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By Michel Devoret, Benjamin Huard, Robert Schoelkopf, Leticia F. Cugliandolo
This e-book gathers the lecture notes of classes given on the 2011 summer season tuition in theoretical physics in Les Houches, France, consultation XCVI.
What is a quantum computing device? will we say that lasers and transistors are quantum machines? finally, physicists promote it those units because the major spin-offs of the certainty of quantum mechanical phenomena. even though, whereas quantum mechanics needs to be used to foretell the wavelength of a laser and the operation voltage of a transistor, it doesn't intrude on the point of the indications processed by way of those structures. signs contain macroscopic collective variables like voltages and currents in a circuit or the amplitude of the oscillating electrical box in an electromagnetic hollow space resonator. In a real quantum computer, the sign collective variables, which either tell the surface at the country of the computer and obtain controlling directions, needs to themselves be handled as quantum operators, simply because the place of the electron in a hydrogen atom. Quantum superconducting circuits, quantum dots, and quantum nanomechanical resonators fulfill the definition of quantum machines. those mesoscopic structures show a number of collective dynamical variables, whose fluctuations are good within the quantum regime and whose dimension is basically constrained in precision by means of the Heisenberg uncertainty precept. different engineered quantum structures in accordance with traditional, instead of man made levels of freedom may also qualify as quantum machines: trapped ions, unmarried Rydberg atoms in superconducting cavities, and lattices of ultracold atoms. This publication presents the fundamental wisdom had to comprehend and examine the physics of those novel platforms.
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Additional info for Quantum Machines: Measurement Control of Engineered Quantum Systems: Lecture Notes of the Les Houches Summer School: Volume 96, July 2011
Example text
Dt i If the Hamiltonian is constant, this can be solved straightforwardly via the operator exponential, i U (t, ti ) = exp [−iH (t − ti ) / ] . Limit theorem for QSDEs; cavity QED relay model 19 We note that any time-dependent operator moment can thus be written O t = ψ (t)| O | ψ (t) = ψ (ti )| U † (t, ti ) OU (t, ti ) | ψ (ti ) , and we note that we can reproduce all such observable quantities in the Heisenberg picture, where the state vector | ψ (ti ) is considered to be constant (held to its initial condition) while the operators evolve according to O (t) = U † (t, ti ) OU (t, ti ) .
Note that this QSDE corresponds to Fig. 5 in this chapter, but Bouter et al. ) We will first take the limit k1 → ∞ and then k2 → ∞. For the first elimination, K = k 2 Y + kA + B, Li = kFi + Gi , Ni j = Wi j , ∗ Y = −κa a∗ a − ga a∗ σge − aσge , A = 0, ∗ ∗ B = −k22 κb b∗ b − k22 κc c∗ c − k2 gb b∗ σgr − bσgr − k2 gb (b∗ σhe − bσhe ) ∗ ∗ −k2 gc (c σhr − cσhr ) , ⎛ √ κa a∗ √ ⎜ κa a∗ F =⎜ ⎝ 0 0 ⎞ ⎟ ⎟, ⎠ ⎛ ⎞ 0 ⎜ 0 ⎟ ⎟ √ G=⎜ ⎝ k2 2κb b∗ ⎠ , √ k2 2κc c∗ Wi j = δi j . We choose H0 = span {| g 0a nb nc , | h 0a nb nc , | r 0a nb nc }, which clearly lies within the kernel of Y .
5 (a) Level diagram for the “atomic” system coupled to cavity modes in the relay construction. (b) Arrangement of resonator modes and correspondence of inputs/outputs to logical signals. (c) Component diagram for the relay, showing logical signals only. Limit theorem for QSDEs; cavity QED relay model 27 This ensures that Y Y˜ P0 = Y˜ Y P0 = 0. We next note that, for na ≥ 1, √ Y | g na nb nc = −κa na | g na nb nc + ga na | e (na − 1)a nb nc , √ Y | e (n − 1)a nb nc = −κa (na − 1) | e (na − 1)a nb nc − ga na | g na nb nc , Y | h na nb nc = −κa na | h na nb nc , Y | r na nb nc = −κa na | r na nb nc .