Qudit Quantum Programming with Projective Cliffords

2024/07/23 by Paykin, Jennifer, Winnick, Sam · 1 citation
#FOS: Computer and information sciences #FOS: Physical sciences #Programming Languages (cs.PL) #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2407.16801

Abstract

This paper introduces a novel abstraction for programming quantum operations, specifically projective Cliffords, as functions over the qudit Pauli group. Generalizing the idea behind Pauli tableaux, we introduce a type system and lambda calculus for projective Cliffords called LambdaPC, which captures well-formed Clifford operations via a Curry-Howard correspondence with a particular encoding of the Clifford and Pauli groups. Importantly, the language captures not just qubit operations, but qudit operations for any dimension d. Throughout the paper we explore what it means to program with projective Cliffords through a number of examples and a case study focusing on stabilizer error correcting codes.

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• Denotational semantics for stabiliser quantum programs

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