We propose a computer method for analyzing physical systems that exhibit quantum mechanical behavior. To analyze a quantum system according to the method of the present invention, one performs the following steps: First, one enters into the computer some information about the physical system by portraying it on the computer screen as a special type of graph (diagram). Next one enters into the computer additional information that is not contained in the graph. Part of this non-graph information is a matrix of complex numbers for each node of the graph. Finally, the computer uses the entered information to do calculations and it outputs the result of these calculations. The computer output consists mainly of conditional probabilities for the outcomes of measurements performed on the quantum system. The method that we are proposing is similar to the method used in the field of Classical Bayesian Nets (also known as Causal Probabilistic Nets). However, the... |
Citations|
| US5133046 | Jan 3, 1991 | Jul 21, 1992 | Pickard, Lowe and Carrick (PLC) | Computer-based diagnostic expert system organized according to Bayesian theory |
Referenced by|
| US6456994 | May 5, 1998 | Sep 24, 2002 | | Computer for a quantum computer | | US6895398 | Jul 18, 2001 | May 17, 2005 | Inferscape, Inc. | Decision engine and method and applications thereof | | US7212974 | Jul 11, 2002 | May 1, 2007 | | System and method for compressing and encoding data | | US7408486 | Apr 21, 2004 | Aug 5, 2008 | Qbit Corporation | System and method for using a microlet-based modem | | US7620672 | May 24, 2004 | Nov 17, 2009 | | Method for performing classical Bayesian net calculations using a quantum computer | | USRE41900 | Sep 22, 2004 | Oct 26, 2010 | | Compiler for a quantum computer |
Claims1. A method that uses a computer having display, storage and calculation means to analyze a physical system that exhibits quantum mechanical behavior, said method comprising the steps of: - displaying on said display means a graph comprising a plurality of N nodes, and a plurality of directed lines connecting certain pairs of said nodes;
- storing in said storage means a knowledge base comprising:
- (a) graph information comprising a label for each of said N nodes, and also comprising, for each said directed line, said node label for the source node and for the destination node of the directed line,
- (b) state information comprising, for each j .di-elect cons. {1,2, . . . N}, a finite set .SIGMA..sub.j containing labels for the states that the j'th node x.sub.j may assume, and
- (c) amplitude information comprising, for each j .di-elect cons. {1,2, . . . N}, a representation of a complex number A.sub.j x.sub.j .vertline.x.sub.k.sbsb.1,x.sub.k.sbsb.2, . . . ,x.sub.k.sbsb..vertline.sj.vertline. ! for each vector (x.sub.j,x.sub.k.sbsb.1,x.sub.k.sbsb.2, . . . ,x.sub.k.sbsb..vertline.sj.vertline.) such that x.sub.j .di-elect cons. .SIGMA..sub.j, x.sub.k.sbsb.1 .di-elect cons. .SIGMA..sub.k.sbsb.1, x.sub.k.sbsb.2 .di-elect cons. .SIGMA..sub.k.sbsb.2, . . . , and x.sub.k.sbsb..vertline.sj.vertline. .di-elect cons. .SIGMA..sub.k.sbsb..vertline.sj.vertline., wherein (x.sub.k.sbsb.1,x.sub.k.sbsb.2, . . . ,x.sub.k.sbsb..vertline.sj.vertline.) are the .vertline.S.sub.j .vertline. nodes connected to x.sub.j by directed lines entering x.sub.j, wherein said directed lines entering x.sub.j transmit the state of their source node, wherein said .vertline.S.sub.j .vertline. is an integer greater or equal to zero;
- calculating with said calculation means and with some parts of said knowledge base, the probability that some said node x.sub.j will be measured to be in a state x.sub.j contained in .SIGMA..sub.j.
2. The method of claim 1, wherein said graph is acyclic. 3. The method of claim 2, comprising the additional step of: - calculating with said calculation means and with some parts of said knowledge base, the eras of said graph.
4. The method of claim 1, comprising the additional step of: - calculating with said calculation means and with some parts of said knowledge base, the probability that some pair (x.sub.j.sbsb.1,x.sub.j.sbsb.2) of said nodes will be measured to be in a state (x.sub.j.sbsb.1,x.sub.j.sbsb.2), wherein x.sub.j.sbsb.1 .di-elect cons. .SIGMA..sub.j.sbsb.1 and x.sub.j.sbsb.2 .di-elect cons. .SIGMA..sub.j.sbsb.2.
5. The method of claim 1, comprising the additional step of: - calculating with said calculation means and with some parts of said knowledge base, a list of all net stories with non-zero amplitude, wherein a net story is a vector (x.sub.1,x.sub.2, . . . ,x.sub.N) such that x.sub.1 .di-elect cons. .SIGMA..sub.1, x.sub.2 .di-elect cons. .SIGMA..sub.2, . . . , and x.sub.N .di-elect cons. .SIGMA..sub.N, and the amplitude of such a net story is ##EQU7##
6. The method of claim 1, comprising the additional steps of: - storing in said storage means, as part of said knowledge base, active state information comprising, for each j .di-elect cons. {1,2, . . . N}, a set E.sub.j of the active states of node x.sub.j, wherein E.sub.j is a subset of .SIGMA..sub.j ; and
- calculating with said calculation means and with some parts of said knowledge base, the probability that some said node x.sub.j will be measured to be in a state x.sub.j contained in E.sub.j, taking into consideration that for each integer k .di-elect cons. {1,2, . . . ,N}, x.sub.k was previously known to lie in one of the states contained in E.sub.k.
7. The method of claim 6, wherein said graph is acyclic. 8. The method of claim 7, comprising the additional step of: - calculating with said calculation means and with some parts of said knowledge base, the eras of said graph.
9. The method of claim 6, comprising the additional step of: - calculating with said calculation means and with some parts of said knowledge base, the probability that some pair (x.sub.j.sbsb.1,x.sub.j.sbsb.2) of said nodes will be measured to be in a state (x.sub.j.sbsb.1,x.sub.j.sbsb.2), wherein x.sub.j.sbsb.1 .di-elect cons. .SIGMA..sub.j.sbsb.1 and x.sub.j.sbsb.2 .di-elect cons. E.sub.j.sbsb.2, taking into consideration that for each integer k .di-elect cons. {1,2, . . . ,N}, x.sub.k was previously known to lie in one of the states contained in E.sub.k.
10. The method of claim 6, comprising the additional step of: - calculating with said calculation means and with some parts of said knowledge base, a list of all net stories with non-zero amplitude and for which all node states are active, wherein a net story for which all node states are active is a vector (x.sub.1,x.sub.2, . . . x.sub.N) such that x.sub.1 .di-elect cons. E.sub.1, x.sub.2 .di-elect cons. E.sub.2, . . . , and x.sub.N .di-elect cons. E.sub.N, and the amplitude of such a net story is ##EQU8##
11. A method that uses a computer having storage and calculation means to analyze a physical system that exhibits quantum mechanical behavior, said method comprising the steps of: - storing in said storage means a knowledge base comprising:
- (a) graph information comprising a label for each node of a plurality of N nodes, and also comprising a plurality of directed lines, wherein a directed line is an ordered pair of said node labels, wherein one member of said label pair labels the source node and the other member labels the destination node of the directed line,
- (b) state information comprising, for each j .di-elect cons. {1,2, . . . ,N}, a finite set .SIGMA..sub.j containing labels for the states that the j'th node x.sub.j may assume, and
- (c) amplitude information comprising, for each j .di-elect cons. {1,2, . . . N}, a representation of a complex number A.sub.J x.sub.j .vertline.x.sub.k.sbsb.1,x.sub.k.sbsb.2, . . . ,x.sub.k.sbsb..vertline.sj.vertline. ! for each vector and x.sub.k.sbsb..vertline.sj.vertline. .di-elect cons. .SIGMA..sub.k.sbsb..vertline.sj.vertline., wherein (x.sub.k.sbsb.1,x.sub.k.sbsb.2, . . . ,x.sub.k.sbsb..vertline.sj.vertline.) are the .vertline.S.sub.j .vertline. nodes connected to x.sub.j by directed lines entering x.sub.j, wherein said directed lines entering x.sub.j transmit the state of their source node, wherein said .vertline.S.sub.j .vertline. is an integer greater or equal to zero;
- calculating with said calculation means and with some parts of said knowledge base, the probability that some said node x.sub.j will be measured to be in a state x.sub.j contained in .SIGMA..sub.j.
12. The method of claim 11, wherein said graph is acyclic. 13. The method of claim 12, comprising the additional step of: - calculating with said calculation means and with some parts of said knowledge base, the eras of said graph.
14. The method of claim 11, comprising the additional step of: - calculating with said calculation means and with some parts of said knowledge base, the probability that some pair (x.sub.j.sbsb.1,x.sub.j.sbsb.2) of said nodes will be measured to be in a state (x.sub.j.sbsb.1,x.sub.j.sbsb.2), wherein x.sub.j.sbsb.1 .di-elect cons. .SIGMA..sub.j.sbsb.1 and x.sub.j.sbsb.2 .di-elect cons. .SIGMA..sub.j.sbsb.2.
15. The method of claim 11, comprising the additional step of: - calculating with said calculation means and with some parts of said knowledge base, a list of all net stories with non-zero amplitude, wherein a net story is a vector (x.sub.1,x.sub.2, . . . ,x.sub.N) such that x.sub.1 .di-elect cons. .SIGMA..sub.1, x.sub.2 .di-elect cons. .SIGMA..sub.2, . . . , and x.sub.N .di-elect cons. .SIGMA..sub.N, and the amplitude of such a net story is ##EQU9##
16. The method of claim 11, comprising the additional steps of: - storing in said storage means, as part of said knowledge base, active state information comprising, for each j .di-elect cons. {1,2, . . . ,N}, a set E.sub.j of the active states of node x.sub.j, wherein E.sub.j is a subset of .SIGMA..sub.j ; and
- calculating with said calculation means and with some parts of said knowledge base, the probability that some said node x.sub.j will be measured to be in a state x.sub.j contained in E.sub.j, taking into consideration that for each integer k .di-elect cons. {1,2, . . . ,N}, x.sub.k was previously known to lie in one of the states contained in E.sub.k.
17. The method of claim 16, wherein said graph is acyclic. 18. The method of claim 17, comprising the additional step of: - calculating with said calculation means and with some parts of said knowledge base, the eras of said graph.
19. The method of claim 16, comprising the additional step of: - calculating with said calculation means and with some parts of said knowledge base, the probability that some pair (x.sub.j.sbsb.1,x.sub.j.sbsb.2) of said nodes will be measured to be in a state (x.sub.j.sbsb.1,x.sub.j.sbsb.2), wherein x.sub.j.sbsb.1 .di-elect cons. E.sub.j.sbsb.1 and x.sub.j.sbsb.2 .di-elect cons. E.sub.j.sbsb.2, taking into consideration that for each integer k .di-elect cons. {1,2, . . . ,N}, x.sub.k was previously known to lie in one of the states contained in E.sub.k.
20. The method of claim 16, comprising the additional step of: - calculating with said calculation means and with some parts of said knowledge base, a list of all net stories with non-zero amplitude and for which all node states are active, wherein a net story for which all node states are active is a vector (x.sub.1,x.sub.2, . . . ,x.sub.N) such that x.sub.1 .di-elect cons. E.sub.1, x.sub.2 .di-elect cons. E.sub.2, . . . , and x.sub.N .di-elect cons. E.sub.N, and the amplitude of such a net story is ##EQU10##
21. A method that uses a computer having input and calculation means to analyze a physical system that exhibits quantum mechanical behavior, said method comprising the steps of: - inputting into said input means a knowledge base comprising:
- (a) graph information comprising a label for each node of a plurality of N nodes, and also comprising a plurality of directed lines, wherein a directed line is an ordered pair of said node labels, wherein one member of said label pair labels the source node and the other member labels the destination node of the directed line,
- (b) state information comprising, for each j .di-elect cons. {1,2, . . . ,N}, a finite set .SIGMA..sub.j containing labels for the states that the j'th node x.sub.j may assume, and
- (c) amplitude information comprising, for each j .di-elect cons. {1,2, . . . ,N}, a representation of a complex number A.sub.j x.sub.j .vertline.x.sub.k.sbsb.1,x.sub.k.sbsb.2, . . .,x.sub.k.sbsb..vertline.sj.vertline. ! for each vector (x.sub.j,x.sub.k.sbsb.1,x.sub.k.sbsb.2, . . . ,x.sub.k.sbsb..vertline.sj.vertline.) such that x.sub.j .di-elect cons. .SIGMA..sub.j, x.sub.k.sbsb.1 .di-elect cons. .SIGMA..sub.k.sbsb.1, x.sub.k.sbsb.2 .di-elect cons. .SIGMA..sub.k.sbsb.2, . . . , and x.sub.k.sbsb..vertline.sj.vertline. .di-elect cons. .SIGMA..sub.k.sbsb..vertline.sj.vertline., wherein (x.sub.k.sbsb.1,x.sub.k.sbsb.2, . . . ,x.sub.k.sbsb..vertline.sj.vertline.) are the .vertline.S.sub.j .vertline. nodes connected to x.sub.j by directed lines entering x.sub.j, wherein said directed lines entering x.sub.j transmit the state of their source node, wherein said .vertline.S.sub.j .vertline. is an integer greater or equal to zero;
- calculating with said calculation means and with some parts of said knowledge base, the probability that some said node x.sub.j will be measured to be in a state x.sub.j contained in .SIGMA..sub.j.
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