Time Evolution of Quantum Computer

Deutsch formulated in 1985 a new computer based on quantummechanics. In quantum computers, the ones and zeros of classical digital computers are replaced by the quantum state of a two-level system which is named qubit. Computation, i.e., a sequence of unitary transformations, simultaneously affects each element of the superposition, generating a massive parallel data processing, albeit within one piece of quantum hardware. Practical quantum computer requires preventing decoherence (uncontrolled interaction of a quantum system with its surrounding environment) in order to maintain the superposition. In 1998, Kane proposed the scheme of implementing a quantum computer on an array of nuclear spins located on donors in silicon. Because nuclear spins are extremely well isolated from environment, operations on nuclear-spin qubits could have low error rates. Quantum logic gate is performed by transitions between the different energy levels of the electron-nuclear spin states, which is induced by a radio-frequency magnetic field B applied at a frequency resonant with the energy-level difference. In this study, we numerically simulated the quantum logic gate of Kane’s quantum computer, by neglecting the complications generated from the band structure in Si. For the calculation of the time evolution of the quantum logic gate, we compute the transition probability between the energy levels of electron-nuclear spin states under the influence of a time-dependent perturbation.