Related papers: Trellis Decoding For Qudit Stabilizer Codes And It…
This paper presents a comprehensive guide to designing minimal trellises for both non-degenerate and degenerate decoding of quantum stabilizer codes. For non-degenerate decoding, various strategies are explored, leveraging insights from…
Trellises play an important theoretical and practical role for classical codes. Their main utility is to devise complexity-efficient error estimation algorithms. Here, we describe trellis representations for quantum stabilizer codes. We…
Qudit toric codes are a natural higher-dimensional generalization of the well-studied qubit toric code. However standard methods for error correction of the qubit toric code are not applicable to them. Novel decoders are needed. In this…
Quantum error correction is indispensable to achieving reliable quantum computation. When quantum information is encoded redundantly, a larger Hilbert space is constructed using multiple physical qubits, and the computation is performed…
Quantum error correction is an important ingredient for scalable quantum computing. Stabilizer codes are one of the most promising and straightforward ways to correct quantum errors, are convenient for logical operations, and improve…
We construct a hybrid quantum-classical Viterbi decoder for the classical error-correcting codes. Viterbi decoding is a trellis-based procedure for maximum likelihood decoding of classical error-correcting codes. In this article, we…
The forthcoming Versatile Video Coding (VVC) standard adopts the trellis-coded quantization, which leverages the delicate trellis graph to map the quantization candidates within one block into the optimal path. Despite the high compression…
Entanglement is essential for quantum information processing, but is limited by noise. We address this by developing high-yield entanglement distillation protocols with several advancements. (1) We extend the 2-to-1 recurrence entanglement…
The color code is a topological quantum error-correcting code supporting a variety of valuable fault-tolerant logical gates. Its two-dimensional version, the triangular color code, may soon be realized with currently available…
We study, by means of the stabilizer formalism, a quantum error correcting code which is alternative to the standard block codes since it embeds a qubit into a qudit. The code exploits the non-commutative geometry of discrete phase space to…
Quantum computers have the potential to provide exponential speedups over their classical counterparts. Quantum principles are being applied to fields such as communications, information processing, and artificial intelligence to achieve…
Fault-tolerant quantum computation relies on scaling up quantum error correcting codes in order to suppress the error rate on the encoded quantum states. Topological codes, such as the surface code or color codes are leading candidates for…
The surface code is one of the most promising candidates for combating errors in large scale fault-tolerant quantum computation. A fault-tolerant decoder is a vital part of the error correction process---it is the algorithm which computes…
We propose a scalable decoding framework for correcting correlated hook errors in stabilizer measurement circuits. Traditional circuit-level decoding attempts to estimate the precise location of faults by constructing an extended Tanner…
Variable length codes exhibit de-synchronization problems when transmitted over noisy channels. Trellis decoding techniques based on Maximum A Posteriori (MAP) estimators are often used to minimize the error rate on the estimated sequence.…
To improve the efficiency of the encoding and the decoding is the important problem in the quantum error correction. In a preceding work, a general algorithm for decoding the stabilizer code is shown. This paper will show an decoding which…
Recently many works attempt to develop image compression models based on deep learning architectures, where the uniform scalar quantizer (SQ) is commonly applied to the feature maps between the encoder and decoder. In this paper, we propose…
Scaling quantum computing to practical applications necessitates reliable quantum error correction. Although numerous correction codes have been proposed, the overall correction efficiency critically limited by the decode algorithms. We…
In this paper, soft-decision (SD) decoders of permutation trellis code (PTC) with $M$-ary frequency shift keying are designed using three optimization algorithms and presented in four decoding schemes. In a concatenated code such as PTC,…
In this work, we develop an efficient decoding method for graph codes, a class of stabilizer quantum error-correcting codes constructed from graph states. While optimal decoding is generally NP-hard, we propose a faster decoder exploiting…