We study the relaxation of an electron spin qubit in a Si quantum dot due to electrical noise. In particular, we clarify how the presence of conduction-band valleys influences spin relaxation. In single-valley semiconductor quantum dots, spin relaxation is through the mixing of spin and envelope orbital states via spin-orbit interaction. In Si, the relaxation could also be through the mixing of spin and valley states. We find that the additional spin relaxation channel, via spinvalley mixing and electrical noise, is indeed important for an electron spin in a Si quantum dot. By considering both spin-valley and intra-valley spin-orbit mixings and Johnson noise in a Si device, we find that the spin relaxation rate peaks at the hot spot, where the Zeeman splitting matches the valley splitting. Furthermore, because of a weaker field dependence, the spin relaxation rate due to Johnson noise could dominate over phonon noise at low magnetic fields, which fits well with recent experiments.

We study decoherence of an electron spin qubit in a quantum dot due to charge noise. We find that at the lowest order, the pure dephasing channel is suppressed for both 1/f charge noise and Johnson noise, so that charge noise leads to a pure relaxation channel of decoherence. Because of the weaker magnetic field dependence, the spin relaxation rate due to charge noise could dominate over phonon noise at low magnetic fields in a gate-defined GaAs or Si quantum dot or a InAs self-assembled quantum dot. Furthermore, in a large InAs self-assembled quantum dot, the spin relaxation rate due to phonon noise could be suppressed in high magnetic field, and the spin relaxation due to charge noise could dominate in both low and high magnetic field. Numerically, in a 1 Tesla field, the spin relaxation time due to typical charge noise is about 100 s in Si, 0.1 s in GaAs for a gate-defined quantum dot with a 1 meV confinement, and 10 µs in InAs self-assembled quantum dot with a 4 meV confinement.

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Long-range quantum communication for spin qubits is an important open problem. Here we study decoherence of an electron spin qubit that is being transported in a moving quantum dot. We focus on spin decoherence due to spin-orbit interaction and a random electric potential. We find that at the lowest order, the motion induces longitudinal spin relaxation, with a rate linear in the dot velocity. Our calculated spin relaxation time ranges from sub µs in GaAs to above ms in Si, making this relaxation a significant decoherence channel. Our results also give clear indications on how to reduce the decoherence effect of electron motion.