Installation
git clone https://github.com/klasmodin/quflow.git
cd quflow
pip install .Basic concepts
Classical
function \(\omega:S^2\to\mathbb{R}\)
spherical harmonics \(\omega = \sum_{l=0}^\infty\sum_{m=-l}^l\omega^{lm}Y_{lm}\)
Quantized
complex matrix \(W\in\mathfrak{u}(N)\)
matrix harmonics \(W = \sum_{l=0}^N\sum_{m=-l}^l\omega^{lm}T_{lm}\)
import quflow as qf
omega = np.random.randn(10)
N = 512
W = qf.shr2mat(omega, N)
qf.plot(W)Units of time
Classical time: seconds
Quantum time: qtime
1 second = \(\displaystyle\frac{1}{\sqrt{16\pi}}N^{3/2}\) qtime
General rule:
- numerical parameters use qtime (e.g. stepsize)
- physical parameters use second (e.g. total simulation time)
import quflow as qf
N = 512
print(qf.seconds2qtime(1.0, N))
print(qf.qtime2seconds(1.0, N))Running simulations
High-level solve function:
- initial data \(W_0\in\mathfrak{u}(N)\)
- simulation step-size (qtime)
- total simulation time (seconds)
- inner simulation time (seconds)
(how often callback) - callback function (typically QuData object)
import quflow as qf
N = 128
W0 = qf.shr2mat(np.random.randn(10), N)
h = 0.1
mysim = qf.QuData("mysim.hdf5")
mysim(W0, 0.0) # Save first output
qf.solve(W0, qstepsize=h, time=3.0, inner_time=0.2, callback=mysim)
mysim.flush()