Quantum Hamiltonian Descent — QHD
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Holder Table

The Holder Table function is defined as:

\(\begin{align}\begin{split} f(x,y) = -\left|\sin(x) \cos(y) \exp\left(\left|1 - \frac{\sqrt{x^2 + y^2}}{\pi}\right|\right)\right| \end{split}\end{align}\)

Comparison of optimization methods on holder
Samples from the distributions of QHD, QAA, NAGD, and SGD at different (effective) evolution times t=[0.1, 0.5, 2, 3, 5, 10] are shown as scatter plots.
3-Phase Diagrams
The three-phase picture of QHD.
  1. Surface plots of the probability density in QHD at different times.
  2. Probability spectrum of QHD.
  3. The success probabilities of QHD and QAA.
  4. The energy ratio E1/E0 in QHD shown as a function of time.

2D Functions

Ackley

ackley preview

Ackley 2

ackley2 preview

Alpine 1

alpine1 preview

Alpine 2

alpine2 preview

Bohachevsky 2

bohachevsky2 preview

Camel 3

camel3 preview

Csendes

csendes preview

Deflected Corrugated Spring

defl_corr_spring preview

Dropwave

dropwave preview

Easom

easom preview

Griewank

griewank preview

Holder Table

holder preview

Hosaki

hosaki preview

Levy

levy preview

Levy 13

levy13 preview

Michalewicz

michalewicz preview

Rastrigin

rastrigin preview

Rosenbrock

rosenbrock preview

Shubert

shubert preview

Styblinski-Tang

styblinski_tang preview

Sum of Squares

sumofsquares preview

Xin-She Yang 3

xinsheyang3 preview
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