Quantum Process Realization of LDPC Code Dualities and Product Constructions

arXiv:2603.13538 · quant-ph, cond-mat.str-el · Submitted 2026-03-13 · Read on arXiv

quant-ph, cond-mat.str-el

Submitted: 2026-03-13

Updated: 2026-09-26

Terminology

• Ancilla Qubits — 27× in this paper · explained in 1 episode
• Hilbert Space — 13× in this paper · explained in 2 episodes
• Effective Hamiltonian — 11× in this paper · explained in 2 episodes
• Quantum Circuits — 6× in this paper · explained in 2 episodes
• Generalization — 5× in this paper · explained in 13 episodes
• Redundancy — 4× in this paper · explained in 2 episodes
• Topological Order — 3× in this paper · explained in 2 episodes
• Unified Framework — 3× in this paper · explained in 5 episodes
• Anyons — 1× in this paper · explained in 2 episodes
• Consistency — 1× in this paper · explained in 3 episodes
• Entanglement — 1× in this paper · explained in 3 episodes
• Phase Transitions — 1× in this paper · explained in 2 episodes
• Robustness — 1× in this paper · explained in 5 episodes
• Symmetry Breaking — 1× in this paper · explained in 3 episodes

Sources

• Quantum Low-Density Parity-Check Codes
• Asymptotically Good Quantum and Locally Testable Classical LDPC Codes
• Quantum Tanner codes
• The Physics of (good) LDPC Codes I. Gauging and dualities
• The Physics of (good) LDPC Codes II. Product constructions
• String-net condensation: A physical mechanism for topological phases
• Non-invertible symmetries act locally by quantum operations
• Quantum operations for Kramers-Wannier duality
• Realizing triality and $p$-ality by lattice twisted gauging in (1+1)d quantum spin systems
• Kennedy-Tasaki transformation and non-invertible symmetry in lattice models beyond one dimension
• Hierarchy of topological order from finite-depth unitaries, measurement and feedforward
• Shortest Route to Non-Abelian Topological Order on a Quantum Processor
• Low-depth unitary quantum circuits for dualities in one-dimensional quantum lattice models
• Preparing Code States via Seed-Entangler-Enriched Sequential Quantum Circuits: Application to Tetra-Digit Topological Error-Correcting Codes
• Non-invertible symmetries and LSM-type constraints on a tensor product Hilbert space
• What's Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries
• Analogs of deconfined quantum criticality for non-invertible symmetry breaking in 1d
• Tensor networks for non-invertible symmetries in 3+1d and beyond
• Fracton Topological Order, Generalized Lattice Gauge Theory and Duality
• Foliated fracton order from gauging subsystem symmetries

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