sympauli 1.0.0

Symbolic Pauli Heisenberg Evolution Engine.

sympauli

Symbolic Pauli Heisenberg Evolution Engine

Evolves quantum observables through parameterized circuits in the Heisenberg picture, keeping all coefficients as exact SymPy expressions. Vibe coded using Claude AI in one afternoon.

Install dependencies

pip install sympy numpy

Usage

from sympauli import PauliSum, evolve, gradient, expectation_value
from sympauli.gates import gate_Ry, gate_CNOT
import sympy as sp
import numpy as np

theta = sp.Symbol('theta', real=True)
n = 2

# Define observable
H = PauliSum.from_dict({'ZZ': 1, 'XI': 1, 'IX': 1}, n=n)

# Define circuit
circuit = [gate_Ry(theta, target=0), gate_Ry(theta, target=1), gate_CNOT(0, 1)]

# Symbolically evolve in the Heisenberg picture: U†·H·U
H_evolved = evolve(H, circuit, n_qubits=n)

# Symbolic gradient w.r.t. theta
dH = gradient(H, circuit, n_qubits=n, param_symbol=theta)

# Expectation value on a state
state = np.array([1, 0, 0, 0], dtype=complex)
ev = expectation_value(H_evolved, state, {theta: 0.5})

Package structure

Module	Contents
pauli_string.py	PauliString — symplectic bitmask representation, multiplication, embedding
pauli_sum.py	PauliSum — symbolic linear combination, arithmetic, adjoint, simplification
gates.py	40+ standard gates as PauliSums: Rx/Ry/Rz, CNOT, CRy, RXX/RYY/RZZ, CCX, …
heisenberg.py	evolve, gradient, expectation_value, validate
example.py	Runnable demo: python -m sympauli.example

Qubit convention

• PauliString.from_string('AB'): A acts on qubit 1 (MSB), B acts on qubit 0 (LSB).
• gate_CNOT(control=0, target=1): control is qubit 0, target is qubit 1.
• to_matrix() uses big-endian ordering: qubit n-1 is the most significant bit.