AI 中文总结
qiskit-qudits是一款Qiskit扩展，通过将d级qudit编码为m=ceil(log₂ d)个量子比特实现模拟，支持2≤d≤16的精确模拟，其电路模型、门层级等经数值验证可用于qudit电路仿真。
AI 中文摘要
qiskit-qudits是一款Qiskit扩展，它通过将每个d级qudit编码为m = ceil(log₂ d)个量子比特来实现模拟。qudit门作为普通的Qiskit Gate和ControlledGate子类被暴露出来，而非酉门操作（测量、复位、屏障、态制备）则作为专用的Instruction子类，通过专用的apply()钩子进行调度；每个门都同时具有密勒编码酉（通过NumPy的数组协议实现）和量子比特级定义。由于d无需是2的幂，编码后的希尔伯特空间通常会大于逻辑希尔伯特空间；该库通过恒等填充约定解决这一问题，即每个门对编码空间的非物理部分执行恒等操作。当每个操作数维度均为2的幂时，门会分解为固定的、 transpiler可识别的标准量子比特门级联；否则该库会回退到精确密勒酉合成，因此支持2 ≤ d ≤ 16的精确模拟，而不仅仅是2的幂。本文介绍了该软件的电路模型、门层级、分解策略以及测量/解码机制，阐明了其局限性，并通过数值方式验证了实现：针对2的幂和非2的幂d的离散傅里叶变换验证qudit量子傅里叶变换，扩展了仅能对d = 2^m运行的基础理论论文的验证；以及整个门集合中每个门的发射分解与其密勒酉的对比验证。
英文摘要
qiskit-qudits is a Qiskit extension that simulates d-level qudits by encoding each one into m = ceil(log_2 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.
