Achieving the limits of automorphism gates

arXiv:2609.19250 · quant-ph · Submitted 2026-09-16 · Read on arXiv

quant-ph

Submitted: 2026-09-16

Updated: 2026-09-16

Comments: 15 pages in the main text (5 figures, 1 table); 104 pages total (5 figures, 10 tables)

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• CSS Codes — 101× in this paper · explained in 2 episodes
• Hypergraph — 20× in this paper · explained in 2 episodes
• Core — 14× in this paper · explained in 2 episodes
• Addressability — 9× in this paper · explained in 1 episode
• Distillation — 3× in this paper · explained in 2 episodes
• Ancillary Qubits — 2× in this paper · explained in 1 episode
• Generalization — 2× in this paper · explained in 13 episodes
• Adam — 1× in this paper · explained in 2 episodes
• Alternation — 1× in this paper · explained in 1 episode
• Ancilla Qubits — 1× in this paper · explained in 1 episode
• Entanglement — 1× in this paper · explained in 3 episodes
• Fidelity — 1× in this paper · explained in 2 episodes
• No-Go Theorem — 1× in this paper · explained in 2 episodes
• Stabilizer States — 1× in this paper · explained in 2 episodes
• Structural Constraints — 1× in this paper · explained in 2 episodes
• Trace — 1× in this paper · explained in 2 episodes
• Unified Framework — 1× in this paper · explained in 5 episodes
• Verification — 1× in this paper · explained in 2 episodes

Sources

• Tour de gross: A modular quantum computer based on bivariate bicycle codes
• The Pinnacle Architecture: Reducing the cost of breaking RSA-2048 to 100 000 physical qubits using quantum LDPC codes
• Shor's algorithm is possible with as few as 10,000 reconfigurable atomic qubits
• Fault-Tolerant Quantum Computing with Trapped Ions: The Walking Cat Architecture
• Computing with many encoded logical qubits beyond break-even
• Magic state cultivation on a superconducting quantum processor
• Extractors: QLDPC Architectures for Efficient Pauli-Based Computation
• Single-Shot Universality in Quantum LDPC Codes via Code-Switching
• Quantum LDPC codes with design rate 1/5 and good performance below 1000 physical qubits
• Thermodynamic limitations on fault-tolerant quantum computing
• Automorphism gadgets in homological product codes
• Entangling logical qubits without physical operations
• Exhaustive Optimisation of Automorphism Groups for Stabiliser Codes
• Clifford gates with logical transversality for self-dual CSS codes
• A Classification of Transversal Clifford Gates for Qubit Stabilizer Codes
• Quantum Logic Codes: Complete Transversal Logical Clifford Instruction Sets for High-Rate Stabilizer Quantum Error Correcting Codes
• Constraints on phantom codes from automorphism group bounds
• Stabilizer Codes and Quantum Error Correction
• Cored product codes for quantum self-correction in three dimensions
• Low-Overhead Surface Code with Delayed Atom-Loss Detection via Pauli Envelope

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