qiskit-qudits: A Qiskit Extension for Simulating Qudit Circuits

qiskit-qudits is a Qiskit extension that simulates d-level qudits by encoding each one into m = ceillog₂ d qubits. Qudit gates are exposed as ordinary Qiskit Gate and ControlledGate subclasses, and operations that are not unitary gates (measurement, reset, barrier, state preparation) as dedicated Instruction subclasses dispatched through a dedicated apply() hook; every gate carries both a dense encoded unitary (via NumPy's array protocol) and a qubit-level definition. Because d need not be a power of two, the encoded Hilbert space is generally larger than the logical one; the library resolves this by the identity-padding convention, in which every gate acts as the identity on the unphysical part of the encoded space. When every operand dimension is a power of two, gates decompose into a fixed, transpiler-recognisable cascade of standard qubit gates; otherwise the library falls back to exact dense unitary synthesis, so that dimensions 2 <= d <= 16 are supported exactly, not only powers of two. This paper describes the software's circuit model, gate hierarchy, decomposition strategy, and measurement/decoding machinery, states its limitations, and verifies the implementation numerically: the qudit QFT against the discrete Fourier transform for both power-of-two and non-power-of-two d, extending the check of the underlying theory paper, which could only be run for d = 2^m, and every gate's emitted decomposition against its dense unitary across the whole gate set.