Article
Multidisciplinary Sciences
Michael Vasmer, Dan E. Browne, Aleksander Kubica
Summary: The proposed error correction procedure based on a cellular automaton, the sweep rule, is applicable to a broad range of codes, particularly the toric code. Numerical benchmarks show that the procedure is robust against measurement errors and insensitive to lattice and noise model details. This work represents a step towards finding simple and high-performance decoding strategies for a wide range of quantum low-density parity-check codes.
SCIENTIFIC REPORTS
(2021)
Article
Quantum Science & Technology
Aleksander Kubica, Nicolas Delfosse
Summary: We propose an efficient decoder, called the Restriction Decoder, for color code in d > 2 dimensions, which combines a d-dimensional toric code decoder and a local lifting procedure to find a recovery operation. We prove that the Restriction Decoder successfully corrects errors in the color code if and only if the corresponding toric code decoding succeeds. We also estimate the Threshold of the Restriction Decoder for 2D and 3D color code against bit-flip and phase-flip noise with perfect syndrome extraction, and find that the 2D color code threshold is asymptotic to 10.2% on the square-octagon lattice.
Article
Quantum Science & Technology
Cibele Cristina Trinca, J. Carmelo Interlando, Reginaldo Palazzo Jr, Antonio Aparecido de Andrade, Ricardo Augusto Watanabe
Summary: This work presents a procedure for constructing toric quantum error-correcting codes. A new class of infinite family of toric quantum codes is provided by constructing cyclic codes on square lattices. The proposed quantum interleaving technique using the constructed toric quantum codes shows better code rate and coding gain compared to Kitaev's toric quantum codes and Bombin and Martin-Delgado's toric quantum codes.
QUANTUM INFORMATION PROCESSING
(2023)
Article
Physics, Multidisciplinary
Hao-Wen Wang, Yun-Jia Xue, Yu-Lin Ma, Nan Hua, Hong-Yang Ma
Summary: This study builds a CNN decoder to correct errors in the toric code, achieving an improved threshold accuracy for the neural network decoder without needing to verify basic noise.
Article
Quantum Science & Technology
Hanwei Xiao, Xiaoguang Chen
Summary: This paper proposes a framework of quantum convolutional codes that can handle continuous errors, by concatenating GKP code and utilizing the output information of the decoding circuit through multiple iterations to further reduce errors.
QUANTUM INFORMATION PROCESSING
(2022)
Article
Optics
Pedro Parrado-Rodriguez, Manuel Rispler, Markus Mueller
Summary: In this study, an efficient decoder for two-dimensional topological color codes on the 4.8.8 lattice was proposed and studied, with a rescaling approach used to process syndrome information and achieve a threshold of 6.0% for code capacity noise.
Article
Materials Science, Multidisciplinary
M. H. Zarei, J. Abouie
Summary: This study introduces an adjustable frustrated toric code system with a topological line that is immune to nonlinear perturbation and remains robust against local projection operations, paving the way for more resilient topological quantum codes essential for large-scale quantum computing.
Article
Computer Science, Hardware & Architecture
Mohamed Amine Belhamra, El Mamoun Souidi
Summary: Network coding is a novel forwarding technique that promises to change many aspects of networking. This paper introduces Error Correction Network Coding (ECNC), a new approach that introduces redundancy in the time domain for error correction in NC schemes. ECNCs can be used jointly with the space domain error-correcting codes proposed for NC.
Article
Quantum Science & Technology
Li-Yun Zhao, Xiu-Bo Chen, Gang Xu, Jing-Wen Zhang, Yi-Xian Yang
Summary: In this paper, a fault-tolerant error correction scheme is proposed to enable smooth correction process in the presence of quantum gate faults. By introducing a flag qudit in the syndrome-extracted circuit, error detection of coding blocks and quantum gates can be performed in parallel to detect noise and correlated errors. A feasible permutation of quantum gates is given to identify error type and location. The results show that the scheme is valid for any quantum Hamming code, and the required qudit overhead is independent of stabilizer generators' weight and quantity, involving only two ancillary qudits. Therefore, the scheme is promising for achieving a low logical error rate in a fault-tolerant manner.
QUANTUM INFORMATION PROCESSING
(2023)
Article
Multidisciplinary Sciences
Ming Gong, Xiao Yuan, Shiyu Wang, Yulin Wu, Youwei Zhao, Chen Zha, Shaowei Li, Zhen Zhang, Qi Zhao, Yunchao Liu, Futian Liang, Jin Lin, Yu Xu, Hui Deng, Hao Rong, He Lu, Simon C. Benjamin, Cheng-Zhi Peng, Xiongfeng Ma, Yu-Ao Chen, Xiaobo Zhu, Jian-Wei Pan
Summary: The study successfully demonstrated the experimental realization of the [5, 1, 3] code, verifying key aspects such as error identification and correction, logical operations, and state decoding.
NATIONAL SCIENCE REVIEW
(2022)
Article
Physics, Multidisciplinary
Youwei Zhao, Yangsen Ye, He-Liang Huang, Yiming Zhang, Dachao Wu, Huijie Guan, Qingling Zhu, Zuolin Wei, Tan He, Sirui Cao, Fusheng Chen, Tung-Hsun Chung, Hui Deng, Daojin Fan, Ming Gong, Cheng Guo, Shaojun Guo, Lianchen Han, Na Li, Shaowei Li, Yuan Li, Futian Liang, Jin Lin, Haoran Qian, Hao Rong, Hong Su, Lihua Sun, Shiyu Wang, Yulin Wu, Yu Xu, Chong Ying, Jiale Yu, Chen Zha, Kaili Zhang, Yong-Heng Huo, Chao-Yang Lu, Cheng-Zhi Peng, Xiaobo Zhu, Jian-Wei Pan
Summary: This article describes an experimental implementation of an error-correcting surface code on a superconducting quantum processor. By executing multiple consecutive error correction cycles, logical errors were significantly reduced, providing a key step towards scalable fault-tolerant quantum computing.
PHYSICAL REVIEW LETTERS
(2022)
Article
Computer Science, Information Systems
Jin Sima, Jehoshua Bruck
Summary: The study introduces a k-deletion correcting code with optimal redundancy for constant k, and presents encoding/decoding algorithms with low complexity.
IEEE TRANSACTIONS ON INFORMATION THEORY
(2021)
Article
Quantum Science & Technology
Hector Bombin, Chris Dawson, Ryan V. Mishmash, Naomi Nickerson, Fernando Pastawski, Sam Roberts
Summary: This paper presents a comprehensive framework for constructing universal fault-tolerant logical gates, using surface codes and introducing logical blocks defined by low-density parity check (LDPC) codes. Numerical simulations verify the threshold consistency and show the impact of boundaries, defects, and twists on the logical error rate scaling. A novel computational scheme based on twist teleportation is also proposed for further resource reduction.
Article
Engineering, Electrical & Electronic
Woorham Bae, Jin-Woo Han, Kyung Jean Yoon
Summary: This article proposes a technique for in-memory error correction using a Hamming error-correcting code. By utilizing the characteristics of resistive switching memristors, combined with a driving scheme, a fully functional stateful xor logic is achieved, which can effectively detect errors.
IEEE TRANSACTIONS ON ELECTRON DEVICES
(2022)
Article
Computer Science, Information Systems
Andreas Lenz, Rawad Bitar, Antonia Wachter-Zeh, Eitan Yaakobi
Summary: This paper studies function-correcting codes designed to protect the function evaluation of a message against errors. It shows the equivalence between FCCs and irregular-distance codes, and derives general upper and lower bounds on the optimal redundancy of irregular-distance codes. Furthermore, simplified suboptimal bounds are provided for easier evaluation. The paper also applies the general results to specific functions and compares them to standard error-correcting codes.
IEEE TRANSACTIONS ON INFORMATION THEORY
(2023)
Article
Multidisciplinary Sciences
J. Pablo Bonilla Ataides, David K. Tuckett, Stephen D. Bartlett, Steven T. Flammia, Benjamin J. Brown
Summary: Research shows that using the XZZX code for fault-tolerant quantum computation offers remarkable performance and can surpass the hashing bound in experimentally relevant noise parameters. In cases where qubit dephasing is the dominant noise, this code has a practical decoder and exceeds previous thresholds. The code demonstrates favorable sub-threshold resource scaling and maintains advantages when performing fault-tolerant quantum computation, showing better performance and requiring fewer resources compared to the surface code.
NATURE COMMUNICATIONS
(2021)
Article
Computer Science, Information Systems
Simon Burton, Dan Browne
Summary: This paper introduces a new technique for limiting the gates of hypergraph product codes in fault-tolerant quantum computers. It provides a necessary condition on these codes and conjectures that this condition applies to a class of Gallagher codes.
IEEE TRANSACTIONS ON INFORMATION THEORY
(2022)
Article
Multidisciplinary Sciences
Lawrence Z. Cohen, Isaac H. Kim, Stephen D. Bartlett, Benjamin J. Brown
Summary: This paper presents a low-overhead fault-tolerant quantum computing scheme based on quantum low-density parity-check (LDPC) codes, which enables many logical qubits to be encoded using a modest number of physical qubits through long-range interactions. In this approach, logic gates operate through logical Pauli measurements, preserving both the protection of LDPC codes and low overheads in terms of required additional qubits. Compared to surface codes with the same code distance, there are estimated order-of-magnitude improvements in overheads for processing about 100 logical qubits using this approach. Given the high thresholds demonstrated by LDPC codes, it is suggested that fault-tolerant quantum computation at this scale may be achievable with a few thousand physical qubits at comparable error rates to current approaches.
Article
Quantum Science & Technology
Lingling Lao, Alexander Korotkov, Zhang Jiang, Wojciech Mruczkiewicz, Thomas E. O'Brien, Dan E. Browne
Summary: This work presents two software methods to mitigate parasitic errors in two-qubit gates in quantum computing. The first approach utilizes the Cartan's KAK decomposition and applies single-qubit rotations to counteract parasitic gates without additional overhead. The second approach uses a numerical optimization algorithm to recompile a target unitary into the error-parasitic two-qubit gate plus single-qubit gates. The results show that different approaches have advantages in different error regimes, providing guidance for error mitigation in near-term quantum computers.
QUANTUM SCIENCE AND TECHNOLOGY
(2022)
Article
Physics, Applied
Samuel C. Smith, Benjamin J. Brown, Stephen D. Bartlett
Summary: A fault-tolerant quantum computer requires a classical decoding system to interface with quantum hardware for quantum error correction. In order to keep up with the quantum clock speed and communication limitations imposed by the physical architecture, a local predecoder is proposed to make greedy corrections and reduce the amount of syndrome data sent to a standard matching decoder. This approach significantly improves the run time of the global decoder and the communication bandwidth.
PHYSICAL REVIEW APPLIED
(2023)
Article
Optics
Yannick Seis, Benjamin J. Brown, Anders S. Sorensen, Joseph F. Goodwin
Summary: In this work, we improve the memory performance of a noise-biased trapped-ion-qubit memory by incorporating error correction through teleportation of information between two repetition codes written on a pair of qubit registers. We show that our protocol can be achieved with a single global entangling phase gate of remarkably low fidelity, and rebalancing the logical spin-flip and dephasing error rates can significantly lower the error rates of our memory.
Article
Physics, Multidisciplinary
Asmae Benhemou, Toonyawat Angkhanawin, Charles S. Adams, Dan E. Browne, Jiannis K. Pachos
Summary: The researchers investigate the generation of quantum gates by allowing Z3 parafermions to interact, achieving universality. They study the form of the nontopological gate that arises through direct short-range interaction of the parafermion edge modes in a Z3 parafermion chain. The interaction gives rise to a dynamical phase gate on the encoded ground space, generating a non-Clifford gate which can be tuned to belong to even levels of the Clifford hierarchy. The researchers propose an experiment that simulates the braiding and dynamical evolutions of the Z3 topological states with Rydberg atom technology.
PHYSICAL REVIEW RESEARCH
(2023)
Article
Physics, Multidisciplinary
Thomas R. Scruby, Michael Vasmer, Dan E. Browne
Summary: Stabilizer error correcting codes have the ability to project arbitrary errors to Pauli errors, simplifying the physical error correction process. However, logical non-Clifford operations can introduce additional correlations, and previous studies have shown the existence of nonlocal linking charge phenomena in the context of applying a transversal T gate to the three-dimensional color code.
PHYSICAL REVIEW RESEARCH
(2022)
Article
Quantum Science & Technology
Mark A. Webster, Benjamin J. Brown, Stephen D. Bartlett
Summary: We propose an extension to the Pauli stabiliser formalism, called the XP stabiliser formalism, which allows for a wider range of states and codespaces to be represented. We demonstrate an equivalence between XP stabiliser states and 'weighted hypergraph states' and present algorithms for determining the codespace and logical operators for an XP code. Finally, we consider whether measurements of XP operators on XP codes can be classically simulated.
Proceedings Paper
Computer Science, Hardware & Architecture
Lingling Lao, Dan E. Browne
Summary: Researchers developed a quantum compiler named 2QAN to optimize quantum circuits for 2-local qubit Hamiltonian simulation problems. The compiler uses permutation-aware techniques for qubit routing, gate optimization, and scheduling to minimize compilation overhead and achieves better performance than existing compilers.
PROCEEDINGS OF THE 2022 THE 49TH ANNUAL INTERNATIONAL SYMPOSIUM ON COMPUTER ARCHITECTURE (ISCA '22)
(2022)
Article
Quantum Science & Technology
T. R. Scruby, D. E. Browne, P. Webster, M. Vasmer
Summary: This study develops and simulates an explicit recipe for just-in-time decoding scheme in three-dimensional surface codes, based on recent work by B. Brown. It can implement a transversal CCZ operation between three two-dimensional surface codes in linear time. The study presents detailed bounded-height lattice slices through the three-dimensional codes, which retain the code distance and measurement-error detecting properties while allowing dimension-jumping process to expand from/collapse to two-dimensional surface codes on the slice boundaries. The simulation results show a threshold p(c) similar to 0.1% in all three codes, indicating potential for improvement with decoder optimization.
Article
Optics
Shraddha Singh, Andrew S. Darmawan, Benjamin J. Brown, Shruti Puri
Summary: Magic state distillation is a resource-intensive subroutine, and our proposed initialization protocol can reduce resource costs by reducing the error rate of input magic states. By utilizing native gate operations of an underlying qubit architecture, our approach offers substantial advantages in the presence of biased noise.
Article
Quantum Science & Technology
Kaavya Sahay, Benjamin J. Brown
Summary: The color code is a promising approach for fault-tolerant quantum computation. This article introduces a new decoder and evaluates its performance in various scenarios.
Article
Physics, Mathematical
Jacob C. Bridgeman, Benjamin J. Brown, Samuel J. Elman
Summary: The topological entanglement entropy is used to measure long-range quantum correlations in topological phases, with closed form expressions obtained for (2+1)- and (3+1)-dimensional loop gas models. The study focuses on the formulation of results using generalized S-matrices, with a conjecture on their general property and proofs provided in specific cases, including categories up to rank 5.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2022)
Article
Physics, Multidisciplinary
Andrew Patterson, Hongxiang Chen, Leonard Wossnig, Simone Severini, Dan Browne, Ivan Rungger
Summary: In the near term, noisy quantum computers require algorithms with low circuit depth and qubit count. Research shows that introducing a smaller circuit ansatz can overcome the limitations of gradient calculation on noisy devices with a large number of parameters. The main effect of noise is to increase the overlap between states as circuit gates are applied, making discrimination more challenging.
PHYSICAL REVIEW RESEARCH
(2021)
