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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.

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Measurement of entanglement remains an important problem for quantum information. We present the design and simulation of an experimental method for an entanglement indicator for a general multiqubit state. The system can be in a pure or a mixed state, and it need not be ``close'' to any particular state. The system contains information about its own entanglement; we use dynamic learning methods to map this information onto a single experimental measurement which is our entanglement indicator. Our method does not require prior state reconstruction or lengthy optimization. An entanglement witness emerges from the learning process, beginning with two-qubit systems, and extrapolating this to three, four, and five qubit systems where the entanglement is not well understood. Our independently learned measures for three-qubit systems compare favorably with known entanglement measures. As the size of the system grows the amount of additional training necessary diminishes, raising hopes for applicability to large computational systems.

Complete characterization of the state of a quantum system made up of subsystems requires determination of relative phase, because of interference effects between the subsystems. For a system of qubits used as a quantum computer this is especially vital, because the entanglement, which is the basis for the quantum advantage in computing, depends intricately on phase. We present here a first step towards that determination, in which we use a two-qubit quantum system as a quantum neural network, which is trained to compute and output its own relative phase.