Clifford-deformed zero-rate LDPC codes with 50% biased noise thresholds

• URL: http://arxiv.org/abs/2605.15348v1
• Date: Thu, 14 May 2026 19:18:25 GMT
• Title: Clifford-deformed zero-rate LDPC codes with 50% biased noise thresholds
• Abstract summary: We study Clifford deformations of the tile codes of Ref. [1], and present numerical evidence for improved performance at finite bias and under circuit-level noise.<n>We estimate this residual bias for different qubit platforms by modeling microscopic implementations of tile-code syndrome extraction.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Applying single-qubit Clifford unitaries to a Pauli stabilizer code produces a Clifford-deformed variant whose stabilizers remain Pauli operators, but with locally rotated Pauli axes. Such deformations provide a simple way to tailor a fixed code to anisotropic noise, and have enabled unusually high thresholds under strongly biased dephasing. In this work, we discuss zero-rate quantum low-density parity-check (LDPC) codes, for which there exist Clifford-deformed variants where the number of biased logical operators scales slower than the distance, or there exists a basis of logical operators whose overlap satisfies certain scaling conditions; in this case, the code-capacity threshold for the Clifford-deformed variant under i.i.d. pure dephasing noise approaches 50%. This property provably explains previously known code examples with 50% biased noise thresholds, such as XY surface code, XZZX surface code, color code, as well as some 3D Clifford-deformed codes. As a concrete new example, we study Clifford deformations of the tile codes of Ref. [1]. Similar to the phase diagram of 50% thresholds for random Clifford deformations of the surface code in Ref. [2], we find a similar phase diagram for the tile codes. We also construct several translationally invariant deformations of the tile code with 50% thresholds, and present numerical evidence for improved performance at finite bias and under circuit-level noise. In the circuit-level setting, performance is governed by the residual bias after a full syndrome-extraction cycle, linking our simulations to phenomenological models commonly used to study Clifford-deformed codes. We estimate this residual bias for different qubit platforms by modeling microscopic implementations of tile-code syndrome extraction.

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