Subdecoherent information encoding in a quantum-dot array

Physical Review B - Condensed Matter and Materials Physics

Volumn 59, Issue 12, 1999, Pages 8170-8181

  Rossi, Fausto ^a  

^a INFM   (Italy)

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EID: 4444325090     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.59.8170     Document Type: Article

References (41)

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31. Here (Formula presented) denotes the Hadamard transformation [i.e., (Formula presented) (Formula presented) on the lth qubit. Moreover (Formula presented) is the controlled-not transformation acting on the lth and mth qubits. If ⊕ denotes addition modulo 2 one has (Formula presented) (Formula presented)
32. Here, only coupling to GaAs bulk phonons has been considered. This, of course, is a simplifying approximation that neglects any interface effect on the phonon dispersion, such as confinement of optical modes in the wells and in the barriers, and the presence of interface modes [H. Rücker, E. Molinari, and P. Lugli, Phys. Rev. B 45, 6747 (1992)].However, while these modifications have important consequences for phonon spectroscopies (like Raman scattering), they are far less decisive for energy-relaxation and dephasing phenomena. Indeed, by now it is well known that the total scattering rates are sufficiently well reproduced if the phonon spectrum is assumed to be bulklike [E. Molinari, in Confined Electrons and Photons: New Physics and Applications, edited by E. Burstein and C. Weisbuch (Plenum, New York, 1994)].
33. With “first excited state” here we mean any linear combination of the two energetically degenerate states.
34. Notice that these matrices are related by a kind of Kramers-Kronig dispersion relation. This stems from the fact that they are basically a real and imaginary part of a single electron propagator obtained by tracing out the phonon field (Ref. 13).
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39. The reader may wonder whether the increase of a makes the various qubits interacting with independent (i.e., uncorrelated) phonon baths. We observe that a lower bound for the acoustic-phonon lifetime in GaAs is tenths of picoseconds, which corresponds to a coherence length much larger than the typical interdot distance a relevant for noiseless encoding. This makes the phonon dynamics fully coherent on the space scale of our QD register.
40. (Formula presented) should more properly defined as the closure of the algebra generated commuting the (Formula presented)
41. (Formula presented)