Geometric phases, adiabaticity and decoherence in qubits Rob Whitney1 Yu. Makhlin2, A. Shnirman3, and Y. Gefen4 1. 2. 3. 4.
ILL, Grenoble Landau Inst. Russia Univ. Karlsruhe, Germany Weizmann Institute, Israel
Mini-atelier cohérence et information quantiques. Grenoble, Juin 2006
Who cares about qubits? Fully controllable quantum systems: A PLAY-GROUND FOR QUANTUM PHYSICS STUDY interplay of quantum effects with decoherence when we have good control of BOTH.
IF we have thousands of qubits, we MIGHT have a quantum computer
Overview " la phase de Berry POUR LES NULS : abelian and non-abelian " Berry phase in qubits
DECOHERENCE: when system is not isolated " phase information in adiabatic limit for non-isolated system? Naïve arguments say NO Experiments say YES
Resolving contradiction
" Berry phase modified by environment : remains geometric (not monopole) also complex ' geometric dephasing
" geometric phases to avoid decoherence?
No!
" symmetries to avoid decoherence? decoh-free subspace, Saclay “quantronium” " geometric/topological/holonomic quantum computing : No such thing as a free lunch !!
What is Berry phase ? Slowly varying B-field : rate of rotation, |#|
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Why does random matrix theory work ? Why does random matrix theory fail ? Ehrenfest time, t. E. : a measure of classical-ness. Random matrix. Classical regime.
Shot noise : fano factor = (RMT result) exp[-tE/ D] ... âwell-explainedâ by random matrix theory (RMT) closed cavity : level-statistics ... Our Procedure : (i) define new basis, {v'i}, such that, v' i. = A' ... but proportion of non-classical mod
Periodic orbit theory is exact. Numerics show GOE level-statistics. B Bonds. N Nodes ... Lengths of all bonds are incommensurate. (2) ... [7] Basics of calculation.
time z. B mem Ï. 1/Ïmem area = Î. Noise spectrum. 000000000. 000000000. 000000000. 000000000 .... + perturbation theory on new H (equiv to NIBA). Terms missed by RG; in x ... Go from strongly time-dependent problem to (almost) ...
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i.e. small matrix elements for spin-flip. ⢠For anisotropic environment : Berry phase modified by environment. ⡠geometric = quadrupole-like. ⡠complex funct. of ...
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Quantum optics: decay of excited atomic state. ⢠Chemical ... Only a microscopic theory can answer certain questions: ... dependence on environ. spectrum?
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sional adjustments25. In a second experiment, we rejected this explanation by presenting two pairs of linear gratings that moved in opposite directions (Fig. 4a).
Why does random matrix theory work so well ? Why doesn't random matrix theory work ? Ehrenfest time, t. E. , a measure of classical-ness. Random matrix.
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