arXiv subjects

Qianfan Wang

Publications and source records attributed to Qianfan Wang.

5 recordsLinked to original sources

arXiv2026

Spatio-temporal Path Optimization for Stabilizer-Code-Protected Quantum Networks

Quantum Error Correction~(QEC)-protected direct transmission is a fundamental approach to preserve fragile quantum states while they are physically forwarded across noisy quantum networks. When a logical qubit traverses multiple hops, selected QEC-capable nodes may recover the encoded state before it continues along the route. The feasibility and cost of the final transmission strategy therefore depend on how we jointly choose the path, the recovery locations, and the protection schemes. In this paper, we formulate and analyze a cross-layer spatio-temporal path optimization problem for block-style stabilizer-code-protected direct transmission. Our main results include fixed-scheme and flexible-scheme single-flow routing algorithms, as well as a multi-flow routing algorithm. The framework developed in this paper can serve as an algorithmic building block for QEC-aware routing under logical-error and logical-lifetime constraints. Simulations show that it reduces single-flow average routing cost by approximately 25--30\% over Decode-Always and lowers multi-flow throughput-normalized congestion by approximately 28--31\% over Greedy-Assignment.

cs.NI↗

arXiv2026

Optimal qudit overlapping tomography and optimal measurement order

Quantum state tomography is essential for characterizing quantum systems, but it becomes infeasible for large systems due to exponential resource scaling. Overlapping tomography addresses this challenge by reconstructing all $k$-body marginals using few measurement settings, enabling the efficient extraction of key information for many quantum tasks. While optimal schemes are known for qubits, the extension to higher-dimensional qudit systems remains largely unexplored. Here, we investigate optimal qudit overlapping tomography, constructing local measurement settings from generalized Gell-Mann matrices. By establishing a correspondence with combinatorial covering arrays, we present two explicit constructions of optimal measurement schemes. For $n$-qutrit systems, we prove that pairwise tomography requires at most $8 + 56\left\lceil \log_{8} n \right\rceil$ measurement settings, and provide an explicit scheme achieving this bound. Furthermore, we develop an efficient algorithm to determine the optimal order of these measurement settings, minimizing the experimental overhead associated with switching configurations. Compared to the worst-case ordering, our optimized schedule reduces switching costs by approximately 50\%. These results provide a practical pathway for efficient characterization of qudit systems, facilitating their application in quantum communication and computation.

quant-ph↗

arXiv2025

Guessing Decoding of Short Blocklength Codes

Future beyond-5G and 6G systems demand ultra-reliable, low-latency communication with short blocklengths, motivating the development of universal decoding algorithms. Guessing decoding, which infers the noise or codeword candidate in order of decreasing (exact or approximate) likelihood, offers a universal framework applicable to short codes. In this paper, we present a unified treatment of two prominent recent families of guessing decoding: guessing random additive noise decoding (GRAND) and guessing codeword decoding (GCD). For each, we (i) present algorithmic implementations and ordering strategies; (ii) prove maximum-likelihood (ML) optimality under appropriate stopping criteria; (iii) derive saddle-point approximations for the average number of queries; and (iv) validate theoretical predictions with simulations. We further analyze the performance degradation due to limited search budgets relative to ML performance, compare key metrics (worst-case and average complexity, hardware considerations), and highlight how advances in one approach transfer naturally to the other. Our results clarify the operating regimes where GRAND and GCD demonstrate superior performance. This work provides both theoretical insights and practical guidelines for deploying universal guessing decoders in next-generation short-blocklength communications.

cs.IT↗

arXiv2024

A High-Performance List Decoding Algorithm for Surface Codes with Erroneous Syndrome

Quantum error-correcting codes (QECCs) are necessary for fault-tolerant quantum computation. Surface codes are a class of topological QECCs that have attracted significant attention due to their exceptional error-correcting capabilities and easy implementation. In the decoding process of surface codes, the syndromes are crucial for error correction, however, they are not always correctly measured. Most of the existing decoding algorithms for surface codes need extra measurements to correct syndromes with errors, which implies a potential increase in inference complexity and decoding latency. In this paper, we propose a high-performance list decoding algorithm for surface codes with erroneous syndromes, where syndrome soft information is incorporated in the decoding, allowing qubits and syndrome to be recovered without needing extra measurements. Precisely, we first use belief propagation (BP) decoding for pre-processing with syndrome soft information, followed by ordered statistics decoding (OSD) for post-processing to list and recover both qubits and syndromes. Numerical results demonstrate that our proposed algorithm efficiently recovers erroneous syndromes and significantly improves the decoding performance of surface codes with erroneous syndromes compared to minimum-weight perfect matching (MWPM), BP and original BP-OSD algorithms.

cs.IT↗

arXiv2024

Random Staircase Generator Matrix Codes: Performance Analysis and Construction

In this paper, we propose a class of codes, referred to as random staircase generator matrix codes (SGMCs), which have staircase-like generator matrices. In the infinite-length region, we prove that the random SGMC is capacity-achieving over binary-input output-symmetric (BIOS) channels. In the finite-length region, we present the representative ordered statistics decoding with local constraints (LC-ROSD) algorithm for the SGMCs. The most distinguished feature of the SGMCs with LC-ROSD is that the staircase-like matrices enable parallel implementation of the Gaussian elimination (GE), avoiding the serial GE of conventional OSD and supporting a potential low decoding latency, as implied from simulations. To analyze the performance of random SGMCs in the finite-length region, we derive the ensemble weight spectrum and invoke the conventional union bound. We also derive a partially random coding union (RCU) bound, which is tighter than the conventional one and is used as a criterion to design the SGMCs. Staircase-like generator matrices allow us to derive a series of (tighter and tighter) lower bounds based on the second-order Bonferroni inequality with the incremental number of codewords. The numerical results show that the decoding performance can match well with the proposed partially RCU bound for different code rates and different profiles. The numerical results also show that the tailored SGMCs with the LC-ROSD algorithm can approach the finite-length performance bound, outperforming the 5G low-density parity-check (LDPC) codes, 5G polar codes, and Reed-Muller (RM) codes.

cs.IT↗