Universal quantum computation with group surface codes

• URL: http://arxiv.org/abs/2603.05502v1
• Date: Thu, 05 Mar 2026 18:59:27 GMT
• Title: Universal quantum computation with group surface codes
• Authors: Naren Manjunath, Vieri Mattei, Apoorv Tiwari, Tyler D. Ellison,
• Abstract summary: Group surface codes are equivalent to quantum double models of finite groups with specific conditions.<n>We show that group codes can be leveraged to perform non-Clifford gates in $mathbbZ$ surface codes.<n>For suitably chosen groups, we demonstrate that arbitrary classical surface gates can be implemented reversiblely in the group surface code.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce group surface codes, which are a natural generalization of the $\mathbb{Z}_2$ surface code, and equivalent to quantum double models of finite groups with specific boundary conditions. We show that group surface codes can be leveraged to perform non-Clifford gates in $\mathbb{Z}_2$ surface codes, thus enabling universal computation with well-established means of performing logical Clifford gates. Moreover, for suitably chosen groups, we demonstrate that arbitrary reversible classical gates can be implemented transversally in the group surface code. We present the logical operations in terms of a set of elementary logical operations, which include transversal logical gates, a means of transferring encoded information into and out of group surface codes, and preparation and readout. By composing these elementary operations, we implement a wide variety of logical gates and provide a unified perspective on recent constructions in the literature for sliding group surface codes and preparing magic states. We furthermore use tensor networks inspired by ZX-calculus to construct spacetime implementations of the elementary operations. This spacetime perspective also allows us to establish explicit correspondences with topological gauge theories. Our work extends recent efforts in performing universal quantum computation in topological orders without the braiding of anyons, and shows how certain group surface codes allow us to bypass the restrictions set by the Bravyi-K{ö}nig theorem, which limits the computational power of topological Pauli stabilizer models.

Related papers

• Do It for HER: First-Order Temporal Logic Reward Specification in Reinforcement Learning (Extended Version) [49.462399222747024]
  We propose a novel framework for the logical specification of non-Markovian rewards in Decision Processes (MDPs) with large state spaces.<n>Our approach leverages Linear Temporal Logic Modulo Theories over finite traces (LTLfMT)<n>We introduce a method based on reward machines and Hindsight Experience Replay (HER) to translate first-order logic specifications and address reward sparsity.
  arXiv  Detail & Related papers  (2026-02-05T22:11:28Z)
• Untangling Surface Codes: Bridging Braids and Lattice Surgery [51.748182660642776]
  We present a systematic method for translating fault-tolerant quantum circuits between their braiding and lattice surgery representations within the surface code.<n>Our framework provides a foundation for the automated verification, compilation, and benchmarking of large-scale surface code computations.
  arXiv  Detail & Related papers  (2025-11-27T10:12:38Z)
• Note on Logical Gates by Gauge Field Formalism of Quantum Error Correction [0.0]
  We show that logical gates can be expressed as exponential qubits of the electric and magnetic gauge fields.<n>Our results offer new insights into the interplay between quantum error correction, topology, and quantum field theory.
  arXiv  Detail & Related papers  (2025-11-19T08:23:50Z)
• Anyon Theory and Topological Frustration of High-Efficiency Quantum Low-Density Parity-Check Codes [12.383649662360302]
  Quantum low-density parity-check (QLDPC) codes offer a promising path to low-overhead fault-tolerant quantum computation.<n>Our Letter provides a rigorous theoretical basis for exploring the fault tolerance of QLDPC codes.
  arXiv  Detail & Related papers  (2025-03-06T18:46:14Z)
• Generating logical magic states with the aid of non-Abelian topological order [0.0]
  In fault-tolerant quantum computing, non-Clifford gates are crucial for universal computation.<n>We propose a new protocol that combines magic state preparation and code transformation to realize logical non-Clifford operations.
  arXiv  Detail & Related papers  (2025-02-03T02:38:32Z)
• Geometric structure and transversal logic of quantum Reed-Muller codes [51.11215560140181]
  In this paper, we aim to characterize the gates of quantum Reed-Muller (RM) codes by exploiting the well-studied properties of their classical counterparts. A set of stabilizer generators for a RM code can be described via $X$ and $Z$ operators acting on subcubes of particular dimensions.
  arXiv  Detail & Related papers  (2024-10-10T04:07:24Z)
• Fiber Bundle Fault Tolerance of GKP Codes [0.0]
  We investigate multi-mode GKP quantum error-correcting codes from a geometric perspective.<n>First, we construct their moduli space as a quotient of groups and exhibit it as a fiber bundle over the moduli space of symplectically integral lattices.<n>We then establish the Gottesman--Zhang conjecture for logical GKP Clifford operations, showing that all such gates arise from parallel transport with respect to a flat connection on this space.
  arXiv  Detail & Related papers  (2024-10-09T18:00:07Z)
• Logical blocks for fault-tolerant topological quantum computation [55.41644538483948]
  We present a framework for universal fault-tolerant logic motivated by the need for platform-independent logical gate definitions. We explore novel schemes for universal logic that improve resource overheads. Motivated by the favorable logical error rates for boundaryless computation, we introduce a novel computational scheme.
  arXiv  Detail & Related papers  (2021-12-22T19:00:03Z)
• 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)
• Finite-Function-Encoding Quantum States [52.77024349608834]
  We introduce finite-function-encoding (FFE) states which encode arbitrary $d$-valued logic functions. We investigate some of their structural properties.
  arXiv  Detail & Related papers  (2020-12-01T13:53:23Z)

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.