Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

IEEE International Symposium on Future Telecommunication Technologies (SOFTT)

Short Quantum Accumulate Codes with High Rate and Multiple Error Corrections Capability

Khoirul Anwar, Mujib Ramadhan, Agung Trisetyarso

Published Dec 6, 2021• 5 citations
Publisher

Abstract

This paper proposes short but high rate quantum codes, derived from the classical accumulate codes, having capability of correcting multiple errors simultaneously. The high coding rate is obtained from k = 2 with minimum blocklength n, but still satisfying both Singletone and Hamming bounds to have error correction capability of t = 2 qubits, We perform an intensive computer search to find the best matrix of parity check that match with the accumulator matrix to provide zero simplectic inner product (SIP) mod 2. We found that it is difficult to obtain a perfect parity check matrix that provide zero diagonal element in SIP to guarantee completely unique syndromes. However, since it may be difficult, we also present in this paper a theoretical quantum word error rate (QWER), when some syndromes do not have unique values to identify the quantum errors of X, Z, and Y. The results in this paper are expected to provide groundbreaking foundation on the development of high rate quantum codes with$k\geq 2$, especially for short blocklength.

DOI
10.1109/softt54252.2021.9673151

Related papers

The Smallest Perfect Quantum Accumulate Codes

Khoirul Anwar, Mujib Ramadhan

Quantum has many unique characteristics for future applications in the sixth telecommunication generation (6G) 2030 based on entanglement and quantum teleportation. However, quantum communications are still vulnerable to errors and require quantum error corrections (QECC). This paper proposes quantum accumulate codes, where idea is coming from the classical accumulate codes that can provide good performances to remove or minimize the error-floor in classical communications. The proposed quantum codes can exactly satisfy both Hamming and Singleton bounds resulting in one of the smallest perfect quantum codes. This paper explains in details the steps to construct the codewords, syndrome extraction, error correction, and the quantum circuits. We perform a series of computer simulations to evaluate the quantum word error rate (QWR) and quantum fidelity performances under the depolarizing channels. Our results confirm that the stabilizers of the proposed codes can extract the syndrome and distinguish all error patterns of any single qubit errors of Pauli X, Y, and Z providing performances confirmed by the theoretical QWER curves. The results are expected to provide contributions to the development of quantum communications and future security issues.

Asia-Pacific Conference on Communications (APCC)•Oct 11, 2021•8 citations

High-Rate Quantum Low-Density Parity-Check Codes Assisted by Reliable Qubits

Yuichiro Fujiwara, Alexander Gruner, Peter Vandendriessche

Quantum error correction is an important building block for reliable quantum information processing. A challenging hurdle in the theory of quantum error correction is that it is significantly more difficult to design error-correcting codes with desirable properties for quantum information processing than for traditional digital communications and computation. A typical obstacle to constructing a variety of strong quantum error-correcting codes is the complicated restrictions imposed on the structure of a code. Recently, promising solutions to this problem have been proposed in quantum information science, where in principle any binary linear code can be turned into a quantum error-correcting code by assuming a small number of reliable quantum bits. This paper studies how best to take advantage of these latest ideas to construct desirable quantum error-correcting codes of very high information rate. Our methods exploit structured high-rate low-density parity-check codes available in the classical domain and provide quantum analogues that inherit their characteristic low decoding complexity and high error correction performance even at moderate code lengths. Our approach to designing high-rate quantum error-correcting codes also allows for making direct use of other major syndrome decoding methods for linear codes, making it possible to deal with a situation where promising quantum analogues of low-density parity-check codes are difficult to find.

arXiv:1309.5587•IEEE Transactions on Information Theory•Jan 30, 2015•14 citations

Towards Ultra-High-Rate Quantum Error Correction with Reconfigurable Atom Arrays

Chen Zhao, Casey Duckering, Andi Gu +2 more

Quantum error correction is widely believed to be essential for large-scale quantum computation, but the required qubit overhead remains a central challenge. Quantum low-density parity-check codes can substantially reduce this overhead through high-rate encodings, yet finite-size instances with practical logical error rates often achieve encoding rates only around or below $1/10$. Here, building on a recent ultra-high-rate construction by Kasai, we identify new structural conditions on the underlying affine permutation matrices that make encoding rates exceeding $1/2$ compatible with efficient implementation on reconfigurable neutral atom arrays. These conditions define a co-designed family of ultra-high-rate quantum codes that supports efficient syndrome extraction and atom rearrangement under realistic parallel control constraints. Using a hierarchical decoder with high accuracy and good throughput, we study the performance under a circuit-level noise model with $p=0.1\%$, achieving per-logical-per-round error rates of $1.3_{-0.9}^{+3.0} \times 10^{-13}$ with a $[[2304,1156,\leq 14]]$ code and $2.9_{-1.5}^{+3.1} \times 10^{-11}$ with a $[[1152,580,\leq 12]]$ code. We compare these codes against a heuristic Pareto frontier for finite-blocklength codes relating block length, encoding rate, and logical error rates, and find that our codes lie near the frontier. These results approach the teraquop regime, highlighting the promise of this code family for practical ultra-high-rate quantum error correction.

quant-pharXiv:2604.16209•Apr 20, 2026•0 citations

On The Design of Non-CSS Quantum Error Correction Codes with High Quantum Information

A. Muh. Mufqi Zuhudi, Khoirul Anwar, Gelar Budiman

In this paper, we propose quantum [[10, 10, 2]] stabilizer codes constructed from the existing quantum [[5, 5, 1]] Hamming codes. The proposed quantum [[10, 10, 2]] codes satisfy the symplectic inner product (SIP) to ensure stabilizer generators commute each other for successful detections and corrections. A comprehensive end-to-end construction from parity-check matrix (PCM) of classical codes is provided to ensure quantum error correction codes (QECC) with higher information. We perform a series of computer simulations to evaluate proposed quantum [[10, 10, 2]] codes in terms of quantum word error rate (QWER) performances under the depolarizing channels. The results confirm that the proposed quantum [[10, 10, 2]] codes can successfully detect and correct all single quantum bit (qubit) errors, which is validated by the curve of QWER performances that coincide with the theoretical QWER performances. The results are expected to contribute to the development of QECC in quantum computing and communication systems.

International Conference on Artificial Intelligence, Blockchain, Cloud Computing, and Data Analytics (ICoABCD)•Nov 13, 2023•2 citations

Near-Hashing-Bound Multiple-Rate Quantum Turbo Short-Block Codes

Daryus Chandra, Zunaira Babar, Soon Xin Ng +1 more

Quantum stabilizer codes (QSCs) suffer from a low quantum coding rate since they have to recover the quantum bits (qubits) in the face of both bit-flip and phase-flip errors. In this treatise, we conceive a low-complexity concatenated quantum turbo code (QTC) design exhibiting a high quantum coding rate. The high quantum coding rate is achieved by combining the quantum-domain version of short-block codes (SBCs) also known as single parity check (SPC) codes as the outer codes and quantum unity-rate codes (QURCs) as the inner codes. Despite its design simplicity, the proposed QTC yields a near-hashing-bound error correction performance. For instance, compared to the best half-rate QTC known in the literature, namely the QIrCC-QURC scheme, which operates at the distance of D = 0.037 from the quantum hashing bound, our novel QSBC-QURC scheme can operate at the distance of D = 0.029. In addition, it is worth mentioning that this is the first instantiation of QTCs capable of adjusting the quantum encoders according to the quantum coding rate required for mitigating the Pauli errors, given the different depolarizing probabilities of the quantum channel.

arXiv:1903.10927•IEEE Access•Jan 1, 2019•22 citations

Constructing a Novel 7-Qubit Quantum Error Correction Code from a Derived Hamming Code Matrix

Robin Sinurat, Melinda Br Ginting, Muhammad Imansyah Basudewa

Quantum technology offers transformative potential for future applications, including secure communications and high-speed computing. However, quantum systems are highly susceptible to decoherence caused by environment interactions, making error correction essential for reliable operation. This paper proposes a new 7-qubit quantum error correction code constructed from classical Hamming codes through a distinct derivation of the parity matrix. Unlike the well-known Steane code, our scheme employs a different parity matrix within the stabilizer framework, resulting in a novel code structure. We detail the step-by-step construction of codewords, syndrome extraction using stabilizer measurements, and the corresponding quantum circuits. Performance evaluation is conducted through simulations under depolarizing channels across error probabilities from to 0, using Quantum Word Error Rate (QWER) as the metric. Simulation results confirm that the proposed stabilizers can uniquely identify all single-qubit error patterns of Pauli X, Y, and Z. Moreover, the scheme achieves a significant error reduction of approximately 28 times (about 96%) compared to uncoded transmission. These findings demonstrate that deriving quantum codes from modified classical matrices offers an effective strategy for enhancing the reliability of future quantum communication systems.

Telekontran Jurnal Ilmiah Telekomunikasi Kendali dan Elektronika Terapan•Apr 30, 2026•0 citations
This paper proposes short but high rate quantum codes, derived from the classical accumulate codes, having capability of correcting multiple errors simultaneously. The high coding rate is obtained from k = 2 with minimum blocklength n, but still satisfying both Singletone and Hamming bounds to have error correction capability of t = 2 qubits, We perform an intensive computer search to find the best matrix of parity check that match with the accumulator matrix to provide zero simplectic inner product (SIP) mod 2. We found that it is difficult to obtain a perfect parity check matrix that provide zero diagonal element in SIP to guarantee completely unique syndromes. However, since it may be difficult, we also present in this paper a theoretical quantum word error rate (QWER), when some syndromes do not have unique values to identify the quantum errors of X, Z, and Y. The results in this paper are expected to provide groundbreaking foundation on the development of high rate quantum codes withk≥2k\geq 2k≥2, especially for short blocklength.
Quantum has many unique characteristics for future applications in the sixth telecommunication generation (6G) 2030 based on entanglement and quantum teleportation. However, quantum communications are still vulnerable to errors and require quantum error corrections (QECC). This paper proposes quantum accumulate codes, where idea is coming from the classical accumulate codes that can provide good performances to remove or minimize the error-floor in classical communications. The proposed quantum codes can exactly satisfy both Hamming and Singleton bounds resulting in one of the smallest perfect quantum codes. This paper explains in details the steps to construct the codewords, syndrome extraction, error correction, and the quantum circuits. We perform a series of computer simulations to evaluate the quantum word error rate (QWR) and quantum fidelity performances under the depolarizing channels. Our results confirm that the stabilizers of the proposed codes can extract the syndrome and distinguish all error patterns of any single qubit errors of Pauli X, Y, and Z providing performances confirmed by the theoretical QWER curves. The results are expected to provide contributions to the development of quantum communications and future security issues.
Quantum error correction is an important building block for reliable quantum information processing. A challenging hurdle in the theory of quantum error correction is that it is significantly more difficult to design error-correcting codes with desirable properties for quantum information processing than for traditional digital communications and computation. A typical obstacle to constructing a variety of strong quantum error-correcting codes is the complicated restrictions imposed on the structure of a code. Recently, promising solutions to this problem have been proposed in quantum information science, where in principle any binary linear code can be turned into a quantum error-correcting code by assuming a small number of reliable quantum bits. This paper studies how best to take advantage of these latest ideas to construct desirable quantum error-correcting codes of very high information rate. Our methods exploit structured high-rate low-density parity-check codes available in the classical domain and provide quantum analogues that inherit their characteristic low decoding complexity and high error correction performance even at moderate code lengths. Our approach to designing high-rate quantum error-correcting codes also allows for making direct use of other major syndrome decoding methods for linear codes, making it possible to deal with a situation where promising quantum analogues of low-density parity-check codes are difficult to find.
Quantum error correction is widely believed to be essential for large-scale quantum computation, but the required qubit overhead remains a central challenge. Quantum low-density parity-check codes can substantially reduce this overhead through high-rate encodings, yet finite-size instances with practical logical error rates often achieve encoding rates only around or below 1/101/101/10. Here, building on a recent ultra-high-rate construction by Kasai, we identify new structural conditions on the underlying affine permutation matrices that make encoding rates exceeding 1/21/21/2 compatible with efficient implementation on reconfigurable neutral atom arrays. These conditions define a co-designed family of ultra-high-rate quantum codes that supports efficient syndrome extraction and atom rearrangement under realistic parallel control constraints. Using a hierarchical decoder with high accuracy and good throughput, we study the performance under a circuit-level noise model with p=0.1%p=0.1\%p=0.1%, achieving per-logical-per-round error rates of 1.3−0.9+3.0×10−131.3_{-0.9}^{+3.0} \times 10^{-13}1.3−0.9+3.0​×10−13 with a [[2304,1156,≤14]][[2304,1156,\leq 14]][[2304,1156,≤14]] code and 2.9−1.5+3.1×10−112.9_{-1.5}^{+3.1} \times 10^{-11}2.9−1.5+3.1​×10−11 with a [[1152,580,≤12]][[1152,580,\leq 12]][[1152,580,≤12]] code. We compare these codes against a heuristic Pareto frontier for finite-blocklength codes relating block length, encoding rate, and logical error rates, and find that our codes lie near the frontier. These results approach the teraquop regime, highlighting the promise of this code family for practical ultra-high-rate quantum error correction.
In this paper, we propose quantum [[10, 10, 2]] stabilizer codes constructed from the existing quantum [[5, 5, 1]] Hamming codes. The proposed quantum [[10, 10, 2]] codes satisfy the symplectic inner product (SIP) to ensure stabilizer generators commute each other for successful detections and corrections. A comprehensive end-to-end construction from parity-check matrix (PCM) of classical codes is provided to ensure quantum error correction codes (QECC) with higher information. We perform a series of computer simulations to evaluate proposed quantum [[10, 10, 2]] codes in terms of quantum word error rate (QWER) performances under the depolarizing channels. The results confirm that the proposed quantum [[10, 10, 2]] codes can successfully detect and correct all single quantum bit (qubit) errors, which is validated by the curve of QWER performances that coincide with the theoretical QWER performances. The results are expected to contribute to the development of QECC in quantum computing and communication systems.
Quantum stabilizer codes (QSCs) suffer from a low quantum coding rate since they have to recover the quantum bits (qubits) in the face of both bit-flip and phase-flip errors. In this treatise, we conceive a low-complexity concatenated quantum turbo code (QTC) design exhibiting a high quantum coding rate. The high quantum coding rate is achieved by combining the quantum-domain version of short-block codes (SBCs) also known as single parity check (SPC) codes as the outer codes and quantum unity-rate codes (QURCs) as the inner codes. Despite its design simplicity, the proposed QTC yields a near-hashing-bound error correction performance. For instance, compared to the best half-rate QTC known in the literature, namely the QIrCC-QURC scheme, which operates at the distance of D = 0.037 from the quantum hashing bound, our novel QSBC-QURC scheme can operate at the distance of D = 0.029. In addition, it is worth mentioning that this is the first instantiation of QTCs capable of adjusting the quantum encoders according to the quantum coding rate required for mitigating the Pauli errors, given the different depolarizing probabilities of the quantum channel.
Quantum technology offers transformative potential for future applications, including secure communications and high-speed computing. However, quantum systems are highly susceptible to decoherence caused by environment interactions, making error correction essential for reliable operation. This paper proposes a new 7-qubit quantum error correction code constructed from classical Hamming codes through a distinct derivation of the parity matrix. Unlike the well-known Steane code, our scheme employs a different parity matrix within the stabilizer framework, resulting in a novel code structure. We detail the step-by-step construction of codewords, syndrome extraction using stabilizer measurements, and the corresponding quantum circuits. Performance evaluation is conducted through simulations under depolarizing channels across error probabilities from to 0, using Quantum Word Error Rate (QWER) as the metric. Simulation results confirm that the proposed stabilizers can uniquely identify all single-qubit error patterns of Pauli X, Y, and Z. Moreover, the scheme achieves a significant error reduction of approximately 28 times (about 96%) compared to uncoded transmission. These findings demonstrate that deriving quantum codes from modified classical matrices offers an effective strategy for enhancing the reliability of future quantum communication systems.