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Manabu Hagiwara

Publications and source records attributed to Manabu Hagiwara.

At least 19 recordsLinked to original sources
arXiv2023

The Tight Upper Bound for the Size of Single Deletion Error Correcting Codes in Dimension 11

A single deletion error correcting code (SDECC) is a set of fixed-length sequences consisting of two types of symbols, 0 and 1, such that the original sequence can be recovered for at most one deletion error. The upper bound for the size of SDECC is expected to be equal to the size of Varshamov-Tenengolts (VT) code, and this conjecture had been shown to be true when the code length is ten or less. In this paper, we discuss a method for calculating this upper bound by providing an integer linear programming solver with several linear constraints. As a new result, we obtained that the tight upper bound for the size of a single deletion error correcting code in dimension 11 is 172.

cs.IT↗
arXiv2023

Photoemission Orbital Tomography Using Robust Sparse PhaseLift

Photoemission orbital tomography (POT) from photoelectron momentum maps (PMMs) has enabled detailed analysis of the shape and energy of molecular orbitals in the adsorbed state. This study proposes a new POT method based on the PhaseLift. Molecular orbitals, including three-dimensional phases, can be identified from a single PMM by actively providing atomic positions and basis. Moreover, our method is robust to noise and can perfectly discriminate adsorption-induced molecular deformations with an accuracy of 0.05 [angstrom]. Our new method enables simultaneous analysis of the three-dimensional shapes of molecules and molecular orbitals and thus paves the way for advanced quantum-mechanical interpretation of adsorption-induced electronic state changes and photo-excited inter-molecular interactions.

cond-mat.mtrl-sci↗
arXiv2023

Quantum Deletion Codes Derived From Quantum Reed-Solomon Codes

This manuscript presents a construction method for quantum codes capable of correcting multiple deletion errors. By introducing two new alogorithms, the alternating sandwich mapping and the block error locator, the proposed method reduces deletion error correction to erasure error correction. Unlike previous quantum deletion error-correcting codes, our approach enables flexible code rates and eliminates the requirement of knowing the number of deletions.

quant-ph↗
arXiv2022

Quantum Deletion Codes derived from Classical Deletion Codes (Extended Abstract)

This manuscript is an extended abstract version of the paper entitled ``Quantum Deletion Codes derived from Classical Deletion Codes.'' The paper contributes to the fundamental theory for quantum deletion error-correcting codes. The paper proposes a code construction condition for a partition of classical deletion error-correcting codes to derive quantum deletion error-correcting codes. The construction methods in this paper give examples of quantum codes that can correct single-quantum deletion errors and have a code rate arbitrarily close to 1, while the previously known quantum deletion code rates are close to 0 for long length. This manuscript omits the proofs of the statements in the paper.

cs.IT↗
arXiv2021

Constructions of $\ell$-Adic $t$-Deletion-Correcting Quantum Codes

We propose two systematic constructions of deletion-correcting codes for protecting quantum information. The first one works with qudits of any dimension, but only one deletion is corrected and the constructed codes are asymptotically bad. The second one corrects multiple deletions and can construct asymptotically good codes. The second one also allows conversion of stabilizer-based quantum codes to deletion-correcting codes, and entanglement assistance.

quant-ph↗
arXiv2021

Permutation-Invariant Quantum Codes for Deletion Errors

This paper presents conditions for constructing permutation-invariant quantum codes for deletion errors and provides a method for constructing them. Our codes give the first example of quantum codes that can correct two or more deletion errors. Also, our codes give the first example of quantum codes that can correct both multiple-qubit errors and multiple-deletion errors. We also discuss a generalization of the construction of our codes at the end.

quant-ph↗
arXiv2020

Decoding algorithms of monotone codes and azinv codes and their unified view

This paper investigates linear-time decoding algorithms for two classes of error-correcting codes. One of the classes is monotone codes which are known as single deletion codes. The other is azinv codes which are known as single balanced adjacent deletion codes. As results, this paper proposes generalizations of Levenshtein's decoding algorithm for Levenshtein's single deletion codes. This paper points out that it is possible to unify our new two decoding algorithms.

cs.IT↗
arXiv2020

Single Quantum Deletion Error-Correcting Codes

In this paper, we discuss a construction method of quantum deletion error-correcting codes. First of all, we define deletion errors for quantum states, an encoder, a decoder, and two conditions which is expressed by only the combinatorial language. Then, we prove that quantum deletion error-correcting codes can be constructed by two sets that satisfy the conditions. In other words, problems that correct the deletion errors for quantum states are reduced to problems that find the sets satisfying the condition by this paper. Also, we performed experiment of the codes over IBM Quantum Experience.

quant-ph↗
arXiv2020

A Four-Qubits Code that is a Quantum Deletion Error-Correcting Code with the Optimal Length

This paper provides a new instance of quantum deletion error-correcting codes. This code can correct any single quantum deletion error, while our code is only of length 4. This paper also provides an example of an encoding quantum circuit and decoding quantum circuits. It is also proven that the length of any single deletion error-correcting codes is greater than or equal to 4. In other words, our code is optimal for the code length.

quant-ph↗
arXiv2017

Multipermutation Ulam Sphere Analysis Toward Characterizing Maximal Code Size

Permutation codes, in the form of rank modulation, have shown promise for applications such as flash memory. One of the metrics recently suggested as appropriate for rank modulation is the Ulam metric, which measures the minimum translocation distance between permutations. Multipermutation codes have also been proposed as a generalization of permutation codes that would improve code size (and consequently the code rate). In this paper we analyze the Ulam metric in the context of multipermutations, noting some similarities and differences between the Ulam metric in the context of permutations. We also consider sphere sizes for multipermutations under the Ulam metric and resulting bounds on code size.

cs.IT↗
arXiv2012

Linear Programming Upper Bounds on Permutation Code Sizes From Coherent Configurations Related to the Kendall Tau Distance Metric

Recent interest on permutation rank modulation shows the Kendall tau metric as an important distance metric. This note documents our first efforts to obtain upper bounds on optimal code sizes (for said metric) ala Delsarte's approach. For the Hamming metric, Delsarte's seminal work on powerful linear programming (LP) bounds have been extended to permutation codes, via association scheme theory. For the Kendall tau metric, the same extension needs the more general theory of coherent configurations, whereby the optimal code size problem can be formulated as an extremely huge semidefinite programming (SDP) problem. Inspired by recent algebraic techniques for solving SDP's, we consider the dual problem, and propose an LP to search over a subset of dual feasible solutions. We obtain modest improvement over a recent Singleton bound due to Barg and Mazumdar. We regard this work as a starting point, towards fully exploiting the power of Delsarte's method, which are known to give some of the best bounds in the context of binary codes.

cs.IT↗
arXiv2012

On ML-Certificate Linear Constraints for Rank Modulation with Linear Programming Decoding and its Application to Compact Graphs

Linear constraints for a matrix polytope with no fractional vertex are investigated as intersecting research among permutation codes, rank modulations, and linear programming methods. By focusing the discussion to the block structure of matrices, new classes of such polytopes are obtained from known small polytopes. This concept, called "consolidation", is applied to find a new compact graph which is known as an approach for the graph isomorphism problem. Encoding and decoding algorithms for our new permutation codes are obtained from existing algorithms for small polytopes. The minimum distances associated with Kendall-tau distance and the minimum Euclidean distance of a code obtained by changing the basis of a permutation code may be larger than the original one.

math.CO↗
arXiv2011

Quantum Error Correction beyond the Bounded Distance Decoding Limit

In this paper, we consider quantum error correction over depolarizing channels with non-binary low-density parity-check codes defined over Galois field of size $2^p$ . The proposed quantum error correcting codes are based on the binary quasi-cyclic CSS (Calderbank, Shor and Steane) codes. The resulting quantum codes outperform the best known quantum codes and surpass the performance limit of the bounded distance decoder. By increasing the size of the underlying Galois field, i.e., $2^p$, the error floors are considerably improved.

cs.IT↗
arXiv2011

LP Decodable Permutation Codes based on Linearly Constrained Permutation Matrices

A set of linearly constrained permutation matrices are proposed for constructing a class of permutation codes. Making use of linear constraints imposed on the permutation matrices, we can formulate a minimum Euclidian distance decoding problem for the proposed class of permutation codes as a linear programming (LP) problem. The main feature of this class of permutation codes, called LP decodable permutation codes, is this LP decodability. It is demonstrated that the LP decoding performance of the proposed class of permutation codes is characterized by the vertices of the code polytope of the code. Two types of linear constraints are discussed; one is structured constraints and another is random constraints. The structured constraints such as pure involution lead to an efficient encoding algorithm. On the other hand, the random constraints enable us to use probabilistic methods for analyzing several code properties such as the average cardinality and the average weight distribution.

cs.IT↗
arXiv2011

Spatially Coupled Quasi-Cyclic Quantum LDPC Codes

We face the following dilemma for designing low-density parity-check codes (LDPC) for quantum error correction. 1) The row weights of parity-check should be large: The minimum distances are bounded above by the minimum row weights of parity-check matrices of constituent classical codes. Small minimum distance tends to result in poor decoding performance at the error-floor region. 2) The row weights of parity-check matrices should not be large: The sum-product decoding performance at the water-fall region is degraded as the row weight increases. Recently, Kudekar et al. showed spatially-coupled (SC) LDPC codes exhibit capacity-achieving performance for classical channels. SC LDPC codes have both large row weight and capacity-achieving error-floor and water-fall performance. In this paper, we design SC LDPC-CSS (Calderbank, Shor and Steane) codes for quantum error correction over the depolarizing channels.

cs.IT↗