Qudit Quantum Programming with Projective Cliffords

• URL: http://arxiv.org/abs/2407.16801v2
• Date: Sun, 06 Jul 2025 18:59:49 GMT
• Title: Qudit Quantum Programming with Projective Cliffords
• Authors: Jennifer Paykin, Sam Winnick,
• Abstract summary: This paper introduces a novel abstraction for programming quantum operations, specifically projective Cliffords, as functions over the Pauli group.<n>LambdaPC captures well-formed Clifford operations via a Curry-Howard correspondence with a particular encoding of the Clifford and Pauli groups.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

Related papers

• Clifford and Non-Clifford Splitting in Quantum Circuits: Applications and ZX-Calculus Detection Procedure [49.1574468325115]
  We propose and analyze use cases that come from quantum circuits that can be written as product between a Clifford and a Non-Clifford unitary. We make use of ZX-Calculus and its assets to detect a limiting border of these circuits that would allow for a separation between a Clifford section and a Non-Clifford section.
  arXiv  Detail & Related papers  (2025-04-22T16:10:34Z)
• A complete theory of the Clifford commutant [0.2796197251957244]
  The Clifford group plays a central role in quantum information science.<n>It is the building block for many error-correcting schemes and matches the first three moments of the Haar measure over the unitary group.<n>At the heart of understanding many properties of the Clifford group lies the Clifford commutant.
  arXiv  Detail & Related papers  (2025-04-16T17:21:34Z)
• An Efficient Quantum Classifier Based on Hamiltonian Representations [50.467930253994155]
  Quantum machine learning (QML) is a discipline that seeks to transfer the advantages of quantum computing to data-driven tasks.<n>We propose an efficient approach that circumvents the costs associated with data encoding by mapping inputs to a finite set of Pauli strings.<n>We evaluate our approach on text and image classification tasks, against well-established classical and quantum models.
  arXiv  Detail & Related papers  (2025-04-13T11:49:53Z)
• Targeted Clifford logical gates for hypergraph product codes [61.269295538188636]
  We construct explicit targeted logical gates for hypergraph product codes. As a concrete example, we give logical circuits for the $[[18,2,3]]$ toric code.
  arXiv  Detail & Related papers  (2024-11-26T02:32:44Z)
• Condensed Encodings of Projective Clifford Operations in Arbitrary Dimension [0.0]
  We provide a careful analysis of the structure theorem for the $n$-qudit projective Clifford group and various encoding schemes for its elements. Our results apply to all integers $dgeq2$, most notably the even case.
  arXiv  Detail & Related papers  (2024-07-23T22:04:10Z)
• Hybrid Quantum-Classical Machine Learning with String Diagrams [49.1574468325115]
  This paper develops a formal framework for describing hybrid algorithms in terms of string diagrams. A notable feature of our string diagrams is the use of functor boxes, which correspond to a quantum-classical interfaces.
  arXiv  Detail & Related papers  (2024-07-04T06:37:16Z)
• Equivalence Classes of Quantum Error-Correcting Codes [49.436750507696225]
  Quantum error-correcting codes (QECC's) are needed to combat the inherent noise affecting quantum processes. We represent QECC's in a form called a ZX diagram, consisting of a tensor network.
  arXiv  Detail & Related papers  (2024-06-17T20:48:43Z)
• Geometry of degenerate quantum states, configurations of $m$-planes and invariants on complex Grassmannians [55.2480439325792]
  We show how to reduce the geometry of degenerate states to the non-abelian connection $A$. We find independent invariants associated with each triple of subspaces. Some of them generalize the Berry-Pancharatnam phase, and some do not have analogues for 1-dimensional subspaces.
  arXiv  Detail & Related papers  (2024-04-04T06:39:28Z)
• The Clifford theory of the $n$-qubit Clifford group [0.0]
  Recent applications have made use of the representation theory of the Clifford group. We find an unexpected correspondence between irreducible characters of the $n$-qubit Clifford group and those of the $(n+1)$-qubit Clifford group.
  arXiv  Detail & Related papers  (2023-07-11T21:21:31Z)
• Homotopy Classification of loops of Clifford unitaries [0.0]
  We study Clifford quantum circuits acting on $mathsfd$-dimensional lattices of prime $p$-dimensional qudits. We calculate homotopy classes of such loops for any odd $p$ and $mathsfd=0,1,2,3$, and $4$. We observe that the homotopy classes of loops of Clifford circuits in $(mathsfd+1)$-dimensions coincide with the quotient of the group of Clifford Quantum Cellular Automata modulo shallow circuits and lattice translations in $mathsfd$-dimensions
  arXiv  Detail & Related papers  (2023-06-16T15:31:34Z)
• A graph-state based synthesis framework for Clifford isometries [2.048226951354646]
  We tackle the problem of synthesizing a Clifford isometry into an executable quantum circuit. We propose a simple framework for synthesis that exploits the elementary properties of the Clifford group and one equation of the symplectic group. We also propose practical synthesis algorithms for Clifford isometries with a focus on Clifford operators, graph states and codiagonalization of Pauli rotations.
  arXiv  Detail & Related papers  (2022-12-13T22:50:24Z)
• TQFTs and quantum computing [0.0]
  Quantum computing is captured in the formalism of the monoidal subcategory of $textbfVect_mathbb C$. We formalize this connection by equipping cobordisms with machinery for producing linear maps by parallel transport. We realize quantum circuits as images of cobordisms under monoidal double functors.
  arXiv  Detail & Related papers  (2022-10-07T13:41:43Z)
• Quantum teleportation in the commuting operator framework [63.69764116066747]
  We present unbiased teleportation schemes for relative commutants $N'cap M$ of a large class of finite-index inclusions $Nsubseteq M$ of tracial von Neumann algebras. We show that any tight teleportation scheme for $N$ necessarily arises from an orthonormal unitary Pimsner-Popa basis of $M_n(mathbbC)$ over $N'$.
  arXiv  Detail & Related papers  (2022-08-02T00:20:46Z)
• Tangelo: An Open-source Python Package for End-to-end Chemistry Workflows on Quantum Computers [85.21205677945196]
  Tangelo is an open-source Python software package for the development of end-to-end chemistry on quantum computers. It aims to support the design of successful experiments on quantum hardware, and to facilitate advances in quantum algorithm development.
  arXiv  Detail & Related papers  (2022-06-24T17:44:00Z)
• Qudit lattice surgery [91.3755431537592]
  We observe that lattice surgery, a model of fault-tolerant qubit computation, generalises straightforwardly to arbitrary finite-dimensional qudits. We relate the model to the ZX-calculus, a diagrammatic language based on Hopf-Frobenius algebras.
  arXiv  Detail & Related papers  (2022-04-27T23:41:04Z)
• Gottesman Types for Quantum Programs [0.0]
  We show that Gottesman's semantics for quantum programs can be treated as a type system. We also show that it can be extended beyond the Clifford set to partially characterize a broad range of programs.
  arXiv  Detail & Related papers  (2021-09-06T01:02:01Z)
• Finding the disjointness of stabilizer codes is NP-complete [77.34726150561087]
  We show that the problem of calculating the $c-disjointness, or even approximating it to within a constant multiplicative factor, is NP-complete. We provide bounds on the disjointness for various code families, including the CSS codes,$d codes and hypergraph codes. Our results indicate that finding fault-tolerant logical gates for generic quantum error-correcting codes is a computationally challenging task.
  arXiv  Detail & Related papers  (2021-08-10T15:00:20Z)
• Realization of arbitrary doubly-controlled quantum phase gates [62.997667081978825]
  We introduce a high-fidelity gate set inspired by a proposal for near-term quantum advantage in optimization problems. By orchestrating coherent, multi-level control over three transmon qutrits, we synthesize a family of deterministic, continuous-angle quantum phase gates acting in the natural three-qubit computational basis.
  arXiv  Detail & Related papers  (2021-08-03T17:49:09Z)
• Decomposition of Clifford Gates [3.7900158137749322]
  We provide a fast algorithm that decomposes any Clifford gate as a $textitminimal$ product of Clifford transvections. The algorithm can be directly used for finding all Pauli matrices that commute with any given Clifford gate.
  arXiv  Detail & Related papers  (2021-02-05T10:32:09Z)
• A Generic Compilation Strategy for the Unitary Coupled Cluster Ansatz [68.8204255655161]
  We describe a compilation strategy for Variational Quantum Eigensolver (VQE) algorithms. We use the Unitary Coupled Cluster (UCC) ansatz to reduce circuit depth and gate count.
  arXiv  Detail & Related papers  (2020-07-20T22:26:16Z)
• Hadamard-free circuits expose the structure of the Clifford group [9.480212602202517]
  The Clifford group plays a central role in quantum randomized benchmarking, quantum tomography, and error correction protocols. We show that any Clifford operator can be uniquely written in the canonical form $F_HSF$. A surprising connection is highlighted between random uniform Clifford operators and the Mallows distribution on the symmetric group.
  arXiv  Detail & Related papers  (2020-03-20T17:51:36Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.