Qudit Quantum Programming with Projective Cliffords
<|reference_start|>Qudit Quantum Programming with Projective Cliffords: This paper introduces a novel abstraction for programming quantum operations, specifically projective Cliffords, as functions over the qudit Pauli group. We define a categorical semantics for projective Cliffords based on Pauli encodings in terms of $\mathbb{Z}_d$-linear maps. We then introduce a type system and lambda calculus for both $\mathbb{Z}_d$-linear maps and projective Cliffords, and prove that these type systems have a sound denotational semantics in terms of the relevant categories. Finally, we explore what it means to program with projective Cliffords through a number of examples and programming constructions.<|reference_end|>
@article{paykin2024qudit,
    title={Qudit Quantum Programming with Projective Cliffords},
    author={Jennifer Paykin and Sam Winnick},
    journal={arXiv preprint arXiv:2407.16801},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.16801},
    primaryClass={quant-ph cs.PL}
}