For PEPS with strong injectivity above a threshold, belief propagation finds fixed points efficiently and cluster-corrected BP approximates observables to 1/poly(N) error in poly(N) time, with local perturbations affecting the fixed point only locally.
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Radial codes from lifted products of quasi-cyclic codes give [[2r²s, 2(r-1)², ≤2s]] quantum LDPC codes whose simulations show comparable circuit-level performance to surface codes at roughly 1/5 the qubit count with single-shot decoding.
Clifford-deformed zero-rate LDPC codes achieve code-capacity thresholds approaching 50% under i.i.d. pure dephasing when the number of biased logical operators scales slower than distance or overlaps satisfy stated conditions, with new examples from tile codes.
citing papers explorer
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Algorithmic Locality via Provable Convergence in Quantum Tensor Networks
For PEPS with strong injectivity above a threshold, belief propagation finds fixed points efficiently and cluster-corrected BP approximates observables to 1/poly(N) error in poly(N) time, with local perturbations affecting the fixed point only locally.
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High-threshold, low-overhead and single-shot decodable fault-tolerant quantum memory
Radial codes from lifted products of quasi-cyclic codes give [[2r²s, 2(r-1)², ≤2s]] quantum LDPC codes whose simulations show comparable circuit-level performance to surface codes at roughly 1/5 the qubit count with single-shot decoding.
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Clifford-deformed zero-rate LDPC codes with 50% biased noise thresholds
Clifford-deformed zero-rate LDPC codes achieve code-capacity thresholds approaching 50% under i.i.d. pure dephasing when the number of biased logical operators scales slower than distance or overlaps satisfy stated conditions, with new examples from tile codes.