Majorana-XYZ subsystem code

• URL: http://arxiv.org/abs/2603.26311v1
• Date: Fri, 27 Mar 2026 11:30:07 GMT
• Title: Majorana-XYZ subsystem code
• Abstract summary: We present a new type of a quantum error correction code, termed Majorana-XYZ code.<n>It is a $[n,k,g,d]$ subsystem code with $n=L2$ physical qubits, $k= lfloor L/2 rfloor$ logical qubits, $g sim L2$ gauge qubits, and distance $d = L$.<n>The code detects every 1- and 2-qubit error, and every error of weight 3 and higher (constrained by the distance) that is not a product of the 3-qubit
• Score: 0.0
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: We present a new type of a quantum error correction code, termed Majorana-XYZ code, where the logical quantum information scales macroscopically yet is protected by topologically non-trivial degrees of freedom. It is a $[n,k,g,d]$ subsystem code with $n=L^2$ physical qubits, $k= \lfloor L/2 \rfloor$ logical qubits, $g \sim L^2$ gauge qubits, and distance $d = L$. The physical check operations, i.e. the measurements needed to obtain the error syndrome, are $3$-local and nearest-neighbour. The code detects every 1- and 2-qubit error, and every error of weight 3 and higher (constrained by the distance) that is not a product of the 3-qubit check operations, however, these products act only on the gauge qubits leaving the code space invariant. The undetected weight-3 and higher operators are confined to the gauge group and do not affect logical information. While the code does not have local stabiliser generators, the logical qubits cannot be modified locally by an undetectable error, and in this sense the Majorana-XYZ code combines notions of both topological and local gauge codes while providing a macroscopic number of topological logical qubits. Taken as a non-gauge stabiliser code we can encode $k \sim L^2 - 3L$ logical qubits into $L^2$ physical qubits; however, the check operators then become weight $2L$. The code is derived from an experimentally promising system of Majorana fermions on the honeycomb lattice with only nearest-neighbour interactions.

Related papers

• A polynomial-time approximation scheme for minimum-weight decoding of topological codes [42.44256445495892]
  Two-dimensional topological translationally in (2D TTI) stabilizer codes lie at the heart of fault-tolerant quantum computation.<n>Minimum-weight decoding of these codes was recently shown to be NP-hard, even in basic settings.
  arXiv  Detail & Related papers  (2026-06-16T16:44:08Z)
• Parallel Logical Measurements via Quantum Code Surgery [42.95092131256421]
  Quantum code surgery is a flexible and low overhead technique for performing logical measurements on quantum error-correcting codes.<n>We present a code surgery scheme, applicable to any qubit stabiliser low-density parity check (LDPC) code, that fault-tolerantly measures many logical Pauli operators in parallel.
  arXiv  Detail & Related papers  (2025-03-06T22:05:52Z)
• Demonstrating dynamic surface codes [118.67046728951689]
  We experimentally demonstrate three time-dynamic implementations of the surface code.<n>First, we embed the surface code on a hexagonal lattice, reducing the necessary couplings per qubit from four to three.<n>Second, we walk a surface code, swapping the role of data and measure qubits each round, achieving error correction with built-in removal of accumulated non-computational errors.<n>Third, we realize the surface code using iSWAP gates instead of the traditional CNOT, extending the set of viable gates for error correction without additional overhead.
  arXiv  Detail & Related papers  (2024-12-18T21:56:50Z)
• Quantum error correction below the surface code threshold [107.92016014248976]
  Quantum error correction provides a path to reach practical quantum computing by combining multiple physical qubits into a logical qubit. We present two surface code memories operating below a critical threshold: a distance-7 code and a distance-5 code integrated with a real-time decoder. Our results present device performance that, if scaled, could realize the operational requirements of large scale fault-tolerant quantum algorithms.
  arXiv  Detail & Related papers  (2024-08-24T23:08:50Z)
• SSIP: automated surgery with quantum LDPC codes [55.2480439325792]
  We present Safe Surgery by Identifying Pushouts (SSIP), an open-source lightweight Python package for automating surgery between qubit CSS codes. Under the hood, it performs linear algebra over $mathbbF$ governed by universal constructions in the category of chain complexes. We show that various logical measurements can be performed cheaply by surgery without sacrificing the high code distance.
  arXiv  Detail & Related papers  (2024-07-12T16:50:01Z)
• How much entanglement is needed for quantum error correction? [10.61261983484739]
  It is commonly believed that logical states of quantum error-correcting codes have to be highly entangled.<n>We show that the validity of this belief depends on the specific code and the choice of entanglement measure.
  arXiv  Detail & Related papers  (2024-05-02T14:35:55Z)
• Creating entangled logical qubits in the heavy-hex lattice with topological codes [0.0]
  In this work we show how this bug can be turned into a feature. We demonstrate entanglement between logical qubits with code distance up to $d = 4$. We verify the violation of Bell's inequality for both the $d=2$ case with post selection featuring a fidelity of $94%$.
  arXiv  Detail & Related papers  (2024-04-24T17:02:35Z)
• Fault-tolerant hyperbolic Floquet quantum error correcting codes [0.4527817188861902]
  We introduce a family of dynamically generated quantum error correcting codes that we call "hyperbolic Floquet codes"<n>One of our hyperbolic Floquet codes uses 400 physical qubits to encode 52 logical qubits with a code distance of 8, i.e., it is a $[[400,52,8]]$ code.<n>At small error rates, comparable logical error suppression to this code requires 5x as many physical qubits (1924) when using the honeycomb Floquet code with the same noise model and decoder.
  arXiv  Detail & Related papers  (2023-09-18T18:00:02Z)
• Homological Quantum Rotor Codes: Logical Qubits from Torsion [47.52324012811181]
  homological quantum rotor codes allow one to encode both logical rotors and logical qudits in the same block of code.<n>We show that the $0$-$pi$-qubit as well as Kitaev's current-mirror qubit are indeed small examples of such codes.
  arXiv  Detail & Related papers  (2023-03-24T00:29:15Z)
• Error-correcting codes for fermionic quantum simulation [4.199246521960609]
  We present methodologies for fermions via qubit systems on a two-dimensional lattice algorithm. We identify a family of stabilizer codes suitable for fermion simulation. Our method can increase the code distances without decreasing the (fermionic) code rate.
  arXiv  Detail & Related papers  (2022-10-16T01:43:07Z)
• Quantum Error Detection Without Using Ancilla Qubits [0.0]
  We describe and experimentally demonstrate an error detection scheme that does not employ ancilla qubits or mid-circuit measurements. This is achieved by expanding the Hilbert space where a single logical qubit is encoded using several physical qubits.
  arXiv  Detail & Related papers  (2022-04-23T17:51:02Z)

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.