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International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN INTERNATIONAL JOURNAL OF ELECTRONICS AND 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 1, January- February (2013), © IAEME COMMUNICATION ENGINEERING & TECHNOLOGY (IJECET) ISSN 0976 – 6464(Print) ISSN 0976 – 6472(Online) Volume 4, Issue 1, January- February (2013), pp. 131-145 IJECET © IAEME: www.iaeme.com/ijecet.asp Journal Impact Factor (2012): 3.5930 (Calculated by GISI) ©IAEME www.jifactor.com BAYESIAN NETWORK BASED MODELING AND RELIABILITY ANALYSIS OF QUANTUM CELLULAR AUTOMATA CIRCUITS Dr.E.N.Ganesh Professor ECE Dept, Rajalakshmi Institute of Technology,Chennai – 600124 TamilNadu, India Email: enganesh50@yahoo.co.in ABSTRACT Quantum cellular automata (QCA) is a new technology in nanometer scale as one of the alternatives to nano cmos technology, QCA technology has large potential in terms of high space density and power dissipation with the development of faster computers with lower power consumption. This paper considers the problem of reliability analysis of Simple QCA circuits at layout level like QCA latches and NOT circuit. The tool used to tackle this problem is Bayesian networks (BN) that derive from convergence of statistics and Artificial Intelligence (AI). It consists of the representation of probabilistic causal relation between variables of a system. Using this we have transformed QCA circuit in to Bayesian framework to find the probability of getting correct output in terms of its polarization with respect to its input configuration and temperature. Reliability analysis also discussed for finding the defective cells in QCA circuit. This will increase overall efficiency of circuit and hence speed of the circuit with lower power consumption. Keywords: BN – Bayesian network, Quantum cellular automata, Reliability, Conditional probability, Join probability distribution 1. INTRODUCTION This paper considers the problem of reliability analysis of QCA circuit organized in parallel and/or in serial given the reliability of the Input cells. The mathematical tool used to tackle this problem is Bayesian networks. Reliability analysis of systems is very important in order to be able to deliver errorless QCA cell at the output. A given QCA system is often composed of many cells organized in serial and parallel, whose failure of one cell in serial 131 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 1, January- February (2013), © IAEME may cause the failure of the whole system or at least reduce its performance. In terms of reliability there are two types of organizations of cells, organization in serial and organization in parallel. These organizations impact on the reliability of the resulting circuit. If a circuit consists of n cells Ci, i=1,…n in serial, the system will be performing well if and only if each component is performing well, so if Pi , is the reliability of the ith component, then the reliability of the system Ps is given by Ps = ∏i = 1 to n Pi (1) On the contrary if a system consists of n cells Ci, i=1,…n in parallel, the system will perform well if at least one of these cells perform well, so if Pi is the reliability of the ith component, then the reliability of the system Pp is given by Pp = 1 - ∏i = 1 to n ( 1 - pi) (2) Eq. (1) and (2) constitute the fundamental relations for computing the reliability of a QCA circuit because any system will consist of cells or groups of cells in serial and/or in parallel. Quantum-dot Cellular Automata (QCA) is an emerging technology that offers a revolutionary approach to computing at nano-level [1][2]. A dot can be visualized as well. Once electrons are trapped inside the dot, it requires higher energy for electron to escape. The fundamental unit of QCA is QCA cell created with four quantum Dots positioned at the vertices of a square. [2] [3.]. Fig 1.a and 1.b below shows quantum cells with electrons occupying opposite vertices. 1.a P = +1 (Binary 1) 1.b P = -1 (Binary0) Fig1 QCA cells with four Quantum dots. [1][3][4][5] This interaction forces between the neighboring cells able to synchronize their polarization. Therefore an array of QCA cells acts as wire and is able to transmit information from one end to another [6] [7][8][9][10]. Figure 2 and 3 Majority functions of QCA Cell. Fig 2.and 3 Majority AND, OR gate [3] [4][5][6] 132 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 1, January- February (2013), © IAEME Clocking is the requirement for synchronization of information flow in QCA circuits [11] [12] [13]. It requires a clock not only to synchronize and control information flow but clock actually provides power to run the circuit [14] [15]. Bayesian Networks (BN) derive from the convergence of statistical methods that permit one to go from information (data) to knowledge (probability laws, relationship between variables,…) with Artificial Intelligence (AI) that permits computers to deal with knowledge (not only information), (see for example [16]). The terminology BN comes from Thomas Bayes’s [17] 18th century work. Its actual development is due to [17]. The main purpose of BN is to integrate uncertainty into expert systems. BN consist in a graphical representation of the causality relation between a cause and its effects. Figure 4 show that A is the cause and B its effect. A B Fig 4 Causality representation in BN But as relation of causality is not strict, the next step is to quantify it by giving the probability of occurrence of B when A is realized. So an BN consists of an oriented graph where nodes represent variables, and oriented arcs represent the causality relation and a set of probabilities. A rigorous definition of a BN is given in [18].Let us consider an acyclic oriented graph g = (v,a) where v and a represents set of nodes and the arcs in the graph. A trial E with whom there is associated a finite probability space and given n random variables ( Xi )1 < i < n, a and E defines Bayesian network, noted B = (G,P). There exists a bisection between the nodes of G and var(Xi). The factorization property for this is P(X1,X2 …….Xn) = Π P ( Xi / C(Xi)) (3) Where C(Xi) depends on the set of causes(parents) of Xi. P (X1, X 2,……Xi) Eq.(3) is the probability of simultaneous realization of variables X1, X2 ….Xi and P(X i / Yi) is the conditionality probability. The main purpose of Bayesian networks is to propagate certain knowledge of the state of one or more partitioned nodes through the network so that one shall learn how the belief’s of the expert ion the Bayesian network will change, given B = (G,P) and set of nodes it returns to compute P ( Xi / Y i ). Using the properties of chains, trees networks and the properties of conditional probability, algorithms can be derived to propagate certain knowledge in term of modifying the belief. BN is completely determined by its structure and some parameters, namely a priori probabilities of nodes without parents and conditional probabilities of intermediate nodes for different configurations of states of their parents. The basic cell of the QCA circuit will be the component of which reliability will be available. Clocked QCA circuits are considered here, the reliability of the cell can be found in terms of probability of getting correct output of the output cell or group of cells in that QCA circuit. Before going in detail about reliability analysis let us deal in detail about simple QCA latch and transforming the latch into Bayesian network according to [19][ 20]. 133 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 1, January- February (2013), © IAEME 2. BAYESIAN MODEL OF COMPUTATION Consider a simple QCA latch of figure 5 drawn through QCA simulator from [21]. Figure 6 shows layout model Bayesian network of QCA latch from [22]. Figure 5 shows the simple QCA latch from [21] Figure 6 shows the simple Bayesian model of QCA latch. Each chance node in figure 7 represents a random variable of each cell in figure6 and directed arc represents direct causal relation with the parent nodes. A link is directed to child node from the parent node. Let us consider 5 QCA cells indexed in a manner of X1, X2, X 3, X 4 and X5. X1 be the input and X5 be the output cell. We use two state approximate model of single QCA cell [20], Two state model can be derived from the quantum formulation based on all possible configuration of pair of electron in a cell. [23] Each state can be observed in one of possible state logical 0 ( x0) or logical 1 ( x1). The probability of observing a state is P (Xi = xi), x denotes the states be in logical 0 or 1. Polarization of cell in terms of state probabilities can be found from conditional and joint probabilities. The joint probability of observing a set under steady state assignments for the cell can be determined from quantum wave function which is cumbersome and requires quantum wave function calculations. Instead as in [20] consider a joint wave function of two cells in terms of product of two variables and representing the product as factored representation. By using Hocktree Fock approximation as in [24] determine state probability, but by determining polarization as in [25] the polarization can be determined from the given equation. 134 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 1, January- February (2013), © IAEME P = (ρ1 + ρ3 ) - (ρ2 + ρ4) / (ρ1 + ρ2 + ρ3 + ρ4 ) (4) Where ρ represents the expectation values of charges of two cells, Using the above equation, Eq.(4) polarization values can be found, expected values of polarization being directly entered in the conditional probability table of a random node or a cell and hence using Genie software the joint probability distribution of the circuit can be found. Using this method it is possible to find the probability of getting output (polarization) for a given temperature and input being found. Consider the QCA latch in figure 6, the joint probability function is decompose in to product of individual conditional probability functions as P ( X1, …..X5 ) = P(X5 / X4, X3). P( X4 / X3 , X2) …..P(X2 / X1) P(X1) (5) But Eq.(5) hold for linear random nodes with easy message passing technique to find joint distribution, we have consider not a linear cell instead a tree like structure. We have used here [18] Joint tree method of message passing technique for propagating the polarization information. Since we have considered as tree like structure, we used above method to form clusters, we decompose the network in to clusters that form tree structures and treat the variable in each cluster as compound variable that is capable of passing message to its neighbor, the above network can be clustered in to three clusters X1,X2 and X3 as one cluster, X2, X3, and X4 as second cluster and X4 and X5 as another cluster. The direct causes or parent of a node depends on inferred causal ordering. The exact message passing scheme depends on tree structure, whose nodes are clique of random variables. This tree of cliques is obtained from the initial DAG structure via a series of transformations that preserve the represented dependencies. These transformations are constructing moral and chordal graph via constructing triangulated undirected graph. The moral graph is obtained by considering DAG structure to a triangulated undirected graph structure called moral graph. Chordal graph is obtained from moral graph by a process of triangulation. Triangulation is the process of breaking all cycles in the graph to be composition of cycles over just 3 nodes by adding additional links. There are many possible ways for achieving this. At one extreme, we can add edges between every pair of nodes to arrive at final graph that is complete. When we transform DAG to junction of cliques the preservation of parameters dependencies must be taken care, here in this process automatically the dependencies are preserved. Figure 7,8, 9 shows the junction of tree clique for the example considered. Figure 7 shows the moral graph of QCA Bayesian network 135 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 1, January- February (2013), © IAEME Figure 8 chordal graph of QCA Bayesian network Figure 9 Junction of cliques Moral graph is obtained by drawing a line between x2 andx3, hence it forms a tree structure and using minimum elimination of clique sets and running intersection property as in [21], a three node clique set is formed which is a subtree from the tree, three set of clique is formed using intersection property, [18]a chordal graph is the triangulation process of finding junction clique set. Finally three sets Clique x1x2x3 , x2x3x4 and x4x5 with potential function as shows in the figure 9. Clique sets c1,c2 and c3 are running with intersection property, a junction tree between these clique is formed by connecting each predecessor to the present clique set. A potential function is associated with each clique set formed from the conditional probability of the variables in the set. Each potential function is determined by the product of conditional probability functions mapped to that clique. Eq.(6) gives Product of Cond .Probability. C(x2x3) = ΠvuPa(x) ε x P ( v / Pa ( X)) (6) The joint probability distribution is given by eq.(7) P(x1…..x5) = Π c(xi) i = 1…5 (7) Now the tree structure is useful for local message passing. Given any evidence, messages consist of the updated probabilities of the common variables between two neighboring cliques. We used average likelihood propagation algorithm for finding expected polarization of output cell with respect to temperature and types of input. The probabilities are propagated through the junction clique by local message passing. Messages are passed from leaf clique to root clique, then again the present clique pass message to next clique and so on. Based on the values of c the marginal are found z(yi) for each clique, when message passed first to second clique, a scaling factor being sent to first clique to scale the marginal for moving to the next clique, this way message being transmitted. 136 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 1, January- February (2013), © IAEME Z(yi) = Σ c( xi) (8) Z(yi) = Zi(yi) / Zj(yi) .Zj(yi) (9) Eq. (8) gives summation of all the values of potential function to give marginal function, Eq.(9) is rescaled depending on present junction clique and next junction clique scaling function. Hence for each passing marginal function are rescaled and value is changed for next clique. We used this technique for QCA latch cell for finding probability of getting correct output at the output cell with respect temperature and inputs. Figure 10 a. shows the probability of getting correct output of logic 1 and logic 0 with respect to input configurations 1 and 0. Figure 10.b and c shows probability of getting correct output in combinational and Flip flop QCA circuits. The output value through Bayesian network gives nearly equal to simulated value, hence Bayesian tools can be used for modeling nano circuits. Fig.10 a. shows the Probability of getting correct output of QCA latch with respect to input 0 and 1. Fig 10.b.Probability of getting correct ouput in Comb circuits through Baeysian networks 137 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 1, January- February (2013), © IAEME Fig 10.c.Probability of getting correct ouput in Flip flops circuits through Baeysian networks 2.1 Simulation Results The simulated values from QCA Designer circuit is taken as input to the bayseian network and cryogenic temperature of 10 K is assumed throughout the Bayesian network. Applying the algorithm and probability of getting correct output is calculated. Figure 10 a to c shows the probability of getting correct ouput for latch, combinational and sequential circuits. It is found that the value more or less the simulated value and the baysian algorithms used to model the nano cicuits for device failures. The next section discuss about the reliability issues of QCA circuits and therbyu the reducing the faults occuring in QCA circuits. 3. RELIABILITY ANALYSIS OF BAYESIAN STRUCTURE QCA circuits are constructed by serial and parallel structures of QCA wires. Reliability analysis can be done on this circuit in order to deliver errorless QCA cells in the QCA circuit. The reliability analysis of these circuits depends on reliability of input cells so that errorless QCA cell can be constructed. Bayesian networks used in chapter 5 are used for reliability analysis of QCA circuits. The failure of a QCA cell in QCA circuit may cause the failure of whole system and a single defective cell in parallel may reduce the overall performance of a QCA circuit. If a circuit consists of n cells Ci, i=1,…n in serial, the system will be performing well if and only if each component is performing well. So if Pi , is the reliability of the ith component, then the reliability of the system Ps is given by equation 3.1. Ps = π i =1ton Pi (3.1) On the contrary if a system consists of n cells Ci, i=1,…n in parallel, the system will perform well if at least one of these cells perform well, so if Pi is the reliability of the ith component, then the reliability of the system Pp is given by equation 3.2. PP = 1 − π i =1ton (1 − Pi ) (3.2) 138 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 1, January- February (2013), © IAEME Equation 1 and 2 constitute the fundamental relations for computing the reliability of a QCA circuit because any system will consists of cells or groups of cells in serial and/or in parallel manner. Consider a simple QCA latch of figure 11 drawn through QCAdesigner tool. All QCA circuits are transformed into Bayesian framework and simulated using Genie software. Each cell in the QCA circuit is a node in Bayesian network. Each chance node has Conditional probability table through which joint probability of entire circuit is found. Figure 11.a QCA latch circuit drawn. Figure 11.b Bayesian using QCA designer representation Each chance node in figure 11 represents a random variable of each cell and directed arc represents direct causal relation with parent nodes. The structure of the resulting BN for QCA latch cell for reliability analysis consists of three groups of nodes, let Nc be the node without parent say X1 Nint is the intermediate nodes consists of Nint,s serial intermediated node and Npar,s parallel intermediate node. Here X3 and X4 are parallel intermediate nodes with X1 as a parent node. X3 with X4, X2 with X4 are serial intermediate node and destination node as Nout (X5). Figure 12 shows the framed Bayesian structure for reliability analysis. Figure 12 reliability analysis of QCA Latch using Bayesian network 139 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 1, January- February (2013), © IAEME The transformation of QCA latch Bayesian structure to reliability analysis is by considering each cell or node as serial or parallel (assuming all cells are in clock zone). This analysis is useful to study the cell failure in terms of polarization and to identify the correct QCA cell for the circuit failure. Once defined the structure of the BN, its parameters must be determined: the parameters to be entered in to the Bayesian network are priori probabilities of states of nodes without parents, that is nodes of type Nc and the conditional probabilities of intermediate nodes, that is nodes of type Nint,s and Nint,p, knowing some configurations of the states of their parents. Though more than two states can be considered for each node, here it is considered that each node has only two states: failure (F) or no failure (NF). The generalization to more than two states would not be very difficult. The parameters of the BN consist of two types: 1. A priori probabilities of basic components given by their reliability or the complement of their reliability. 2. Conditional probabilities of the intermediate nodes given the configurations of their parents. A priori probabilities of nodes of type Nc are fully determined by the reliability of the corresponding components. 4.0 RELIABILITY ALGORITHM OF QCA CIRCUITS. If nc is the basic cell of Nc and pi is the reliability of the component Nc, P ( N ci = NF ) = Pi and i P ( N = F ) = 1 − Pi , i = 1....nc c (4.1) Similarly for Nint,p and Nint,s Parameters can be defined as P ( N int, p = NF / C ( N int, p )) = 0UN ∈ C ( N int, p ), N = Failure (4.2) Else P ( N int, p = NF / C ( N int, p )) = 1 (4.3) and P ( N int, p = F / C ( N int, p )) = 1UN ∈ C ( N int, p ), N = Failure (4.4) Else P ( N int, p = F / C ( N int, p )) = 0 (4.5) P ( N int, s = NF / C ( N int, s )) = 1UN ∈ C ( N int, s ), N = NoFailure (4.6) Else P ( N int, s = NF / C ( N int, s )) = 0 (4.7) And P ( N int, s = F / C ( N int, s )) = 1UN ∈ C ( N int, s ), N = NoFailure (4.8) Else P ( N int, s = F / C ( N int, s )) = 1 (4.9) Equations 6.3 to 6.11 gives conditional probability defined for intermediate nodes with conditions failure (F) and no- failure (NF). The polarization is defined for each cell, for example P (Ci = NF ) = 0.9 (4.10) P (Ci = F ) = 0.1, i = 1....4. 140 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 1, January- February (2013), © IAEME Full polarization value (logic 1) is 0.9 to +1 and -0.9 to -1, partially polarized values are 0.5 to 0.8 or -0.5 to 0-0.8, and logic 0 polarization values are -0.5 to + 0.5. Let X1 cell be the Nc node, interaction between X2 and X4 be G1 as intermediate node, interaction between X3 and X4 be G2, second node be either G1 or G2 of Nint,p, third intermediate node be Nint,s and finally destination or output node Nout. Now the Bayesian network defined over QCA latch according to above statements as shown in figure 13, assume logic 1 as input decision and searching for utility at the output node in terms of its probability. Figure 13 a Decision and utility nodes for evaluating logic1 probability at the output node which is 0.832 with intermediate node CPT is shown in table 4.1. Table 4.1 Intermediate node G1 node CPT Table 4.1 shows the intermediate CPT table, if the entries in the CPT are changed slightly from 0.9 to 0.6 less polarized that leads to decrease the probability then intermediated nodes has to be checked. Next is to examine the cell which is less polarized by G1 or G2 nodes. Figure 14 Decision and utility nodes for evaluating logic1 probability at the output node which is 0.822, decreased than in figure 13. 141 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 1, January- February (2013), © IAEME Table 4.1 and 4.2 gives G1 and G2 CPT, the failure of the whole system means that component X4 and cell G1 will surely fail. The element responsible for the failure of G1 is X3 and X4 with 71.00% of chances against G2 with 29.00% of chances. So the system critical elements, in terms of reliability, are G1( X3 and X4) and X4 . One can simulate many other configurations to find the error occurred in terms of probability of output. Table 4.2 CPT of node G2 due to X2 and X4 QCA cells (0.71 – 1, 0.3 -0) Cell X2 Failure No - Failure Cell X4 F NF F NF Failure 1 0 0 0 No 0 1 1 1 failure Table 4.3 CPT of node G1 due to X3 and X4 QCA cells ( 0.71 -1, 0.3 -0) Cell X3 Failure No - Failure Cell X4 F NF F NF Failure 1 1 1 0 No 0 0 0 1 failure 4.1 QCA NOT circuit with CLOCK Zone A QCA circuit organized in parallel is more reliable than one which is organized in serial. Serial QCA circuits require clocking for group of cells whereas a parallel QCA cell (circuit with more layers in parallel) which has clock zones running for more no of layers. One way to improve the reliability of a QCA circuit is to put two or more layers in parallel instead of one layer. But this process will increase the complexity of the circuit. An example of a system composed of QCA cells is given in Figure 6.5. The system has two main parallel branches, one branch consisting only of the components C4 and the other one consisting of component C1 in serial with a group formed by C2 and C3 in parallel. Figure 15.QCA not circuit with serial and parallel layers a input and y output 142 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 1, January- February (2013), © IAEME C1 C2 C3 C4 Figure 16 Equivalent Component structure for reliability analysis of QCA not circuit Table 4.4 CPT of node G2 Cells c2 Failure No - Failure Cells c3 F NF F NF Failure 1 0 0 0 No 0 1 1 1 failure Table 4.5 CPT of node G1 Cells c1 Failure No - Failure Cells G2 F NF F NF Failure 1 1 1 0 No 0 0 0 1 failure Table 4.6 CPT of intermediates node. Cells c4 Failure No - Failure Cells G1 F NF F NF Failure 1 0 0 0 Nofailure 0 1 1 1 Figure 15 is QCA NOT circuit and 16 gives the reliability transformation of finding the components in 15. QCA NOT circuit has two parallel branches and one loop in one of the parallel branches. As discussed in the previous section, C1 has group of cells in upper parallel arm, C2 and C3 form the smaller loop in upper parallel arms and C4 form the lower parallel arm. Let us define the components (group of cells) • C1, C2, C3 and C4 are nodes of type Nc; • G2 is a node of type Nint,s formed by regrouping the component C1 act in parallel components C2 and C3; • G1 is a node of type Nint,s formed by regrouping the component C1 and the subsystem G2; • Finally the subsystem G1 and the component C4 act in parallel on the system so that this one is a node of type Nint,p. 143 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 1, January- February (2013), © IAEME Table 4.4, 4.5, 4.6 gives Conditional Probability of cells of G1 and G2 intermediate nodes. The failure of the whole system means that component C4 and subsystem G1 will surely fail. The element responsible for the failure of G1 is C1 with 91.74% of chances against G2 with 9.17% of chances. So the system critical elements, in terms of reliability, are C1 and C4. The group of cells in C1 and C4 have to be examined to find particular defect cell in terms of its probability of getting correct polarization or not. The same way analysis can be carried out for QCA system to find defective cells. The reliability of QCA cell can be found using this Bayesian network of transforming QCA circuits to its Bayesian framework. The QCA latch circuit failure is due to one of the intermediate nodes as its probability decreases when it is a defect one, similarly QCA not circuit also is used to find reliability of group of cells in serial and parallel arms. This can be extended for simulating errorless QCA systems. The extension of this work is to assume the type of defects or device level uncertainties in QCA circuits and by using different algorithm simulating its Bayesian framework to find defective cells in terms of its polarization. 5. CONCLUSION Bayesian network can be used to find the probability based modelling of QCA cells in terms of its temperature and input configurations. We have simulated the probability based Bayesian modelling of finding the correct output of simple latch circuit. We discussed reliability analysis of QCA latch and Not circuit, we found the probability decreases as we move to higher nodes when present cell or node is a defect one, reliability of the cell can be found using this Bayesian network of transforming qca circuits to its Bayesian framework. We discussed qca latch circuit failure is due to one of the intermediate nodes as its probability decreases when it is a defect one, we analysed QCA not circuit also to find reliability of group of cells in serial and parallel arms. This can be extended for simulating errorless QCA systems. We have not considered the type of defects occur for particular cell. The extension of this work is to assume the type of defects or device level uncertainties in QCA circuits and by using different algorithm simulating its Bayesian framework. REFERENCE [1] C. Lent and P. Tougaw etal Proceeding of the IEEE, vol. 85-4, pp. 541.557, April 1997 [2] K.Walus, Wei Wang and Julliaen et al, Proc IEEE Nanotechnology conf, vol 3 December 2004. [3] A. Vetteth et al., Proc. 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