Article
Quantum Science & Technology
Yang Li, Ruhao Wan, Shixin Zhu
Summary: In this paper, several new classes of maximum distance separable (MDS) codes are constructed using (extended) generalized Reed-Solomon (GRS) codes, and their Euclidean or Hermitian hulls are determined. As applications, new families of entanglement-assisted quantum error-correcting codes (EAQECCs) and MDS EAQECCs are further constructed. Examples of Euclidean self-orthogonal and one-dimensional Euclidean hull MDS codes are shown. Additionally, new general methods for constructing extended GRS codes with (k - 1)-dimensional Hermitian hull and Hermitian self-orthogonal extended GRS codes are provided.
QUANTUM INFORMATION PROCESSING
(2023)
Article
Computer Science, Information Systems
Emmanuel Abbe, Jan Hazla, Ido Nachum
Summary: The paper investigates a new type of linear code that can correct random errors with high probability under a certain level of data loss. This differs from the performance of traditional Reed-Muller codes.
IEEE TRANSACTIONS ON INFORMATION THEORY
(2021)
Article
Engineering, Electrical & Electronic
Nghia Doan, Seyyed Ali Hashemi, Marco Mondelli, Warren J. J. Gross
Summary: This paper presents a novel recursive list decoding algorithm for Reed-Muller codes based on successive permutations. By utilizing a low-complexity successive permutation scheme, the algorithm reduces computational complexity and decoding latency while maintaining error-correction performance and memory consumption.
IEEE TRANSACTIONS ON COMMUNICATIONS
(2022)
Article
Physics, Multidisciplinary
Francisco Revson Fernandes Pereira, Stefano Mancini
Summary: This paper presents a general framework called quantum reading for statistical discrimination of an ensemble of quantum channels. A simple yet effective protocol is proposed to reduce the error probability in distinguishing the ensemble of channels using classical error-correcting codes. The results show that BCH codes in conjunction with Dolinar receivers are the optimal strategy for error mitigation in quantum reading.
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
Computer Science, Information Systems
Dor Elimelech, Hengjia Wei, Moshe Schwartz
Summary: This study focuses on the generalized covering radii of linear codes and their application in data-query protocols. It proves lower and upper bounds on the generalized covering radii of Reed-Muller codes, and also constructs a covering algorithm which can find corresponding codewords efficiently.
IEEE TRANSACTIONS ON INFORMATION THEORY
(2022)
Article
Computer Science, Information Systems
Hiram H. Lopez, Gretchen L. Matthews, Daniel Valvo
Summary: In this work, linear exact repair schemes are proposed for one or two erasures in decreasing monomial-Cartesian codes. Families of augmented Reed-Muller codes and augmented Cartesian codes are used for the repair schemes. Unlike the repair scheme for two erasures in decreasing monomial-Cartesian codes, the repair scheme for two erasures in the augmented codes has no restrictions on the positions of the erasures. Examples are provided where the augmented codes have lower bandwidth compared to other codes.
IEEE TRANSACTIONS ON INFORMATION THEORY
(2022)
Article
Quantum Science & Technology
Jeongwan Haah, Matthew B. Hastings
Summary: This study presents detailed measurement sequences for magic state distillation protocols, which can suppress arbitrary errors on any part of a protocol assuming errors across qubits are independent. The protocol operates on a two-dimensional square grid by measuring ZZ on horizontal qubit pairs, XX on vertical pairs, and Z, X on single qubits when provided with input magic states.
Article
Engineering, Electrical & Electronic
Vera Miloslavskaya, Branka Vucetic, Yonghui Li, Giyoon Park, Ok-Sun Park
Summary: A novel method for recursively constructing a set of precoded polar codes of various rates and lengths is presented, aiming to minimize decoding error probability under constraints such as minimum distance, supercode, and subcode. Simulation results show that the proposed precoded polar codes offer better frame error rate compared to polar codes with CRC and e-BCH polar subcodes under certain decoding algorithms.
IEEE TRANSACTIONS ON COMMUNICATIONS
(2021)
Article
Physics, Multidisciplinary
Oliver Hahn, Alessandro Ferraro, Lina Hultquist, Giulia Ferrini, Laura Garcia-Alvarez
Summary: Quantum resource theories offer a powerful framework for understanding and quantifying quantum phenomena. This paper introduces a resource measure, based on bosonic codes, for the sought-after property of "magic" in fault-tolerant quantum computers. By utilizing the Gottesman-Kitaev-Preskill code and considering the Wigner negativity, the authors provide analytical expressions that extend the current analysis to systems of up to 12 qubits.
PHYSICAL REVIEW LETTERS
(2022)
Article
Mathematics, Applied
Jose Joaquin Bernal, Juan Jacobo Simon
Summary: In this paper, a modified permutation decoding algorithm is proposed for affine-invariant codes with respect to certain type of information sets. The algorithm is applied to the first-order Reed-Muller codes with the information sets introduced in [2], significantly improving the error correction capability compared to existing results in this field.
FINITE FIELDS AND THEIR APPLICATIONS
(2023)
Article
Mathematics
Claude Carlet, Patrick Sole
Summary: This paper determines the weight spectra of the Reed-Muller codes RM(m-3, m) for m > 6 and RM(m-4, m) for m > 8. The method used is induction on m, utilizing the property that the sum of two weights in RM(r-1, m-1) is a weight in RM(r, m), and the characterization by Kasami and Tokura of weights in RM(r, m) between its minimum distance 2m-r and double this minimum distance. The weights of RM(3, 8) and RM(4, 9) are also derived using the same technique. The paper concludes with a conjecture on the weights of RM(m-c, m) for a fixed c and sufficiently large m.
DISCRETE MATHEMATICS
(2023)
Review
Quantum Science & Technology
Yiting Liu, Zhi Ma, Lan Luo, Chao Du, Yangyang Fei, Hong Wang, Qianheng Duan, Jing Yang
Summary: This paper provides a survey on magic states, which have been widely studied as resource states for fault-tolerant universal quantum computing. It is found that magic states can combine with Clifford gates to achieve universal quantum computation. However, preparing the magic state with high fidelity and low overhead is a crucial problem for realizing universal quantum computation.
QUANTUM SCIENCE AND TECHNOLOGY
(2023)
Article
Computer Science, Information Systems
Rina Miyajima, Ryutaroh Matsumoto
Summary: This paper introduces classical secret sharing schemes and quantum secret sharing schemes, and proposes a quantum secret sharing scheme that allows for more flexible design of access structures and higher efficiency.
Article
Engineering, Electrical & Electronic
Nghia Doan, Seyyed Ali Hashemi, Warren J. Gross
Summary: A novel permuted fast successive-cancellation list decoding algorithm with fast Hadamard transform is proposed in this paper. By reducing computational complexity, decoding latency, and memory consumption, the proposed algorithm achieves similar error-correction performance compared to the state-of-the-art simplified successive-cancellation decoder.
IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY
(2022)
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
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
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, 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)
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.
Proceedings Paper
Computer Science, Hardware & Architecture
Lingling Lao, Prakash Murali, Margaret Martonosi, Dan Browne
Summary: The study aims to balance between application expressivity and calibration overhead in near-term quantum computing systems. By using numerical optimization, NuOp efficiently decomposes application operations into different hardware gate types. Results show that implementing 4-8 types of 2Q gates can achieve similar expressivity as a full continuous gate family while significantly reducing calibration overheads.
2021 ACM/IEEE 48TH ANNUAL INTERNATIONAL SYMPOSIUM ON COMPUTER ARCHITECTURE (ISCA 2021)
(2021)
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)
Article
Quantum Science & Technology
T. R. Scruby, D. E. Browne
Article
Quantum Science & Technology
Sergey Bravyi, Dan Browne, Padraic Calpin, Earl Campbell, David Gosset, Mark Howard
Article
Optics
Michael Vasmer, Dan E. Browne
Article
Optics
Luciana Henaut, Lorenzo Catani, Dan E. Browne, Shane Mansfield, Anna Pappa
Article
Optics
Lorenzo Catani, Dan E. Browne
Article
Optics
James M. Auger, Hussain Anwar, Mercedes Gimeno-Segovia, Thomas M. Stace, Dan E. Browne
