantage of the electronic social networking that is prevalent among students today.

One useful feature of the virtual system is that each avatar may optionally show the student name above the graphical image of the avatar. In a most preferred embodiment, users can access biographical information about the student represented by any avatar. As noted above, the biographical information is maintained in the database connected to the virtual campus. In this way, the students know a little more about the avatar before choosing to work with that person. As shown in the figures herein, students usually have first and last names displayed above their avatar image, while teachers only have first names. This allows the citizens of the virtual campus to distinguish the identities and roles of other avatars on campus. The system also encompasses the technical capabilities for users to link to the database and learn more in-depth information about a particular avatar that the user encounters in the virtual reality world.

Once a team has been organized, the team gets a notebook (e.g. a virtual work space within the system) at a geographical location on the virtual reality campus. The team, therefore, will be able to access a shared workspace in the virtual world. The shared workspace allows simultaneous viewing of websites, documents, slide presentations, and other web conferencing functions. The team members have access to the notebook and the shared workspace for collaborative editing of deliverables. The system accounts for certain traditional checkpoints along the way in a course by providing means for students to give virtual world presentations to their classmates,

Students are not expected to be as immediately familiar with the virtual campus as they may be with a physical campus. One of the first assignments, therefore, within the virtual campus is to get to know the surrounding areas. The faculty may also assign tasks, such as meeting an avatar from a different course or a different section of the same course. The assignments, therefore, are geared to encourage discourse among students on a wide variety of topics by ensuring that their avatars bump into one another somewhere in the virtual geography. By communicating with other citizens in the virtual world, particularly peer groups, the student has more opportunities for serendipitous learning.

The virtual campus is particularly suited for interaction among users in different degree programs on a virtual campus or even among professionals in different fields. For example, cross-collaboration is possible when different skills are necessary to complete a bigger goal, e.g., projects that require educators, technology experts, administrators, and other specialties. The virtual campus of this invention includes a systematic way to organize each individual's deliverables, making discrete information available globally. By sharing information in the virtual campus and using a database infrastructure to track progress in multiple areas, teammates can share and interpret data as a group rather than just submitting one piece of the puzzle with no vision of the bigger picture at hand. The system encourages cross-collaboration among users from all different programs and walks of life. For instance, one feature allows the users to access time zone conversion software to assist in planning meetings "in world" when the users are in different time zones in the physical world.

One concept that may be implemented via this system is that of "augmented reality." In this embodiment, teams or cohorts experience certain portions of the system in common. Other portions of the system are customized for that particular user. For example, each member of the team may be able to access a shared workspace and certain deliverables, electronic content, or other common information. As part of an assignment, however, individual users would also access user-specific information, or content, regarding a project so that the team as a whole would have to work together with common information and specific assignments to realize a goal. The individualized information would be available via clickable objects in the virtual world, and the database linked to that user would control the access rights for that user. Those access rights would determine the content that the particular user experienced in the virtual setting. This particularized content ability could lead to user-specific messaging, advertising, and other experiences in the virtual world.

The invention described herein can be used in multiple settings and not just a traditional educational environment. There are numerous applications to the virtual campus in corporate life as well as government, scientific research and development, or any venture that uses multimedia applications in its business. Those having skill in the art will recognize that the invention may be embodied in many different virtual reality scenarios. Accordingly, the invention is not limited to the particular programs illustrated herein.

Claims (6)

WE CLAIM

1) Our Invention "QCIU- Education Environment System" is a computer implemented, quantum computer method provides an educational environment in a virtual reality setting and individuals navigate a virtual reality campus by using an avatar to interact with other users and to engage in learning experiences in the virtual setting. The invented technology also individual's complete projects in virtual reality by accessing educational materials in electronic format and communicating with one another via text-based chats and real time audio. The invented technology also includes virtual reality campus emulates a physical campus by providing meeting spaces and work areas where students spontaneously share information and complete pre-planned tasks. An electronic database tracks biographical and educational information about each user that users progress in achieving study goals and the deliverables that the student produces to fulfil requirements of virtual instruction. The database also links to other systems such as a registration database so that the student's entire learning experience on both a physical campus and in virtual reality can be conveniently accessed electronically.

2) According to claims# the invention is to a computer-implemented, quantum computer method provides an educational environment in a virtual reality setting and individuals navigate a virtual reality campus by using an avatar to interact with other users and to engage in learning experiences in the virtual setting.

3) According to claim1,2# the invention is to a individual's complete projects in virtual reality by accessing educational materials in electronic format and communicating with one another via text-based chats and real time audio.

4) According to claiml,2,3# the invention is to a virtual reality campus emulates a physical campus by providing meeting spaces and work areas where students spontaneously share information and complete pre-planned tasks.

5) According to claiml,2,4# the invention is to a electronic database tracks biographical and educational information about each user that users progress in achieving study goals and the deliverables that the student produces to fulfil requirements of virtual instruction.

6) According to claim,2,4,5# the invention is to a links to other systems such as a registration database so that the student's entire learning experience on both a physical campus and in virtual reality can be conveniently accessed electronically.

FIG. 1: SHOWS A LABELLED GRAPH AND THE FOUR NODE MATRICES ASSOCIATED WITH THE FOUR NODES OF THE GRAPH. A QB NET CONSISTS OF 2 PARTS: A LABELLED GRAPH AND A COLLECTION OF NODE MATRICES, ONE MATRIX FOR EACH NODE.

FIG. 2: SHOWS A QB NET FOR TELEPORTATION THIS FIGURE ALSO SHOWS THE NUMBER OF QUANTUM OR CLASSICAL BITS CARRIED BY EACH ARROW.

FIG. 3: SHOWS THE ROOT NODE ERAS FOR THE TELEPORTATION NET.

FIG. 4: SHOWS THE EXTERNAL NODE ERAS FOR THE TELEPORTATION NET.

FIG. 5: SHOWS AN EXAMPLE OF A QB NET IN WHICH AN EXTERNAL NODE IS NOT IN THE FINAL ERA.

FIG. 6: SHOWS A BINARY TREE. EACH NODE Β HAS A SINGLE PARENT. IF THE PARENT IS TO Β'S RIGHT (DITTO, LEFT), THEN Β CONTAINS THE NAMES OF THE MATRICES PRODUCED BY APPLYING THE CS DECOMPOSITION THEOREM TO THE L MATRICES (DITTO. R MATRICES) OF Β'S PARENT.

FIG. 7: IS A FLOWCHART OF THE OVERALL TEACHING METHOD IMPLEMENTED WITHIN THE VIRTUAL CAMPUS OF THIS INVENTION.

FIG. 8: IS AN ILLUSTRATION OF A STUDENT DATABASE RECORD LINKED TO THE VIRTUAL CAMPUS OF THIS INVENTION.

FIG. 9: IS AN ILLUSTRATION OF A COURSE DATABASE RECORD LINKED TO THE VIRTUAL CAMPUS OF THIS INVENTION.