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Decomposition API Reference

SU3Decomposition

Decompose any 3×3 unitary into a canonical product of native qutrit rotations:

\[U = U_d(\phi_6, \phi_5, \phi_4) \cdot r_{01}(\phi_3, \theta_3) \cdot r_{12}(\phi_2, \theta_2) \cdot r_{01}(\phi_1, \theta_1)\]

This is the qutrit analogue of the qubit ZYZ Euler decomposition. Based on Vitanov, Phys. Rev. A 85, 032331 (2012).

from qutritium import SU3Decomposition

Constructor

SU3Decomposition(su3: NDArray, qutrit_index: int, n_qutrits: int)
  • su3 — 3×3 unitary matrix
  • qutrit_index — which qutrit this decomposition targets
  • n_qutrits — total qutrit count in the register

Methods

reconstruct() → NDArray

Reconstruct the unitary from the decomposed factors. Should match su3 to numerical precision.

to_native() → NativeDecomposition

Return virtual-Z phases and a list of native g01/g12 Instruction objects.

to_circuit() → QutritCircuit

Build a QutritCircuit from the decomposition using G01, G12, Ud gates.

Properties

  • .angles — DecompositionAngles named tuple with all 9 angles
  • .su3 — the input unitary

Example

import numpy as np
from qutritium import SU3Decomposition

# Generate a random unitary
rng = np.random.default_rng(42)
A = rng.standard_normal((3, 3)) + 1j * rng.standard_normal((3, 3))
Q, _ = np.linalg.qr(A)

# Decompose
dec = SU3Decomposition(Q, qutrit_index=0, n_qutrits=1)

# Verify fidelity
fidelity = np.abs(np.trace(Q.conj().T @ dec.reconstruct())) / 3
print(f"Fidelity: {fidelity:.10f}")  # 1.0000000000

# Get a circuit
qc = dec.to_circuit()
print(qc)  # QutritCircuit(n_qutrit=1, ops=4)