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
Physics, Multidisciplinary
Nathanan Tantivasadakarn, Ruben Verresen, Ashvin Vishwanath
Summary: This study demonstrates the existence of a wide range of non-Abelian states, specifically those with a Lagrangian subgroup, that can be created using minimal ingredients of a finite-depth circuit and a single round of measurement. It also shows that D4 non-Abelian topological order can be realized on Google's quantum processors using a depth-11 circuit and a single layer of measurements, highlighting counterintuitive features of non-Abelian phases.
PHYSICAL REVIEW LETTERS
(2023)
Article
Optics
Ze Zhang, Xinyue Long, Xiuzhu Zhao, Zidong Lin, Kai Tang, Hongfeng Liu, Xiaodong Yang, Xinfang Nie, Jiansheng Wu, Jun Li, Tao Xin, Keren Li, Dawei Lu
Summary: This paper proposes a method based on quantum scattering circuit to directly and efficiently measure the modular transformation matrix of topological orders. The method is successfully implemented in a nuclear magnetic resonance quantum simulator to simulate both Abelian and non-Abelian topological orders. This work opens up new possibilities for studying topological orders in circuit-based quantum simulators.
Article
Materials Science, Multidisciplinary
Yu-Hsueh Chen, Ching-Yu Huang, Ying-Jer Kao
Summary: The research proposes a unified scheme to identify phase transitions out of the Z(2) Abelian topological order, including the transition to a non-Abelian chiral spin liquid. By computing the overlap of minimally entangled states, the study demonstrates the transition between Abelian and non-Abelian topological orders, as well as the transformation of anyons in the process. Furthermore, the research shows that both LG and SG states have infinite correlation length in the non-Abelian regime, consistent with the no-go theorem regarding the gaplessness of a chiral PEPS.
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
Ying-Hai Wu, Hong-Hao Tu
Summary: In this study, a chiral spin liquid constructed using the parton theory is investigated. It is found that the edge physics of this state exhibits an emergent SO(5) symmetry, which is calculated by counting the edge states in the low-lying SO(5)1 CFT towers. The entanglement spectrum of the chiral spin liquid generated through tensor network methods confirms the SO(5)1 counting and reveals an additional feature of multiple branches.
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
Mathematics
J. Carmelo Interlando, Trajano Pires da Nobrega Neto, Jose Valter Lopes Nunes, Jose Othon Dantas Lopes
Summary: A construction of laminated lattices of full diversity in odd dimensions from 3 to 15 is presented using a combination of number fields and error-correcting codes. The lattice is obtained through two steps involving the Abelian number field and the Minkowski homomorphism of a Z-submodule of F's ring of integers. This submodule is defined by parity-check matrices of Reed-Solomon codes and a chosen linear code over GF(p) or Z/4Z.
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS
(2021)
Article
Materials Science, Multidisciplinary
Takumi Sanno, Shunsuke Miyazaki, Takeshi Mizushima, Satoshi Fujimoto
Summary: The study shows that after the interchange of vortices, the lowest vortex-bound states accumulate a geometric phase, while errors caused by dynamical phases are negligibly small, regardless of interactions of MZMs.
Article
Materials Science, Multidisciplinary
Yixuan Huang, W. Zhu, Shou-Shu Gong, Hong-Chen Jiang, D. N. Sheng
Summary: In this study, the ground-state properties of a spin-1 Heisenberg model on a square lattice were investigated. Using density matrix renormalization group calculation, a global phase diagram including various magnetic order phases and an emergent quantum spin liquid phase was mapped out. It was found that the spin liquid is a bosonic non-Abelian Moore-Read state, and a stripe magnetic order coexists with the spin liquid.
Article
Materials Science, Multidisciplinary
Yusuke Masaki, Takeshi Mizushima, Muneto Nitta
Summary: In this paper, the researchers demonstrate the existence and stability of non-Abelian half-quantum vortices (HQVs) in P-3(2) superfluids. They find that a singly quantized vortex is destabilized into a pair of two non-Abelian HQVs and each HQV carries a topologically protected Majorana fermion, characterizing twofold non-Abelian anyons.
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
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
Quantum Science & Technology
Julio Carlos Magdalena de la Fuente, Nicolas Tarantino, Jens Eisert
Summary: Long-ranged entangled topological phases can protect quantum information from unwanted local errors, but using general topological orders for practical error correction remains largely unfulfilled. This work shows that Abelian twisted quantum double models can be used for quantum error correction, establishing a new connection between condensed matter physics and quantum information theory.
Article
Computer Science, Information Systems
Wentu Song, Nikita Polyanskii, Kui Cai, Xuan He
Summary: This paper explores the construction of deletion and substitution correcting codes with low redundancy and efficient encoding/decoding. By simplifying existing methods and modifying syndrome compression techniques, a family of binary deletion and substitution correcting codes is proposed, with slight improvements for specific cases, as well as systematic deletion correcting codes being constructed.
IEEE TRANSACTIONS ON INFORMATION THEORY
(2022)
Article
Physics, Multidisciplinary
Daniel Miller, Daniel Loss, Ivano Tavernelli, Hermann Kampermann, Dagmar Bruss, Nikolai Wyderka
Summary: The Shor-Laflamme distribution is a set of local unitary invariants that measure k-body correlations in a quantum state. We demonstrate that the distribution of graph states can be obtained by solving a graph-theoretical problem, allowing for the calculation of mean and variance using graph properties. We also derive closed expressions for the distribution of certain graph state families. Our results provide insights into quantum error-correcting codes and the geometry of quantum states. We propose an entanglement criterion based on the Shor-Laflamme distribution, which can be applied to higher-dimensional systems.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2023)
Article
Physics, Multidisciplinary
J. Yoneda, J. S. Rojas-Arias, P. Stano, K. Takeda, A. Noiri, T. Nakajima, D. Loss, S. Tarucha
Summary: Research shows strong noise correlation between neighboring silicon spin qubits, with electric field fluctuations creating strongly correlated errors.
Article
Materials Science, Multidisciplinary
Katharina Laubscher, Dmitry Miserev, Vardan Kaladzhyan, Daniel Loss, Jelena Klinovaja
Summary: We study the spin configurations of magnetic impurities near the edge of a two-dimensional topological superconductor through both analytical and numerical methods. We find that the spin of a single impurity tends to align along the edge due to the interaction between the impurity and the gapless Majorana edge states. Additionally, when two impurities are placed close to the edge, the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between them is mainly mediated by the Majorana edge states, resulting in a ferromagnetic alignment of the spins along the edge. This effect can be utilized for detecting the helical Majorana edge states.
Article
Materials Science, Multidisciplinary
Alexander Mook, Rhea Hoyer, Jelena Klinovaja, Daniel Loss
Summary: We study quantum condensed matter systems where particle number is not conserved, leading to topological anticrossings in the spectrum due to hybridization of states from different particle-number sectors. This phenomenon is observed in fully saturated spin-anisotropic quantum magnets, where single magnons hybridize with magnon bound pairs. The resulting chiral edge excitations are composite particles with mixed spin-multipolar character, showing genuine quantum mechanical effects that vanish in the classical limit. These findings have implications for intrinsic anomalous Hall-type transport, suggesting that fully polarized quantum magnets can serve as a promising platform for studying topological effects caused by hybridizations between particle-number sectors.
Article
Materials Science, Multidisciplinary
Melina Luethi, Katharina Laubscher, Stefano Bosco, Daniel Loss, Jelena Klinovaja
Summary: Planar Josephson junctions made of semiconductors with strong spin-orbit interaction (SOI) offer a promising platform for hosting Majorana bound states (MBSs). Previous studies focused on electron gases with linear momentum-dependent SOI, whereas a two-dimensional hole gas in planar germanium (Ge) exhibits cubic momentum-dependent SOI. However, we demonstrate that due to its particularly large SOI, Ge is a favorable material for MBS emergence. Using a discretized model, we numerically simulate a Ge planar Josephson junction and find that even cubic SOI can lead to the formation of MBSs. Interestingly, we observe an asymmetric phase diagram in the presence of cubic SOI. Furthermore, trivial Andreev bound states can mimic the signatures of MBSs in a Ge planar Josephson junction, posing challenges for experimental detection.
Article
Materials Science, Multidisciplinary
Silas Hoffman, Daniel Loss, Yaroslav Tserkovnyak
Summary: Spin superfluidity in low-dimensional systems with small spins suffers from strong quantum fluctuations, affecting its topological protection. By studying spin transport through a finite spin-1/2 magnetic chain, we investigate the inheritance of spin superfluidity from classical magnets. We show that the topological properties of semiclassical spin superfluids are related to topological superconductivity in the fermionic representation. In particular, we observe efficient spin transmission through the magnetic region at a characteristic resonant length, which is influenced by the boundary Majorana zero modes.
Article
Materials Science, Multidisciplinary
Melina Luethi, Henry F. Legg, Katharina Laubscher, Daniel Loss, Jelena Klinovaja
Summary: In this study, we investigate superconductor-normal-superconductor-normal-superconductor (SNSNS) planar Josephson junctions in hole systems. By manipulating the superconducting phase difference, we demonstrate the possibility of achieving a topological superconducting phase with Majorana bound states, which overcomes previous experimental challenges.
Article
Physics, Applied
J. S. Rojas-Arias, A. Noiri, P. Stano, T. Nakajima, J. Yoneda, K. Takeda, T. Kobayashi, A. Sammak, G. Scappucci, D. Loss, S. Tarucha
Summary: In this study, we detected correlations in qubit-energy fluctuations of non-neighboring qubits in isotopically purified Si/Si-Ge quantum dots. The correlation coefficient reached 10% for a next-nearest-neighbor qubit-pair separated by 200 nm at low frequencies where the noise is strongest. We also found correlations with the charge-sensor signal reaching up to 70%, proving the electrical origin of the observed noise. A simple theoretical model accurately reproduced the measurements and predicted a polynomial decay of correlations with interqubit distance. These results quantify the long-range correlations of noise in quantum-dot spin-qubit arrays, which are essential for scalability and fault tolerance.
PHYSICAL REVIEW APPLIED
(2023)
Article
Materials Science, Multidisciplinary
Henry F. Legg, Daniel Loss, Jelena Klinovaja
Summary: This paper investigates the superconducting diode effect caused by the magnetic field and proximity effect, and explores its applications in detecting inversion symmetry breaking and topological superconductivity phase transition.
Article
Materials Science, Multidisciplinary
Richard Hess, Henry F. Legg, Daniel Loss, Jelena Klinovaja
Summary: This study investigates the prevalence of zero-energy bound states in helical spin-chain systems and finds that they are less common than previously thought. This discovery reduces the experimental barrier to identifying Majorana bound states.
Article
Materials Science, Multidisciplinary
Tamas Haidekker Galambos, Flavio Ronetti, Bence Hetenyi, Daniel Loss, Jelena Klinovaja
Summary: In this hybrid quantum Hall-superconductor system, nonlocal crossed Andreev reflection can occur due to the distortion effect of the Maxwell equations, resulting in a gap in the spectrum of the edge states. Numerical calculations also reveal the existence of negative resistance and stable zero-energy local density of states, which may be related to the emergence of Majorana bound states.
Review
Physics, Applied
Peter Stano, Daniel Loss
Summary: This Technical Review collects and curates experimentally achieved values of selected performance characteristics of semiconductor spin qubits in electrically controlled nanostructures. It aims to provide a community source for comparing different spin-qubit platforms using agreed definitions of figures of merit. The focus is on the values of these characteristics reported in the literature, rather than their motivation or significance. The Review surveys the progress of semiconducting spin qubits over the past two decades in terms of coherence, speed, fidelity, and multi-qubit array size.
NATURE REVIEWS PHYSICS
(2022)
Article
Materials Science, Multidisciplinary
Aleksandr E. Svetogorov, Daniel Loss, Jelena Klinovaja
Summary: In this theoretical study, we investigate a Josephson junction between superconductors in the presence of quasiparticle poisoning. We find that the voltage signals from the junction in both the trivial and topological phases are distinctive enough to distinguish between trivial Andreev and topological Majorana bound states. Furthermore, these voltage signatures can be used to directly measure the quasiparticle poisoning rates in both phases.
Article
Materials Science, Multidisciplinary
Henry F. Legg, Daniel Loss, Jelena Klinovaja
Summary: This study investigates the effects of coupling between a superconducting layer and a topological insulator nanowire. The research shows that metallization of states in the nanowire caused by the superconductor leads to a shift of energy sub-bands and a reduction in the sub-band gap size. However, metallization effects in the nanowires can also enhance the sub-band splitting, which is crucial for achieving topological superconductivity. Unlike in semiconductors, the metallization effects in topological insulator nanowires can be relatively easily mitigated.
Article
Materials Science, Multidisciplinary
Flavio Ronetti, Daniel Loss, Jelena Klinovaja
Summary: We theoretically investigate the spiral-staircase Heisenberg spin-1/2 ladder with antiferromagnetic long-range spin interactions and a uniform magnetic field. We show that the system exhibits a partially gapped magnetic phase with fractional spin excitations when the magnetizations of the two chains forming the ladder satisfy certain resonance conditions. These fractional spin excitations can be probed and measured through magnetization and spin currents, and in some cases, the spin conductance reaches universal values.