We present a dynamic learning paradigm for ``programming'' a general quantum computer. A learning algorithm is used to find the control parameters for a coupled qubit system, such that the system at an initial time evolves to a state in which a given measurement corresponds to the desired operation. This can be thought of as a quantum neural network. We first apply the method to a system of two coupled superconducting quantum interference devices (SQUIDs), and demonstrate learning of both the classical gates XOR and XNOR. Training of the phase produces a gate similar to the CNOT. Striking out for somewhat more interesting territory, we attempt learning of an entanglement witness for a two qubit system. Simulation shows a reasonably successful mapping of the entanglement at the initial time onto the correlation function at the final time for both pure and mixed states. For pure states this mapping requires knowledge of the phase relation between the two parts; however, given that knowledge, this method can be used to measure the entanglement of an otherwise unknown state. The method is easily extended to multiple qubits or to quNits.
A method of frame-to-frame coding is proposed in which the changes from one frame to the next are first detected and then transmitted as an intraframe coded signal rather than as frame-to-frame differences. A coder was constructed to test the proposal using DPCM for the intraframe encoding.Three aspects of the coder design presented particular problems. They were:(i) Movement detection (as a result of the increase in frame-to-frame noise caused by the intraframe coding). (ii) Smooth reduction of bit-rate and picture quality so as to take advantage of the reduction in spatial quality that a viewer tolerates when areas are moving fast. (iii) Control strategy for linking the operation of the buffer, the move ment detector, and the operating stale of the coder.The coder gave good picture quality at a transmission rate of 1.5 megabits per second (0.75 bit per picture element), except in extreme situations where the moving area covered almost the entire screen. The performance is described in detail at bit rates of 2.0, 1.5, and 0.5 megabits per second.The experimental coder has a number of desirable properties from an overall systems point of view when compared with transmission of frame differences. These include high tolerance to transmission errors and small frame storage requirements.
We present extensions of our earlier published ordering techniques for efficient coding of two-level (black and white) facsimile pictures. Ordering techniques use the two-dimensional correlation present in spatially close picture elements to change the relative order of trans mission of elements in a scan line so as to increase the average length of the runs of consecutive black or white elements in the ordered line, making the data more amenable to one-dimensional run-length coding. The extensions that we consider allow us to use different run-length codes to match the statistics of different parts of the ordered data, and to drop certain runs from transmission. Computer simulations using the eight standard CCITT pictures, which have a resolution of ap proximately 200 dots/inch, indicate that these extensions can result in transmission bit rates which are about 11 to 21 percent lower than the ordering schemes described in our earlier work. The entropies vary between 0.021 and 0.125 bits/pel for the eight pictures.
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