• Subhash Kak

      Articles written in Pramana – Journal of Physics

    • On training feedforward neural networks

      Subhash Kak

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      A new algorithm that mapsn-dimensional binary vectors intom-dimensional binary vectors using 3-layered feedforward neural networks is described. The algorithm is based on a representation of the mapping in terms of the corners of then-dimensional signal cube. The weights to the hidden layer are found by a corner classification algorithm and the weights to the output layer are all equal to 1. Two corner classification algorithms are described. The first one is based on the perceptron algorithm and it performs generalization. The computing power of this algorithm may be gauged from the example that the exclusive-Or problem that requires several thousand iterative steps using the backpropagation algorithm was solved in 8 steps. Another corner classification algorithm presented in this paper does not require any computations to find the weights. However, in its basic form it does not perform generalization.

    • Quantum key distribution using three basis states

      Subhash Kak

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      This note presents a method of public key distribution using quantum communication of n photons that simultaneously provides a high probability that the bits have not been tampered. It is a variant of the quantum method of Bennett and Brassard (BB84) where the transmission states have been decreased from 4 to 3 and the detector states have been increased from 2 to 3. Under certain assumptions regarding method of attack, it provides superior performance (in terms of the number of usable key bits) for n<18m, where m is the number of key bits used to verify the integrity of the process in the BB84-protocol.

    • Statistical constraints on state preparation for a quantum computer

      Subhash Kak

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      Quantum computing algorithms require that the quantum register be initially present in a superposition state. To achieve this, we consider the practical problem of creating a coherent superposition state of several qubits. We show that the constraints of quantum statistics require that the entropy of the system be brought down when several independent qubits are assembled together. In particular, we have: (i) not all initial states are realizable as pure states; (ii) the temperature of the system must be reduced. These factors, in addition to decoherence and sensitivity to errors, must be considered in the implementation of quantum computers.

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