arXiv subjects

Weilei Zeng

Publications and source records attributed to Weilei Zeng.

7 recordsLinked to original sources

arXiv2026

Approximate maximum-likelihood decoding via truncated free energies

Maximum-likelihood decoding (MLD) achieves the minimum logical error rate of stabilizer codes under known i.i.d. Pauli noise, but its exact evaluation is \#P-hard. Practical pipelines therefore approximate MLD by minimum-weight decoding (MWD), retaining only the lowest-weight recovery per syndrome and discarding the coset degeneracy. The minimum-weight search is in turn implemented by stochastic solvers. We introduce approximate maximum-likelihood decoding (AMLD), a black-box framework that recycles the candidate samples discarded by stochastic inner decoders into a per-class truncated free-energy estimator. For every logical class represented in the candidate pool, the estimator is provably bounded below by the exact free energy and above by the empirical minimum weight. AMLD returns the logical class minimizing the estimated free energy with linear classical overhead. In SA-based Ising-decoder benchmarks, AMLD closes up to $83\%$ of the MWD--MLD threshold gap across the toric and color codes under bit-flip and depolarizing noise. The largest threshold improvement, from $17.28\%$ to $18.62\%$, occurs on the $6.6.6$ color code under depolarizing noise. We further demonstrate AMLD on the $[[144,12,12]]$ bivariate-bicycle code, whose bit-flip decoding problem has a hypergraph structure. This application requires neither matching-based enumeration nor code-specific tensor-network contraction. At $p=0.05$, AMLD reduces the logical error rate by $13\%$ relative to MWD evaluated on the same BP-OSD candidate pool.

quant-ph↗

arXiv2026

An iterative Ising decoder for quantum error correction codes

The Ising framework maps the decoding problem in quantum error correction onto ground-state optimization of a classical Hamiltonian, in which $X$-$Z$ error correlations enter as cross terms. Under phenomenological depolarizing noise, the exact joint formulation contains up to 8-body interactions for the toric code and 10-body for the $6.6.6$ color code. These high-order terms degrade solver convergence, inflate runtime, and raise the auxiliary spin overhead when embedding into native 2-body Ising hardware. In this work, we propose the iterative low-order decoding (ILOD) algorithm, which alternates between $X$- and $Z$-type sub-Hamiltonians, approximating cross-type correlations through Bayesian priors that reweight each type's couplings using the other type's inferred error configuration. This halves the maximum body count of interaction terms in the Hamiltonian, accelerating the solver, restoring convergence at larger code distances, and reducing the total spin count for 2-body embedding by a factor of $2.5$. For the toric code, ILOD attains a threshold of $4.73%$ versus $4.83%$ for the joint formulation, with the empirical runtime ratio scaling as $(0.81)^d$. For the $6.6.6$ color code, their thresholds agree within statistical uncertainty for small code distances, and ILOD remains convergent for larger distances where the joint formulation fails to converge despite a larger annealing budget.

quant-ph↗

arXiv2024

Exact anomalous mobility edges in one-dimensional non-Hermitian quasicrystals

Recent research has made significant progress in understanding localization transitions and mobility edges (MEs) that separate extended and localized states in non-Hermitian (NH) quasicrystals. Here we focus on studying critical states and anomalous MEs, which identify the boundaries between critical and localized states within two distinct NH quasiperiodic models. Specifically, the first model is a quasiperiodic mosaic lattice with both nonreciprocal hopping term and on-site potential. In contrast, the second model features an unbounded quasiperiodic on-site potential and nonreciprocal hopping. Using Avila's global theory, we analytically derive the Lyapunov exponent and exact anomalous MEs. To confirm the emergence of the robust critical states in both models, we conduct a numerical multifractal analysis of the wave functions and spectrum analysis of level spacing. Furthermore, we investigate the transition between real and complex spectra and the topological origins of the anomalous MEs. Our results may shed light on exploring the critical states and anomalous MEs in NH quasiperiodic systems.

cond-mat.dis-nn↗

arXiv2024

Exact non-Hermitian mobility edges and robust flat bands in two-dimensional Lieb lattices with imaginary quasiperiodic potentials

The mobility edge (ME) is a critical energy delineates the boundary between extended and localized states within the energy spectrum, and it plays a crucial role in understanding the metal-insulator transition in disordered or quasiperiodic systems. While there have been extensive studies on MEs in one-dimensional non-Hermitian (NH) quasiperiodic lattices recently, the investigation of exact NH MEs in two-dimensional (2D) cases remains rare. In the present study, we introduce a 2D dissipative Lieb lattice (DLL) model with imaginary quasiperiodic potentials applied solely to the vertices of the Lieb lattice. By mapping this DLL model to the 2D NH Aubry-Andr{\'e}-Harper (AAH) model, we analytically derive the exact ME and find it associated with the absolute eigenenergies. We find that the eigenvalues of extended states are purely imaginary when the quasiperiodic potential is strong enough. Additionally, we demonstrate that the introduction of imaginary quasiperiodic potentials does not disrupt the flat bands inherent in the system. Finally, we propose a theoretical framework for realizing our model using the Lindblad master equation. Our results pave the way for further investigation of exact NH MEs and flat bands in 2D dissipative quasiperiodic systems.

cond-mat.dis-nn↗

arXiv2021

Minimal distances for certain quantum product codes and tensor products of chain complexes

We use a map to quantum error-correcting codes and a subspace projection to get lower bounds for minimal homological distances in a tensor product of two chain complexes of vector spaces over a finite field. Homology groups of such a complex are described by the Künneth theorem. We give an explicit expression for the distances when one of the complexes is a linear map between two spaces. The codes in the construction, subsystem product codes and their gauge-fixed variants, generalize several known families of quantum error-correcting codes.

quant-ph↗

arXiv2019

Quantum convolutional data-syndrome codes

We consider performance of a simple quantum convolutional code in a fault-tolerant regime using several syndrome measurement/decoding strategies and three different error models, including the circuit model.

quant-ph↗

arXiv2018

Higher-dimensional quantum hypergraph-product codes

We describe a family of quantum error-correcting codes which generalize both the quantum hypergraph-product (QHP) codes by Tillich and Zémor, and all families of toric codes on $m$-dimensional hypercubic lattices. Similar to the latter, our codes form $m$-complexes ${\cal K}_m$, with $m\ge2$. These are defined recursively, with ${\cal K}_m$ obtained as a tensor product of a complex ${\cal K}_{m-1}$ with a $1$-complex parameterized by a binary matrix. Parameters of the constructed codes are given explicitly in terms of those of binary codes associated with the matrices used in the construction.

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