Related papers: Asymptotically good CSS-T codes and a new construc…
Algebraic-geometric codes on Garcia-Stichtenoth family of curves are used to construct the asymptotically good quantum codes.
In this paper, necessary and sufficient conditions for the self-orthogonality of t-generator quasi-cyclic (QC) codes are presented under the Euclidean, Hermitian, and symplectic inner products, respectively. Particularly, by studying the…
This is a manuscript of a chapter prepared for a book. The good codes possess large information length and large minimum distance. A class of codes is said to be asymptotically good if there exists a positive real $\delta$ such that, for…
Quantum error correction is an essential ingredient for reliable quantum computation for theoretically provable quantum speedup. Topological color codes, one of the quantum error correction codes, have an advantage against the surface codes…
This paper introduces a new class of error-correcting codes constructed from the ideal lattices of finite commutative ternary Gamma-semirings (TGS). Unlike classical linear or ring-linear codes, which rely on binary operations, TGS codes…
Due to some practical applications, linear complementary dual (LCD) codes and self-orthogonal codes have attracted wide attention in recent years. In this paper, we use simplicial complexes for construction of an infinite family of binary…
We investigate the emergence of quantum chaos and unitary T-design behavior in derandomized Clifford+T circuits using causal cover architectures. Motivated by the need for deterministic constructions that can exhibit chaotic behavior across…
Encoding quantum information onto bosonic systems is a promising route to quantum error correction. In a cat code, this encoding relies on the confinement of the system's dynamics onto the two-dimensional manifold spanned by Schr\"odinger…
Special functions, coding theory and $t$-designs have close connections and interesting interplay. A standard approach to constructing $t$-designs is the use of linear codes with certain regularity. The Assmus-Mattson Theorem and the…
We develop a framework for constructing quantum error-correcting codes and logical gates for three types of spaces -- composite permutation-invariant spaces of many qubits or qudits, composite constant-excitation Fock-state spaces of many…
Coherent errors are a dominant noise process in many quantum computing architectures. Unlike stochastic errors, these errors can combine constructively and grow into highly detrimental overrotations. To combat this, we introduce a simple…
The overhead cost of performing universal fault-tolerant quantum computation for large scale quantum algorithms is very high. Despite several attempts at alternative schemes, magic state distillation remains one of the most efficient…
Quantum low-density parity check (qLDPC) codes are among the leading candidates to realize error-corrected quantum memories with low qubit overhead. Potentially high encoding rates and large distance relative to their block size make them…
We introduce a flexible and graphically intuitive framework that constructs complex quantum error correction codes from simple codes or states, generalizing code concatenation. More specifically, we represent the complex code constructions…
A method for the implementation of a universal set of fault-tolerant logical gates is presented using homological product codes. In particular, it is shown that one can fault-tolerantly map between different encoded representations of a…
We revisit computationally relaxed locally decodable codes (crLDCs) (Blocki et al., Trans. Inf. Theory '21) and give two new constructions. Our first construction is a Hamming crLDC that is conceptually simpler than prior constructions,…
In sphere of research of discrete optimization algorithms efficiency the important place occupies a method of polynomial reducibility of some problems to others with use of special purpose components. In this paper a novel method of compact…
The threshold theorem promises a path to fault-tolerant quantum computation, provided the physical error rate is below a critical threshold. While transversal gates efficiently implement logical operations, they propagate errors and can…
Topological codes have many desirable properties that allow fault-tolerant quantum computation with relatively low overhead. A core challenge for these codes, however, is to achieve a low-overhead universal gate set with limited…
Topological subsystem codes in three spatial dimensions allow for quantum error correction with no time overhead, even in the presence of measurement noise. The physical origins of this single-shot property remain elusive, in part due to…