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We examine a 31P donor electron spin in a Si crystal to be used for thepurposes of quantum computation. The interaction with an uncontrolled system of29Si nuclear spins influences the electron spin dynamics appreciably. Thehyperfine field at the 29Si nuclei positions is non-collinear with the externalmagnetic field. Quantum operations with the electron wave function, i.e. usingmagnetic field pulses or electrical gates, change the orientation of hyperfinefield and disturb the nuclear spin system. This disturbance produces adeviation of the electron spin qubit from an ideal state, at a short time scalein comparison with the nuclear spin diffusion time. For H_ext=9 T, theestimated error rate is comparable to the threshold value required by thequantum error correction algorithms. The rate is lower at higher externalmagnetic fields.Comment: 11 pages, 2 figure

physical review. b, condensed matter

Nonideality of quantum operations with the electron spin of a<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow /><mml:mrow><mml:mn>31</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mi mathvariant="normal">P</mml:mi></mml:math>donor in a Si crystal due to interaction with a nuclear spin system

Nonideality of quantum operations with the electron spin of a31Pdonor in a Si crystal due to interaction with a nuclear spin system