Non-ideality of quantum operations with the electron spin of a 31P donor in a Si crystal due to interaction with a nuclear spin system

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  • 19 December 2002
Abstract
We consider the evolution of a single electron spin of a 31P donor embedded in a Si crystal lattice interacting with a system of neighbor 29Si nuclear spins in an external magnetic field. The magnetic dipole-dipole interaction defines different axes of quantization for electron spin and nuclear spins. The quantum operations with the electron wave function, i.e. by magnetic field pulses or by electrical gates, reorient the quantization axes of nuclear spins and change the dynamics of the nuclear spin system. This effect leads to a deviation of the qubit density matrix from an ideal state at the short time scale, in comparison with nuclear spin diffusion time. We estimate the error of the pi/2 electron spin rotation, due to interaction with single nuclear spin located at the different silicon lattice positions. This error is comparable with error rate threshold for the successful application of fault-tolerant quantum error correction algorithms. It can be observed in experiments on the modulation of the electron spin echo.

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