Quantum algorithm design using dynamic learning

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 qubitsystem, such that the system at an initial time evolves to a state in which a given measurementcorresponds to the desired operation. This can be thought of as a quantumneural network. We first apply the method to a system of two coupled superconductingquantum interference devices (SQUIDs), and demonstrate learning of both the classicalgates XOR and XNOR. Training of the phase produces a gate congruent to the CNOTmodulo a phase shift. Striking out for somewhat more interesting territory, we attemptlearning of an entanglement witness for a two qubit system. Simulation shows a reasonablysuccessful mapping of the entanglement at the initial time onto the correlationfunction at the final time for both pure and mixed states. For pure states this mappingrequires knowledge of the phase relation between the two parts; however, giventhat knowledge, this method can be used to measure the entanglement of an otherwiseunknown state. The method is easily extended to multiple qubits or to quNits.

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