Covariant Approximate Quantum Codes for Protected Analog Computation

• URL: http://arxiv.org/abs/2607.07607v1
• Date: Wed, 08 Jul 2026 16:25:25 GMT
• Title: Covariant Approximate Quantum Codes for Protected Analog Computation
• Abstract summary: Eastin-Knill theorem forbids exact codes with continuous symmetries.<n>We construct explicit $SU(d)$-covariant approximate codes that exploit permutation symmetry.<n>These results provide explicit non-Abelian covariant codes and a framework for robust analog quantum simulation.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum error correction compatible with continuous symmetries is a fundamental problem in quantum information and a possible route to robust analog quantum simulation. Because the Eastin-Knill theorem forbids exact codes with continuous transversal symmetries, we construct explicit $SU(d)$-covariant approximate codes that exploit permutation symmetry to spread logical information uniformly across all physical subsystems. For one-, two-, and three-qudit erasures at known locations, we prove worst-case purified-distance scaling $Θ(1/N)$, matching approximate Eastin-Knill lower bounds up to constants, and we extend the reduced-state analysis to general flagged local noise. For single-qudit erasure, we construct an explicit near-optimal decoder from the Petz recovery map. We then use these codes as building blocks for encoded analog dynamics. Symmetry-preserving Hamiltonians generate block-structured dynamical Lie algebras implementable transversally, while controlled symmetry-breaking terms serve as non-transversal resources for universal dynamics. These results provide explicit non-Abelian covariant codes and a framework for robust analog quantum simulation.

Related papers

• Symmetry Constrained Quantum Error Mitigation for the Schwinger Model [39.146761527401424]
  We exploit the parity and fermion-number symmetries of a gauge theory under depolarising noise.<n>We investigate symmetry verification under digital quantum simulation.
  arXiv  Detail & Related papers  (2026-08-21T13:49:11Z)
• Spin-coherent quantum designs [0.0]
  We show that the canonical finite coherent-state formula reconstructs every operator in the rank-$S$ sector exactly if and only if the sampling points form a spherical $(2J+S)$-design.<n>We derive practical protocols for estimating moments of spin operators from these constructions, with direct applications to polarimetry, magnetometry, and quantum state tomography.
  arXiv  Detail & Related papers  (2026-08-11T18:00:06Z)
• Decoded Quantum Interferometry Beyond Hamming: Rank-Metric and Translation Association Schemes [39.146761527401424]
  Decoded Quantum Interferometry (DQI) uses coherent decoding and a quantum Fourier transform to find high-quality solutions of structured optimisation problems.<n>We extend the core DQI mechanism beyond Hamming space to finite geometries with translation symmetry.<n>We find solutions with an effective-rank proxy near min(m,n)-l, and the corresponding expected score can be converted into a constant-probability bound on the residual rank of a sample.
  arXiv  Detail & Related papers  (2026-06-03T13:12:15Z)
• Fault-Tolerant Resource Comparison of Qudit and Qubit Encodings for Diagonal Quadratic Operators [36.94429692322632]
  Finite local Hilbert-space truncations arise naturally in quantum simulations of lattice field theories and motivate qudit encodings.<n>We compare the non-Clifford cost of implementing diagonal evolutions, exemplified by $U=e-it_x2$ in a uniform field-amplitude discretization of a real scalar field, using either one logical $d$-level qudit or $n_b=eil log drceil$ logical qubits.
  arXiv  Detail & Related papers  (2026-04-29T15:25:08Z)
• Explicit Block Encodings of Discrete Laplacians with Mixed Boundary Conditions [45.88028371034407]
  Block encoding provides the standard method for accessing matrix data within quantum circuits.<n>We present a unified framework for efficiently block encoding finite-difference discretizations of the Laplacian.
  arXiv  Detail & Related papers  (2026-03-12T19:35:16Z)
• Profusion of Symmetry-Protected Qubits from Stable Ergodicity Breaking [0.0]
  We show how combining a discrete symmetry with topological space fragmentation can give rise to exponentially many topologically stable qubits protected by a single discrete symmetry.<n>We also comment on the combination of symmetry enrichment and topological fragmentation more generally, and the implications for use of systems exhibiting Hilbert space fragmentation as quantum memories.
  arXiv  Detail & Related papers  (2025-12-23T14:30:06Z)
• Explicit Quantum Circuits for Simulating Linear Differential Equations via Dilation [0.0]
  We present a concrete pipeline that connects the dilation formalism with explicit quantum circuit constructions.<n>On the analytical side, we introduce a discretization of the continuous dilation operator that is tailored for quantum implementation.<n>We prove that the resulting scheme achieves a global error bound of order $O(M-3/2)$, up to exponentially small boundary effects.
  arXiv  Detail & Related papers  (2025-09-20T18:54:49Z)
• Fault Tolerant Quantum Simulation via Symplectic Transvections [3.4137115855910762]
  We propose a framework that enables the execution of entire logical circuit blocks at once, preserving their global structure.<n>This whole-block approach allows for the direct implementation of logical Trotter circuits on any stabilizer code.<n>At the heart of our approach lies a deep structural correspondence between symplectic transvections and Trotter circuits.
  arXiv  Detail & Related papers  (2025-04-15T17:56:07Z)
• Predicting symmetries of quantum dynamics with optimal samples [41.42817348756889]
  Identifying symmetries in quantum dynamics is a crucial challenge with profound implications for quantum technologies.<n>We introduce a unified framework combining group representation theory and subgroup hypothesis testing to predict these symmetries with optimal efficiency.<n>We prove that parallel strategies achieve the same performance as adaptive or indefinite-causal-order protocols.
  arXiv  Detail & Related papers  (2025-02-03T15:57:50Z)
• Covariant Quantum Error-Correcting Codes with Metrological Entanglement Advantage [1.6018724979340826]
  We show that a subset of the basis for the irreducible representations of a tensor-product SU(2) forms an approximate quantum error-correcting code with U(1) logical gates.<n>We demonstrate that this family of codes protects a probe state with quantum information surpassing the standard quantum limit when the sensing parameter couples to the generator of the U(1) logical gate.
  arXiv  Detail & Related papers  (2024-09-30T17:59:01Z)
• General quantum algorithms for Hamiltonian simulation with applications to a non-Abelian lattice gauge theory [44.99833362998488]
  We introduce quantum algorithms that can efficiently simulate certain classes of interactions consisting of correlated changes in multiple quantum numbers. The lattice gauge theory studied is the SU(2) gauge theory in 1+1 dimensions coupled to one flavor of staggered fermions. The algorithms are shown to be applicable to higher-dimensional theories as well as to other Abelian and non-Abelian gauge theories.
  arXiv  Detail & Related papers  (2022-12-28T18:56:25Z)
• Near-optimal covariant quantum error-correcting codes from random unitaries with symmetries [1.2183405753834557]
  We analytically study the most essential cases of $U(1)$ and $SU(d)$ symmetries. We show that for both symmetry groups the error of the covariant codes generated by Haar-random symmetric unitaries, typically scale as $O(n-1)$ in terms of both the average- and worst-case distances against erasure noise.
  arXiv  Detail & Related papers  (2021-12-02T18:46:34Z)

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.