Asymptotically Good Quantum Codes with Addressable and Transversal Non-Clifford Gates

• URL: http://arxiv.org/abs/2507.05392v1
• Date: Mon, 07 Jul 2025 18:24:40 GMT
• Title: Asymptotically Good Quantum Codes with Addressable and Transversal Non-Clifford Gates
• Authors: Zhiyang He, Vinod Vaikuntanathan, Adam Wills, Rachel Yun Zhang,
• Abstract summary: This paper builds a family of over qubits of good quantum codes supporting addressable non-Clifford gates.<n>More precisely, given any three logical qubits across one, two, or three code, the logical $mathsfCCZ$ gate can be executed on those three logical qubits via a depth-one physical circuit.
• Score: 8.194994143531677
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: Constructing quantum codes with good parameters and useful transversal gates is a central problem in quantum error correction. In this paper, we continue our work in arXiv:2502.01864 and construct the first family of asymptotically good quantum codes (over qubits) supporting transversally addressable non-Clifford gates. More precisely, given any three logical qubits across one, two, or three codeblocks, the logical $\mathsf{CCZ}$ gate can be executed on those three logical qubits via a depth-one physical circuit of $\mathsf{CCZ}$ gates. This construction is based on the transitive, iso-orthogonal algebraic geometry codes constructed by Stichtenoth (IEEE Trans. Inf. Theory, 2006). This improves upon our construction from arXiv:2502.01864, which also supports transversally addressable $\mathsf{CCZ}$ gates and has inverse-polylogarithmic rate and relative distance.

Related papers

• On the Addressability Problem on CSS Codes [0.6445605125467574]
  We show that CSS codes with non-zero rate cannot address a logical H, HP, PH, nor CNOT to any non-empty strict subset of logical qubits.<n>We can show a similar no-go result for CNOTs and CZs between two such high-rate codes.<n>This work pioneers the study of distance-preserving addressability in quantum codes, mainly by considering automorphisms of the code.
  arXiv  Detail & Related papers  (2025-02-19T17:18:52Z)
• Quantum Codes with Addressable and Transversal Non-Clifford Gates [8.194994143531677]
  We study codes that support gates which induce $textitaddressable$ logical gates.<n>We develop a formalism for constructing quantum codes with $textitaddressable and $ell neq 2$ gates.
  arXiv  Detail & Related papers  (2025-02-03T22:24:34Z)
• Classifying Logical Gates in Quantum Codes via Cohomology Operations and Symmetry [0.0]
  We construct and classify fault-tolerant logical gates implemented by constant-depth circuits for quantum codes.<n>We present a formalism for addressable and parallel logical gates in LDPC codes viasymmetries.<n>As a byproduct, we find new topological responses of finite higher-form symmetries using higher Pontryagin powers.
  arXiv  Detail & Related papers  (2024-11-24T14:01:37Z)
• 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)
• Error-corrected Hadamard gate simulated at the circuit level [42.002147097239444]
  We simulate the logical Hadamard gate in the surface code under a circuit-level noise model. Our paper is the first to do this for a unitary gate on a quantum error-correction code.
  arXiv  Detail & Related papers  (2023-12-18T19:00:00Z)
• Non-Clifford and parallelizable fault-tolerant logical gates on constant and almost-constant rate homological quantum LDPC codes via higher symmetries [1.3194391758295114]
  We study fault-tolerant quantum computing for families of homological quantum low-density parity-check codes defined on 3-manifolds with constant or almost-constant encoding rate. We have developed a generic formalism to compute the triple intersection invariants for 3-manifolds.
  arXiv  Detail & Related papers  (2023-10-25T20:33:59Z)
• 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)
• Quantum process tomography of continuous-variable gates using coherent states [49.299443295581064]
  We demonstrate the use of coherent-state quantum process tomography (csQPT) for a bosonic-mode superconducting circuit. We show results for this method by characterizing a logical quantum gate constructed using displacement and SNAP operations on an encoded qubit.
  arXiv  Detail & Related papers  (2023-03-02T18:08:08Z)
• Universal qudit gate synthesis for transmons [44.22241766275732]
  We design a superconducting qudit-based quantum processor. We propose a universal gate set featuring a two-qudit cross-resonance entangling gate. We numerically demonstrate the synthesis of $rm SU(16)$ gates for noisy quantum hardware.
  arXiv  Detail & Related papers  (2022-12-08T18:59:53Z)
• A Quantum Algorithm for Computing All Diagnoses of a Switching Circuit [73.70667578066775]
  Faults are by nature while most man-made systems, and especially computers, work deterministically. This paper provides such a connecting via quantum information theory which is an intuitive approach as quantum physics obeys probability laws.
  arXiv  Detail & Related papers  (2022-09-08T17:55:30Z)
• 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)

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.