Numerical Simulation of Leakage Effect for Quantum NOT Operation on Three-Josephson-Junction Flux Qubit

Superconducting flux qubits with three Josephson junctions are promising candidates for the building blocks of a quantum computer. We have applied the imaginary time evolution method to study the model of this qubit accurately by calculating its wavefunctions and eigenenergies. Because such qubits are manipulated with magnetic flux microwave pulses, they might be irradiated into non-computational states, which is called the leakage effect. By the evolution of the density matrix of the qubit under either hard-shaped π-pulse or Gaussian-shaped π-pulse to carry out quantum NOT operation, it has been demonstrated that the leakage effect for a flux qubit is very small even for hard-shaped microwave pulses while Gaussian-shaped pulses may
suppress the leakage effect to a negligible level.