Decoherence in crystal lattice quantum computation

Nuclear magnetic resonance (NMR) quantum computation in a crystal lattice holds more promise for scalability than its solution NMR counterpart, but dephasing is a severe concern. Pulse sequence refocusing can help bring the qubit dephasing time closer to the limit of the intrinsic decoherence time, but the intrinsic transverse relaxation time (T₂) and the longitudinal relaxation time (T₁) of the crystal must be sufficiently long for a successful implementation. We discuss these time scales and their relation to parameters relevant to quantum computation for several crystal types, discussing in detail the examples of CaF₂, MnF₂, and CeP. Included in the calculation of coherence times for CeP is the development of spin-wave spectra in a type-1 antiferromagnetic FCC lattice.