Article
Quantum Science & Technology
Clarice Dias de Albuquerque, Giuliano Gadioli La Guardia, Reginaldo Palazzo, Catia Regina de Oliveira Quilles Queiroz, Vandenberg Lopes Vieira
Summary: This paper presents constructions of asymmetric quantum error-correcting codes, including topological quantum codes and hyperbolic asymmetric codes. By investigating the structure and properties of topological quantum codes on Euclidean and hyperbolic surfaces and analyzing parameters such as encoding rates and distances, the performance of topological codes can be determined. By introducing asymmetry and different tessellations, quantum codes with different error protection characteristics can be generated.
QUANTUM INFORMATION PROCESSING
(2022)
Article
Quantum Science & Technology
Eric Huang, Arthur Pesah, Christopher T. Chubb, Michael Vasmer, Arpit Dua
Summary: Tailored three-dimensional topological codes are customized for enhanced storage performance under biased Pauli noise. By applying Clifford deformations, these codes exhibit a threshold error rate of 50% under infinitely biased Pauli noise. Various topological codes and fracton models are used as examples to study the threshold error rates at finite bias, and a rotated layout for the three-dimensional surface code is presented.
Article
Quantum Science & Technology
Arpit Dua, Tomas Jochym-O'Connor, Guanyu Zhu
Summary: In this study, the performance of fractal surface codes as fault-tolerant quantum memories is investigated. Decoding strategies for bit-flip and phase-flip errors in these codes are proven to exist. The sweep decoder, originally designed for regular 3D surface codes, is successfully adapted to the fractal surface codes by making suitable modifications on the boundaries. The minimum-weight-perfect-matching (MWPM) decoder is employed for phase-flip errors. The results show sustainable fault-tolerant threshold and code capacity threshold for specific fractal surface codes.
Article
Engineering, Electrical & Electronic
Hiteshvi Manish Solanki, Pradeep Kiran Sarvepalli
Summary: This study focuses on the performance of topological subsystem color codes (TSCCs) over the erasure channel. Two erasure decoders are proposed, employing a mapping of TSCCs to topological color codes (TCCs) and the technique of gauge fixing. Experimental results show the threshold of fault-tolerant gates derived from TSCCs, and the performance can be further improved by combining with an optimal erasure decoder for topological color codes.
IEEE TRANSACTIONS ON COMMUNICATIONS
(2023)
Article
Multidisciplinary Sciences
Marcelo Amaral, David Chester, Fang Fang, Klee Irwin
Summary: The concrete realization of topological quantum computing using low-dimensional quasiparticles, known as anyons, remains an important challenge. This study proposes quasicrystal materials as a natural platform for topological quantum computing and shows their anyonic behavior. The correspondence between different-dimensional quasicrystals and the fusion Hilbert spaces of the Fibonacci anyons is studied, and a concrete encoding method for topological quantum information processing on quasicrystals is presented.
Article
Optics
Pengcheng Liao, Barry C. Sanders, David L. Feder
Summary: Determining whether a given family of quantum states is topologically ordered is a significant problem in condensed matter physics and quantum information theory. Researchers have derived necessary and sufficient conditions for graph states to be in a specific class of quantum error-correction code states. They have applied these conditions to various graph families, including star and complete graphs, and discussed which ones are topologically ordered and how to construct the codewords. The researchers have also used this formalism to construct several codes with macroscopic distance, including a three-dimensional topological code with a large number of encoded logical qubits.
Article
Physics, Multidisciplinary
Kai Meinerz, Chae-Yeun Park, Simon Trebst
Summary: This study introduces a neural network based decoder that is scalable for large-scale quantum circuits, faster and more effective than traditional decoders, can significantly reduce error rates in practical applications, and increase the actual error threshold to more than 15% above conventional error correction algorithms, even in the presence of measurement errors.
PHYSICAL REVIEW LETTERS
(2022)
Article
Physics, Multidisciplinary
Florian Venn, Jan Behrends, Benjamin Beri
Summary: Statistical mechanics mappings provide insights on quantum error correction, but existing mappings ignore coherent errors. We map the surface code with coherent errors to a 2D Ising model with complex couplings, and further to a 2D Majorana scattering network. Our mappings reveal commonalities and differences in correcting coherent and incoherent errors. The theoretically achievable storage threshold for coherent errors is represented by the rotation angle 0th, which we numerically find to be 0.14x.
PHYSICAL REVIEW LETTERS
(2023)
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
Physics, Particles & Fields
Claudio Bonanno, Claudio Bonati, Massimo D'Elia
Summary: The study simulated 4d SU(N) pure-gauge theories at large N using a parallel tempering scheme, reducing the autocorrelation time and refining the quartic coefficient of the theta-dependence of the vacuum energy b(2) with high accuracy. This approach achieved results comparable to the large-N limit of the topological susceptibility.
JOURNAL OF HIGH ENERGY PHYSICS
(2021)
Article
Astronomy & Astrophysics
Mamiya Kawaguchi, Shinya Matsuzaki, Akio Tomiya
Summary: The study reveals a significant impact of nonperturbative thermal loop corrections on the QCD topological susceptibility around the pseudo-critical temperature of the chiral crossover, leading to flavor breaking in the axial anomaly and QCD theta vacuum in high temperature QCD. This critical flavor violation cannot be explained by chiral perturbation theory or the dilute instanton gas approximation, and may have implications on the thermal history and cosmological evolution of QCD axion.
Article
Physics, Multidisciplinary
Christophe Piveteau, David Sutter, Sergey Bravyi, Jay M. Gambetta, Kristan Temme
Summary: The Eastin-Knill theorem states the impossibility of a universal set of transversal gates for any quantum error-correcting code; implementing noisy encoded T gates remains a challenge and may hinder practical applications in the near future; combining error correction and error mitigation methods allows for the implementation of Clifford + T circuits on small error-corrected devices, potentially surpassing state-of-the-art classical simulation algorithms.
PHYSICAL REVIEW LETTERS
(2021)
Article
Physics, Multidisciplinary
Xiaoyang Shen, Zhengzhi Wu, Linhao Li, Zhehan Qin, Hong Yao
Summary: This Letter investigates the fracton topological order of higher dimensional fracton models at nonzero critical temperature T-c, and demonstrates the existence of a finite critical temperature T-c. By analyzing the free energy of a typical 4D X-cube model using duality, it is shown that a finite critical temperature T-c exists. The expectation value of the 't Hooft loops in the 4D X-cube model reveals a confinement-deconfinement phase transition at finite temperature. Additionally, an alternative no-go theorem for finite-temperature quantum fracton topological order is proposed.
PHYSICAL REVIEW RESEARCH
(2022)
Article
Multidisciplinary Sciences
Lin Zhang, Wei Jia, Xiong-Jun Liu
Summary: This study uncovers the universal topological quench dynamics associated with equilibrium topological phases and establishes a general framework. The study finds that the dimension-reduced topology of a generic d-dimensional topological phase, represented by a Dirac-type Hamiltonian with Z2 invariant defined on high symmetry momenta, can be characterized by certain arbitrary discrete momenta on the highest-order bandinversion surfaces of the Brillouin zone. This dimension-reduced topology has a unique correspondence to the topological pattern emerging in far-from-equilibrium quantum dynamics, thereby providing the dynamical hallmark of the equilibrium topological phase.
Article
Multidisciplinary Sciences
Renyu Wang, Leonid P. Pryadko
Summary: Generalized bicycle codes are a type of quantum error-correcting code constructed from binary circulant matrices. They have linear distance scaling and low-weight stabilizer generators, which can potentially improve performance in the presence of measurement errors.
