arXiv subjects

Ruipan Yang

Publications and source records attributed to Ruipan Yang.

4 recordsLinked to original sources

arXiv2026

Quantum bivariate bicycle codes with weight-8 checks surpassing the BB benchmark

Bivariate bicycle (BB) codes of Bravyi \emph{et al.}~\cite{Bravyi2024} are quantum low-density parity-check codes with weight-$6$ checks, exemplified by $[[144,12,12]]$ with $kd^2/n=12$. We develop the algebraic structure theory of BB-type codes with weight-$8$ checks (weight-$4$ generator polynomials) and use it, together with an exactly validated search pipeline, to construct and certify new codes. We prove an exact dimension formula $k=2\dim R/(A,B)$ (forcing even $k$), a $4\ell m$-element symmetry group on generator pairs, an $X/Z$ distance equality $d_X=d_Z$, and a family of subgroup-coset kernel vectors giving rigorous distance upper bounds and a design rule for high-distance constructions; all distances are computed exhaustively by a cross-validated bit-mask verifier. At $n=144$ the pipeline returns a census of $53$ codes whose strongest members surpass the BB benchmark: $[[144,6,d\ge 15]]$ exceeds the benchmark distance $12$ (certified $d\ge 15$), $[[144,10,12]]$ reaches it with weight-$8$ checks, and $[[144,16,10]]$ encodes a third more logical qubits at $kd^2/n=11.11$ ($7.4\%$ below benchmark) while decoding no worse. At $n=72$, $[[72,14,8]]$ attains $kd^2/n=12.44$---more than twice the same-length BB code---and decodes better; a circuit-level memory experiment places our weight-$8$ codes at $\approx 0.1\%$ pseudo-threshold versus $\approx 0.4\%$ for the BB reference under an identical model, quantifying the threshold cost of the heavier checks. All structural statements are verified numerically on the whole census.

quant-ph↗

arXiv2026

Quantum Locally Repairable Codes from Negacyclic and Repeated-Root Cyclic Codes over Small Fields

Quantum locally recoverable codes (qLRCs), introduced recently by Golowich and Guruswami, allow any single-qudit erasure to be recovered from a small set of other qudits. Most known constructions require a large alphabet. We systematically investigate qLRCs obtained, via the CSS construction, from classical constacyclic codes over small fields $\Ff_q$ with $q\in\{2,3,4,5,7\}$. First, we prove that a nonzero dual-containing $\lambda$-constacyclic code exists only when $\lambda^2=1$, so that negacyclic and (repeated-root) cyclic codes exhaust the constacyclic route to qLRCs. Second, we show that the locality of a constacyclic code equals the minimum distance of its dual minus one, and we give a simple purity criterion for the resulting quantum codes. Third, we show that odd-like duadic codes whose splitting is given by $\mu_{-1}$ yield pure qLRCs; specializing to $q$-ary quadratic residue codes of prime length $p\equiv 3 \pmod 4$ gives an infinite family of pure qLRCs with unbounded minimum distance and certified locality. Finally, by means of concrete computations, we obtain a classification of qLRCs from cyclic, negacyclic, and repeated-root cyclic codes of moderate lengths, which contains the first binary qLRCs from repeated-root cyclic codes and many parameter sets that cyclic codes cannot attain.

cs.IT↗

arXiv2026

Quantum Bicycle LDPC Codes with High $kd^2/n$ from Divisor-Driven Search

Bicycle (two-block circulant) quantum low-density parity-check (LDPC) codes include some of the best known small quantum codes, yet their design has relied on group-algebra formulations in which the dimension and distance are accessible only through matrix computation. We show that in the cyclic case the construction collapses into the polynomial ring $\F_2[x]/(x^{l}-1)$: self-orthogonality is automatic, the quantum dimension is read off from a polynomial gcd, and the minimum distance is certified exactly through the Calderbank correspondence to additive codes over $\F_4$, turning code search into an algebraically pre-filtered enumeration that reaches parameter regimes poorly covered by existing tables. A computer search based on this framework recovers the short codes $[[42,12,4]]_2$ and $[[62,12,4]]_2$ and produces a family of codes with competitive figure of merit $kd^2/n$, including $[[66,20,7]]_2$ with $kd^2/n=14.85$, above the bivariate bicycle code $[[144,12,12]]_2$ ($kd^2/n=12$) at less than half the block length, together with $[[46,2,8]]_2$, $[[66,2,9]]_2$, $[[66,4,8]]_2$, $[[66,6,8]]_2$ and, at $n=90$, $[[90,16,6]]_2$, $[[90,18,6]]_2$, $[[90,20,6]]_2$. An exhaustive census at $n=48$ delineates the boundary of this picture: we exhibit a $[[48,10,6]]_2$ code from a minimal $48$-element group (the Aydin--Tamo--Barg realization uses $72$ elements), and prove that distance $5$ forces a stabilizer-rank loss, which excludes $[[48,10,5]]_2$ from the weight-$8$ symmetric coset family. The framework thus opens a systematic route to bicycle-type quantum LDPC codes beyond the reach of group-theoretic searches, and identifies exactly where genuinely coset-theoretic phenomena begin.

cs.IT↗

arXiv2026

Quantum Codes from $r$-Nearly Self-Orthogonal Linear Codes via Jordan Canonical Form over $\mathbb{F}_{q^2}$

We introduce a Jordan-canonical-form framework for constructing $q$-ary quantum stabilizer codes from arbitrary classical linear codes over $\F_{q^2}$. The framework does not require the classical linear code $\mathcal{C}$ to satisfy the dual-containing condition (i.e., self-orthogonality). Given a classical code $\mathcal{C}=[n,k,d]_{q^2}$ with parity-check matrix $H$, we measure the obstruction to Hermitian self-orthogonality by the rank $r=(n-k)-\dim_{\F_{q^2}}(\mathcal{C}^{\perp_h}\cap \mathcal{C})$. The ingredient code $\mathcal{C}$ is $r$-nearly dual containing, or, equivalently, $\mathcal{C}^{\perp_h}$ is $r$-nearly self-orthogonal, by which we mean that $r=\Rank(HH^{\dagger})=\dim_{\F_{q^2}}(\mathcal{C}^{\perp_h})-\dim_{\F_{q^2}}(\mathcal{C}^{\perp_h}\cap \mathcal{C})$. By systematically reducing the rank of the Hermitian inner-product matrix $A=HH^{\dagger}$ through rank-one perturbations along the Jordan basis $W=P^{-1}$ of the decomposition $A=PJ_AP^{-1}$, we construct an explicit Hermitian self-orthogonal code $\mathcal{C}_{\mathrm{so}}=[n+r,n-k]_{q^2}$. A sufficient distance-preservation criterion guarantees that the resulting $q$-ary quantum code has parameters $[[n+r,2k-n+r,\geq d]]_q$. Applying this construction to classical codes produces several record quantum codes that improve or supplement the best-known parameters in Grassl's tables.

cs.IT↗