Static Qubit Example

Static Qubit Example#

Physics: Compile a simple static two-level system (qubit) Hamiltonian.

The Model

In a typical quantum optics or AMO setup, you start with a static qubit:

\[H = \frac{\omega_0}{2} \sigma_z\]

where:

  • \(\omega_0\) is the qubit transition frequency (in units where \(\hbar = 1\))

  • \(\sigma_z = |0\rangle\langle 0| - |1\rangle\langle 1|\) is the Pauli Z operator

  • The factor \(1/2\) places the ground state at \(-\omega_0/2\) and excited state at \(+\omega_0/2\)

This is the simplest possible Hamiltonian — static (no time dependence), single qubit, no dissipation.

What you’ll learn

  • How to express a static Hamiltonian in LaTeX.

  • How to call compile_model and inspect the returned object.

  • The minimal inputs needed: a LaTeX string, parameters, and Hilbert space configuration.

Code

 1# flake8: noqa
 2"""
 3Static qubit Hamiltonian compiled from LaTeX.
 4
 5What this shows:
 6- Minimal inputs to get a working Hamiltonian (`qubits=1`, no collapse ops).
 7- Default backend dispatch (QuTiP) via `compile_latex_model`.
 8- Inspecting the compiled `H` object that you can pass to solvers.
 9
10Tip: change `t_name` or add `backend="numpy"` to explore other backends.
11"""
12
13from __future__ import annotations
14
15import sys
16from pathlib import Path
17
18ROOT = Path(__file__).resolve().parents[1]
19if str(ROOT) not in sys.path:
20    sys.path.insert(0, str(ROOT))
21
22from latex_parser.latex_api import compile_latex_model
23
24
25def main() -> None:
26    H_latex = r"\frac{\omega_0}{2} \sigma_{z,1}"
27    params = {"omega_0": 2.0}
28    model = compile_latex_model(H_latex=H_latex, params=params, qubits=1, t_name="t")
29    print("Static qubit Hamiltonian:\n", model.H)
30
31
32if __name__ == "__main__":
33    main()

Run it

From the project root:

python examples/example_static_qubit.py

What happens

  1. The LaTeX string r"\frac{\omega_0}{2} \sigma_{z,1}" is canonicalized

  2. It’s parsed into an IR with one term: \(\frac{\omega_0}{2}\) (scalar) × \(\sigma_z\) (operator)

  3. The parameter omega_0 = 2.0 is substituted

  4. QuTiP compiles it to a Qobj (quantum object):

    Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True
Qobj data =
[[ 1.  0.]
 [ 0. -1.]]

Try this

  • Change omega_0 to other values (e.g., 1.0, 10.0) and re-run to see eigenvalues scale.

  • Switch backend to "numpy" to get a dense ndarray instead of a Qobj.

  • Add a second qubit parameter (e.g., qubits=2) and modify the LaTeX to r"\omega_1 \sigma_{z,1} + \omega_2 \sigma_{z,2}" to compile a two-qubit system.

Next steps