Gauss law codes identify the full gauge-invariant sector as the code space while vacuum codes restrict to the matter vacuum, with the two shown to be unitarily equivalent for finite gauge groups.
Good Quantum Error-Correcting Codes Exist
4 Pith papers cite this work. Polarity classification is still indexing.
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abstract
A quantum error-correcting code is defined to be a unitary mapping (encoding) of k qubits (2-state quantum systems) into a subspace of the quantum state space of n qubits such that if any t of the qubits undergo arbitrary decoherence, not necessarily independently, the resulting n qubits can be used to faithfully reconstruct the original quantum state of the k encoded qubits. Quantum error-correcting codes are shown to exist with asymptotic rate k/n = 1 - 2H(2t/n) where H(p) is the binary entropy function -p log p - (1-p) log (1-p). Upper bounds on this asymptotic rate are given.
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A homological framework identifies necessary and sufficient obstruction conditions for transversal logical diagonal gates in quantum CSS codes.
List decoding of entanglement-free quantum polar codes yields logical error rates competitive with surface codes and LDPC codes of similar size, with class-probability approximation providing further improvement.
Postselection on erasure qubits fully mitigates erasure noise in QFT for erasure-check error rates below 3% and enables dual-rail systems to exceed noise floors unreachable by single-rail at kiloquop scale.
citing papers explorer
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Gauss law codes and vacuum codes from lattice gauge theories
Gauss law codes identify the full gauge-invariant sector as the code space while vacuum codes restrict to the matter vacuum, with the two shown to be unitarily equivalent for finite gauge groups.
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Homological origin of transversal implementability of logical diagonal gates in quantum CSS codes
A homological framework identifies necessary and sufficient obstruction conditions for transversal logical diagonal gates in quantum CSS codes.
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Improved Logical Error Rate via List Decoding of Quantum Polar Codes
List decoding of entanglement-free quantum polar codes yields logical error rates competitive with surface codes and LDPC codes of similar size, with class-probability approximation providing further improvement.
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The limits of erasure-based postselection for quantum error mitigation
Postselection on erasure qubits fully mitigates erasure noise in QFT for erasure-check error rates below 3% and enables dual-rail systems to exceed noise floors unreachable by single-rail at kiloquop scale.