Related papers: Projective plane and planar quantum codes
The surface code is one of the most successful approaches to topological quantum error-correction. It boasts the smallest known syndrome extraction circuits and correspondingly largest thresholds. Defect-based logical encodings of a new…
Errors are inevitable during all kinds quantum informational tasks and quantum error-correcting codes (QECCs) are powerful tools to fight various quantum noises. For standard QECCs physical systems have the same number of energy levels.…
Single-shot quantum error correction has the potential to speed up quantum computations by removing the need for multiple rounds of syndrome extraction in order to be fault-tolerant. Using Quantinuum's H2 trapped-ion quantum computer, we…
A common approach to studying the performance of quantum error correcting codes is to assume independent and identically distributed single-qubit errors. However, the available experimental data shows that realistic errors in modern…
The spin states of single electrons in gate-defined quantum dots satisfy crucial requirements for a practical quantum computer. These include extremely long coherence times, high-fidelity quantum operation, and the ability to shuttle…
We develop a point of view on reduction of multiplicative proof nets based on quantum error-correcting codes. To each proof net we associate a code, in such a way that cut-elimination corresponds to error correction.
An efficient coding circuit is given for the perfect quantum error correction of a single qubit against arbitrary 1-qubit errors within a 5 qubit code. The circuit presented employs a double `classical' code, i.e., one for bit flips and one…
A Q-homology plane is a normal complex algebraic surface having trivial rational homology. We obtain a structure theorem for Q-homology planes with smooth locus of non-general type. We show that if a Q-homology plane contains a non-quotient…
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…
This paper presents a computer program, written in Maple, that allows a user to simulate certain aspects of Shor's quantum factoring algorithm on a desktop or laptop computer. The program does not simulate the unitary operations carried out…
We describe a family of quantum error-correcting codes which generalize both the quantum hypergraph-product (QHP) codes by Tillich and Z\'emor, and all families of toric codes on $m$-dimensional hypercubic lattices. Similar to the latter,…
The rotation of trapped molecules offers a promising platform for quantum technologies and quantum information processing. In parallel, quantum error correction codes that can protect quantum information encoded in rotational states of a…
In the implementation of quantum information systems, one type of Pauli error, such as phase-flip errors, may occur more frequently than others, like bit-flip errors. For this reason, quantum error-correcting codes that handle asymmetric…
Of the many potential hardware platforms, superconducting quantum circuits have become the leading contender for constructing a scalable quantum computing system. All current architecture designs necessitate a 2D arrangement of…
Foliated quantum codes are a resource for fault-tolerant measurement-based quantum error correction for quantum repeaters and for quantum computation. They represent a general approach to integrating a range of possible quantum error…
Topological error-correcting codes, such as surface codes and color codes, are promising because quantum operations are realized by two-dimensionally (2D) arrayed quantum bits (qubits). However, physical wiring of electrodes to qubits is…
Given their potential for fault-tolerant operations, topological quantum states are currently the focus of intense activity. Of particular interest are topological quantum error correction codes, such as the surface and planar stabilizer…
The all-photonic quantum repeater (APQR) is a promising repeater scheme to realize long-distance quantum communication. For a practical APQR, an indispensable requirement is the robustness of the repeater graph state (RGS) against photon…
For each integer $k \in [0,9]$, we count the number of plane cubic curves defined over a finite field $\mathbb{F}_q$ that do not share a common component and intersect in exactly $k\ \mathbb{F}_q$-rational points. We set this up as a…
We report an experimental demonstration of a complied version of Shor's algorithm using four photonic qubits. We choose the simplest instance of this algorithm, that is, factorization of N=15 in the case that the period $r=2$ and exploit a…