Perturbation approach for nuclear magnetic resonance solid-state quantum computation (Q1864543)

Several solid state quantum systems are considered nowadays as candidates for quantum computers. In this paper the implementation of quantum logic gates by radio-frequency pulses in the nuclear-spin one-dimensional solid state system is considered. The dynamics of such a quantum computer with a large number \((L=1000)\) of qubits is studied using a perturbation approach. This approach allows estimation of errors in implementation of quantum logic operations without recourse to either exact solution of quantum dynamical equations or direct diagonalization of large matrices. Small parameters are introduced and used to compute the error in an implementation of an entanglement between remote qubits, using a sequence of radio-frequency pulses. The error is computed up to the different orders of the perturbation theory and tested using exact numerical solution. The procedure describes the behavior of the quantum system in large Hilbert space and predicts the final quantum state of the system after action of the sequence of pulses with different frequencies. This approach provides tools for choosing the optimal parameters for operation of the scalable quantum computer with a large number of qubits.