arXiv subjects

Feroz Ahmed Mian

Publications and source records attributed to Feroz Ahmed Mian.

3 recordsLinked to original sources

arXiv2026

Quantum Tanner Codes at Moderate Blocklength

We present explicit constructions of quantum Tanner (QT) codes with good rate and distance, obtained through two complementary approaches: the left-right Cayley complex (LRCC) description and the "lifting" perspective, in which a seed Calderbank-Shor-Steane (CSS) code is lifted by commuting left-right regular actions of a finite group $\mathcal{G}$. Through an extensive search over non-abelian groups from GAP's SmallGrp library, we investigate the moderate-blocklength regime ($n \in [500,1000]$) and identify several new code instances with distance upper bounds exceeding $20$. These include $[[480,8,(\leq 21,\leq 21)]]$, $[[504,4,(\leq 36,\leq 27)]]$, $[[672,4,(\leq 48,\leq 28)]]$, $[[720,6,(\leq 30,\leq 30)]]$, and $[[864,8,(\leq 39,\leq 31)]]$, with these bounds obtained using up to $350$ million trials of sQetch, a randomized distance estimator. The code instances presented have check weights ranging from $9$ to $20$. Using the Tesseract decoder, we estimate pseudo-thresholds of $3.6\%$-$4.6\%$ under phenomenological noise and $0.14\%$-$0.27\%$ under circuit-level noise, comparable to prior results at shorter code lengths. We also provide QuantumExpanders$.$jl, an open-source Julia library for constructing QT codes and explicit constructions of Ramanujan graphs.

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arXiv2026

Multivariate Multicycle Codes for Complete Single-Shot Decoding

We introduce multivariate multicycle (MM) codes, a new family of quantum error-correcting codes (QECCs) that unifies bivariate bicycle, multivariate bicycle, abelian two-block group algebra, generalized bicycle, trivariate tricycle, and toric codes. MM codes are Calderbank-Shor-Steane (CSS) codes defined from length-$\textit{t+1}$ chain complexes with $\textit{$t \ge 4$}$. The chief advantage of these codes is that they possess metachecks and high confinement that permit complete single-shot decoding. We offer a framework that facilitates the construction of long-length chain complexes through the use of Koszul complex. In particular, obtaining explicit boundary maps (parity check and metacheck matrices) is particularly straightforward in our approach. This simple but very general parameterization of codes permitted us to efficiently perform a numerical search, where we identify several MM code candidates that demonstrate these capabilities at high rates and high code distances. Examples of new codes with parameters $[[n,k,d]]$ include $[[96, 12, 8]]$, $[[144, 12, 12]]$, $[[216, 12, 14]]$, $[[288, 12, 16]]$, $[[324, 12, 20]]$, $[[432, 12, 27]]$, $[[486, 24, 12]]$, $[[630, 70, 9]]$, and $[[648, 18, 23]]$. Notably, our codes achieve confinement profiles that surpass all known single-shot-decodable quantum CSS codes of practical blocksize. Our codes are also the first explicit instances of collapsed 5D through 9D higher dimensional QECCs, with check weights significantly lower than those of recent small instances of quantum Tanner codes.

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arXiv2026

Optimizing compilation of error correction codes for 2xN quantum dot arrays and its NP-hardness

The ability to physically move qubits within a register allows the design of hardware-specific error-correction codes, which can achieve fault-tolerance while respecting other constraints. In particular, recent advancements have demonstrated the shuttling of electron and hole spin qubits through a quantum dot array with high fidelity. It is therefore timely to explore error correction architectures consisting merely of two parallel quantum dot arrays, an experimentally validated architecture compatible with classical wiring and control constraints. Upon such an architecture, we develop a suite of heuristic methods for compiling any Calderbank-Shor-Steane (CSS) error-correcting code's syndrome-extraction circuit to run with a reduced number of shuttling operations. We demonstrate how column-regular qLDPC codes can be compiled in a provably minimal number of shuttles that is exactly equal to the column weight of the code when Shor-style syndrome extraction is used. We provide tables stating the number of required shuttles for many contemporary codes of interest. In addition, we provide a proof of the NP hardness of minimizing the number of shuttle operations for general codes, even when using Shor syndrome extraction. We also discuss how one could get around this by placing blanks in the ancilla array to achieve minimal shuttles with Shor syndrome extraction on any CSS code, at the cost of longer ancilla arrays.

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