Related papers: Non-Pauli Observables for CWS Codes
The most well-known tool for studying contextuality in quantum computation is the n-qubit stabilizer state tableau representation. We provide an extension that describes not only the quantum state, but is also outcome deterministic. The…
While stabilizer tableaus have proven exceptionally useful as a descriptive tool for additive quantum codes, they offer little guidance for concrete constructions or coding algorithm analysis. We introduce a representation of stabilizer…
The quantum hashing bound guarantees that rates up to $1-H(p_I, p_X, p_Y, p_Z)$ are achievable for memoryless Pauli channels, but it is not generally tight. A known way to improve achievable rates for certain asymmetric Pauli channels is to…
Quantum error-correction codes (QECCs) are a vital ingredient of quantum computation and communication systems. In that context it is highly desirable to design QECCs that can be represented by graphical models which possess a structure…
Additive codes and some nonadditive codes use the single and multiple invariant subspaces of the stabilizer G, respectively, to construct quantum codes, so the selection of the invariant subspaces is a key problem. In this paper, I provide…
We introduce new algorithms and provide example constructions of stabilizer models for the gapped boundaries, domain walls, and $0D$ defects of Abelian composite-dimensional twisted quantum doubles. Using the physically intuitive concept of…
We construct explicitly two infinite families of genuine nonadditive 1-error correcting quantum codes and prove that their coding subspaces are 50% larger than those of the optimal stabilizer codes of the same parameters via the linear…
In this paper, based on the nonbinary graph state, we present a systematic way of constructing good non-binary quantum codes, both additive and nonadditive, for systems with integer dimensions. With the help of computer search, which…
Quantum low density parity check (qLDPC) codes are an attractive alternative to the surface code due to their relatively high code rate and distance. However, unlike the surface code which has simple, geometrically local, stabilizer checks,…
We consider the problem of a generic stabilizer Hamiltonian under local, incoherent Pauli errors. Using two different approaches -- (i) Haah's polynomial formalism arXiv:1204.1063 and (ii) the homological perspective on CSS codes -- we…
We study the hardness of the problem of finding the distance of quantum error-correcting codes. The analogous problem for classical codes is known to be NP-hard, even in approximate form. For quantum codes, various problems related to…
Storing quantum information in a quantum error correction code can protect it from errors, but the ability to transform the stored quantum information in a fault tolerant way is equally important. Logical Pauli group operators can be…
Entanglement is a central concept in quantum information and a key resource for many quantum protocols. In this work we propose and analyze a class of entanglement witnesses that detect the presence of entanglement in subsystems of…
This paper utilizes the recently proposed cubic observer to estimate the state of a class of nonlinear systems. The cubic observer is proposed as an alternative to linear observers for improved convergence rate and robustness. It is shown…
We obtain novel nonlinear Schr\"{o}dinger-Pauli equations through a formal non-relativistic limit of appropriately constructed nonlinear Dirac equations. This procedure automatically provides a physical regularisation of potential…
Floquet codes are a recently discovered type of quantum error correction code. They can be thought of as generalising stabilizer codes and subsystem codes, by allowing the logical Pauli operators of the code to vary dynamically over time.…
We propose a nonuniform quantized decoder for polar codes. The design metric of the quantizers is to minimize the distortion incurred by quantization. The quantizers are obtained via dynamic programming and the optimality of the quantizer…
Tailored topological stabilizer codes in two dimensions have been shown to exhibit high storage threshold error rates and improved subthreshold performance under biased Pauli noise. Three-dimensional (3D) topological codes can allow for…
The stochastic quantisation technique of Parisi and Wu is extended to study non-equilibrium statistical mechanics. We show that this scheme is capable of handling white as well as coloured noises. PACS numbers: 64.60.-i; 64.60.Ak; 64.60.Fr;…
We introduce homological measurement, a framework for measuring the logical Pauli operators encoded in CSS stabilizer codes. The framework is based on the algebraic description of such codes as chain complexes. Protocols such as lattice…