QuickQudits: A Framework for Efficient Simulation of Noisy Qudit Clifford Circuits via an Extended Stabilizer Tableau Formalism

TL;DR

QuickQudits introduces an efficient classical simulation framework for noisy Clifford circuits on qudits of arbitrary dimension, extending stabilizer tableau formalism to handle noise, composite dimensions, and measurement, with practical tools and visualizations.

Contribution

It develops a comprehensive stabilizer tableau-based simulation method for qudits of any dimension, including noise modeling and efficient fidelity estimation, with open-source implementation.

Findings

Efficient simulation of noisy qudit Clifford circuits achieved.

Generalized tableau formalism handles composite dimensions.

Noise can be consolidated into a single phase update for fidelity estimation.

Abstract

We present a comprehensive and self-contained framework for the efficient classical simulation of Clifford circuits acting on $d$-dimensional qudits, including realistic Pauli/Weyl noise via stochastic simulation. Our approach uses the stabilizer tableau formalism for qudits of arbitrary dimension and tracks both stabilizer and destabilizer generators under Clifford updates. The classical simulation remains efficient with simple algebraic Clifford update rules over $\mathbb{Z}_d$. Computational basis measurements in prime dimensions are handled by a generalized Aaronson-Gottesman (CHP) procedure. In composite dimensions, $\mathbb{Z}_d$ is not a field and the standard tableau reduction fails, so we employ an exact Smith normal form decomposition to enable efficient sampling. Noise is modelled as probabilistic mixtures of Weyl operators that act only on the tableau's phase column. For fast simulation of noisy circuits, we support Pauli frames, respectively generalized Weyl frames, and introduce a noise-pushing technique that allows all noise processes to be consolidated into a single phase update at the end of the circuit. Using this representation, circuit fidelity can be determined entirely by the single accumulated phase-shift parameter $\Delta \tau$, reducing fidelity estimation to a simple phase check per shot. Our codebase supports tableau simulation and conventional state-vector and density-matrix backends for qudits, and also includes circuit and tableau visualisations. Additionally, we provide tests and Jupyter notebooks for validation and illustration. This framework forms the basis for a scalable, open-source strong+weak stabilizer simulator including noise and can be found publicly available at https://github.com/QUICK-JKU/QuickQudits.