Pauli Propagation of Parametrized Circuits

Try it without installation via Binder:

Overview

Convert the expectation values of a circuit’s observables into explicit functions of the circuit’s parameters.

Usage

• First import all the necessary libraries:

import pennylane as qml # To define the circuit
from pprop.propagator import Propagator # For Pauli Propagation

• Define the circuit as a function of the parameters

# Function of parameters
def ansatz(params : list[float]):
    qml.RX(params[0], wires=0)
    qml.RX(params[1], wires=1)

    qml.RY(params[2], wires=0)
    qml.RY(params[3], wires=1)

    qml.Hadamard(wires = 2)

    qml.Barrier()

    qml.CNOT(wires = [0, 1])
    qml.CNOT(wires = [1, 2])

    qml.Barrier()

    qml.RY(params[4], wires=0)
    qml.RY(params[5], wires=1)
    qml.RY(params[6], wires=2)
    
    return [qml.expval(qml.PauliZ(qubit)) for qubit in range(1)] + [qml.expval(qml.PauliX(0)@qml.PauliX(1)@qml.PauliX(2))] + [qml.expval(qml.PauliY(2))] + [qml.expval(-qml.PauliX(0)@qml.PauliX(1)@qml.PauliX(2) + 13*qml.PauliZ(2))]

• Define the propagator

prop = Propagator(
    ansatz, 
    k1 = None, # Cutoff on the Pauli Weight
    k2 = None, # Cutoff on the frequencies
    k2_mode = "frequency", # or "sine": k2 counts only sin factors (exact at theta = 0)
)

>>> prop
Propagator
  Number of qubits : 3
  Trainable parameters : 7

>>> prop.show()
0: ──RX(0.00)──RY(2.00)──||─╭●─────||──RY(4.00)─┤  <Z> ╭<X@X@X>      ╭<𝓗(-1.00,13.00)>
1: ──RX(1.00)──RY(3.00)──||─╰X─╭●──||──RY(5.00)─┤      ├<X@X@X>      ├<𝓗(-1.00,13.00)>
2: ──H───────────────────||────╰X──||──RY(6.00)─┤      ╰<X@X@X>  <Y> ╰<𝓗(-1.00,13.00)>

• Propagate the observables (this runs in the Rust extension pprop_rs):

prop.propagate()

• Get the output expectation values by calling the class and feeding the circuit's parameters

random_params = qml.numpy.arange(prop.num_params)
prop_output = prop(random_params)
[ 0.32448205 -0.52806187  0.          4.1604633 ]

• You can inspect the explicit functions using .expression()

>>> prop.expression(0)
-1.0*sin(θ2)*sin(θ3)*sin(θ4)*cos(θ0)*cos(θ1) + 1.0*cos(θ0)*cos(θ2)*cos(θ4)

Installation

pip install pauli-propagator

This pulls in the Rust extension pprop_rs as a prebuilt wheel (Linux x86_64/aarch64, macOS arm64, Windows x64; Python 3.12+). On other platforms pip builds it from source, which needs a Rust toolchain (rustup).

Running on IBM hardware (optional)

pprop.qasm exports a trained circuit to OpenQASM 3 with no extra dependencies. To load it into Qiskit (pprop.qasm.to_qiskit) and run it on IBM Quantum devices, install the qiskit extra, which adds qiskit, qiskit-qasm3-import and qiskit-ibm-runtime:

pip install "pauli-propagator[qiskit]"

For a development install, use pip install -e ".[qiskit]" in the last step below.

Development install

pip install maturin
cd native/pprop_rs
maturin develop --release
cd ../..
pip install -e .

maturin develop builds pprop_rs and installs it straight into the active virtual environment. Re-run it after pulling changes to native/pprop_rs.

Examples

For detailed examples, please refer to the notebooks directory, which contains Jupyter notebooks that demonstrate various use cases and tests of the propagator.

Citation

If you use this software in your research or publications, please cite the following:

@software{monaco_2026_23020043,
    author    = {Monaco, Saverio and
                 Lipponen, Aapo},
    doi       = {10.5281/zenodo.23021244},
    month     = sep,
    publisher = {Zenodo},
    swhid     = {swh:1:dir:ce152d847302ce6b14f1197f106986050d09c0f4
                 ;origin=https://doi.org/10.5281/zenodo.16028009;vi
                 sit=swh:1:snp:a9b8558798b8b9e8375e83e7aca935976731
                 18b2;anchor=swh:1:rel:6f6cac02e75daff2e374b752bb49
                 f157960d3915;path=SaverioMonaco-Pauli-
                 Propagator-4bb7e0d
                 },
    title     = {Pauli-Propagator},
    url       = {https://doi.org/10.5281/zenodo.23021244},
    version   = {v3.1.0},
    year      = 2026
}