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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We introduce a scheme for realizing arbitrary controlled-unitary operations in a two-qubit system. If the 2 ϫ 2 unitary matrix is special unitary ͑has unit determinant͒, the controlled-unitary gate operation can be realized in a single pulse operation. The pulse in our scheme will constitute varying one of the parameters of the system between an arbitrarily maximum and a "calculated" minimum value. This parameter will constitute the variable parameter of the system while the other parameters, which include the coupling between the two qubits, will be treated as fixed parameters. The values of the parameters are what we solve for using our approach in order to realize an arbitrary controlled-unitary operation. We further show that the computational complexity of the operation is no greater than that required for a controlled-NOT ͑CNOT͒ gate. Since conventional schemes realize a controlled-unitary operation by breaking it into a sequence of single-qubit and CNOT gate operations, our method is an improvement because we not only require less time duration, but also fewer control lines to implement the same operation. To demonstrate improvement over other schemes, we show, as examples, how two controlled-unitary operations, one being the controlled-Hadamard gate, can be realized in a single pulse operation using our scheme. Furthermore, our method can be applied to a wide range of coupling schemes and can be used to realize gate operations between two qubits coupled via Ising, Heisenberg, and anisotropic interactions.

We introduce an efficient scheme for quantum state transfer that uses a parity-based mirror inversion technique. We design efficient circuits for implementing mirror inversion in Ising