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QuantumPlaybook

Guides

  • QuantumPlaybook

Tech Notes

  • Addition of Numbers
  • Baker-Hausdorff Lemma
  • Chiral Fermion Random Circuit
  • Clifford Operators: How to Test
  • Commutation Relations for Qubits
  • Entanglement Distillation
  • Generalized Pauli Operators: Implementation
  • Hatano-Nelson-Kitaev Model: Monte Carlo Simulation
  • Hatano-Nelson Model: Monte Carlo Simulation
  • Kitaev Chain
  • Kitaev Random Circuit
  • Λ-Matter in a Cavity
  • Measurement of Total Pauli Z
  • Non-Unitary Dynamics of Quantum States
  • Partial Trace: Physical Meaning
  • Quantum Dot Systems
  • A Quantum Playbook
  • Magnetic Exchange Coupling
  • Solovay-Kitaev Algorithm
  • Spin Code
  • Symmetry Effects On Quantum Master Equations
  • Transmon: Quantum Phase Model
  • Transposition as a Supermap
  • Variational Quantum Classifier: Iris
  • Variational Quantum Classifier: Parity
  • Variational Quantum Eigensolver: Transverse-Field Ising Model

Symbols

  • BlochEnergy
  • BlochFunction
  • QuantumPlaybookCheckUpdate
  • QuantumPlaybookEdition
  • QuantumPlaybookUpdate
  • TransmonEnergy
  • TransmonExponent
  • TransmonFunction
  • TransmonHamiltonian
QuantumMob`Transmon`
BlochEnergy
​
BlochEnergy
[ν,α]
returns the energy of the wave function with characteristic exponent ν for the Bloch Hamiltonian with MacCumber parameter α.
​
Details and Options

Examples  
(1)
Basic Examples  
(1)
Here is an example of the dispersion relation in the charging limit. The dispersion relation resembles a quadratic curve.
In[1]:=
α=2.;​​d=0.005;​​fig1a=ListPlot​​Tablen+nu,
BlochEnergy
[n+nu,α],{n,0,2,1/2},{nu,0,0.5-d,d},​​JoinedTrue;​​fig1b=ListPlot​​Tablen+nu,
BlochEnergy
[n+nu,α],{n,0,-2,-1/2},{nu,0,-0.5+d,-d},​​JoinedTrue;​​fig1=Show[{fig1a,fig1b},FrameLabel{"ν","Energy"},PlotRangeAll]
Out[1]=
Here is an example of the dispersion relation in the Josephson limit. The allowed values of energy are almost discrete and are similar to those of simple harmonic oscillator.
In[2]:=
α=0.5;​​d=0.005;​​fig2a=ListPlot​​Tablen+nu,
BlochEnergy
[n+nu,α],{n,0,2,1/2},{nu,0,0.5-d,d},​​JoinedTrue;​​fig2b=ListPlot​​Tablen+nu,
BlochEnergy
[n+nu,α],{n,0,-2,-1/2},{nu,0,-0.5+d,-d},​​JoinedTrue;​​fig2=Show[{fig2a,fig2b},FrameLabel{"ν","Energy"},PlotRangeAll]
Out[2]=
SeeAlso
BlochFunction
 
▪
TransmonEnergy
 
▪
TransmonFunction
TechNotes
▪
Transmon: Quantum Phase Model
▪
Mathieu and Related Functions
▪
Quantum Information Systems with Q3
▪
Quantum Many-Body Systems with Q3
▪
Quantum Spin Systems with Q3
RelatedGuides
▪
Quantum Information Systems
▪
Quantum Many-Body Systems
▪
Quantum Spin Systems
RelatedLinks
▪
G. Blanch (1972)
, "Mathieu Functions" in
Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables
, edited by M. Abramowitz and I. A. Stegun (John Wiley & Sons, 1972).
""

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