Analytic solutions for quantum logic gates and modeling pulse errors in a quantum computer with a Heisenberg interaction
We analyze analytically and numerically quantum logic gates in a one-dimensional spin chain with Heisenberg interaction. Analytic solutions for basic one-qubit gates and swap gate are obtained for a quantum computer based on logical qubits. We calculated the errors caused by imperfect pulses which implement the quantum logic gates. It is numerically demonstrated that the probability error is proportional to epsilon(4), while the phase error is proportional to epsilon, where epsilon is the characteristic deviation from the perfect pulse duration.
logical qubits exchange interaction