Related papers: Topological graph states and quantum error correct…
The codeword stabilized ("CWS") quantum codes formalism presents a unifying approach to both additive and nonadditive quantum error-correcting codes (arXiv:0708.1021). This formalism reduces the problem of constructing such quantum codes to…
Topological quantum field theories (TQFT) encode quantum correlations in topological features of spaces. In this work, we leverage this feature to explore how information encoded in TQFTs can be stored and retrieved in the presence of local…
Quantum error correction is essential for bridging the gap between the error rates of physical devices and the extremely low logical error rates required for quantum algorithms. Recent error-correction demonstrations on superconducting…
Hypergraph states are multiqubit states whose combinatorial description and entanglement properties generalize the well-studied class of graph states. Graph states are important in applications such as measurement-based quantum computation…
Topological quantum computing has recently proven itself to be a very powerful model when considering large- scale, fully error corrected quantum architectures. In addition to its robust nature under hardware errors, it is a software driven…
We explore the design of quantum error-correcting codes for cases where the decoherence events of qubits are correlated. In particular, we consider the case where only spatially contiguous qubits decohere, which is analogous to the case of…
Mixed-state phases of matter under local decoherence have recently garnered significant attention due to the ubiquitous presence of noise in current quantum processors. One of the key issues is understanding how topological quantum memory…
Subsystem codes protect quantum information by encoding it in a tensor factor of a subspace of the physical state space. Subsystem codes generalize all major quantum error protection schemes, and therefore are especially versatile. This…
We consider universal statistical properties of systems that are characterized by phase states with macroscopic degeneracy of the ground state. A possible topological order in such systems is described by non-linear discrete equations. We…
We compute the error threshold of color codes, a class of topological quantum codes that allow a direct implementation of quantum Clifford gates, when both qubit and measurement errors are present. By mapping the problem onto a…
We provide a detailed study of the general structure of two-dimensional topological stabilizer quantum error correcting codes, including subsystem codes. Under the sole assumption of translational invariance, we show that all such codes can…
Symmetric extendibility of quantum states has recently drawn attention in the context of quantum cryptography to judge whether quantum states shared between two distant parties can be purified by means of one-way error correction protocols.…
We present a family of algorithms, combining real-space renormalization methods and belief propagation, to estimate the free energy of a topologically ordered system in the presence of defects. Such an algorithm is needed to preserve the…
The stabilization of a quantum computer by repeated error correction can be reduced almost entirely to repeated preparation of blocks of qubits in quantum codeword states. These are multi-particle entangled states with a high degree of…
Series of maximum distance quantum error-correcting codes are developed and analysed. For a given rate and given error-correction capability, quantum error-correcting codes with these specifications are constructed. The codes are explicit…
Quantum graph states are critical resources for various quantum algorithms, and also determine essential interconnections in distributed quantum computing. There are two schemes for generating graph states probabilistic scheme and…
A mathematical topology with matrix is a natural representation of a coding relational structure that is found in many fields of the world. Matrices are very important in computation of real applications, s ce matrices are easy saved in…
Gapped fracton phases of matter generalize the concept of topological order and broaden our fundamental understanding of entanglement in quantum many-body systems. However, their analytical or numerical description beyond exactly solvable…
Topological color codes defined by the 4.8.8 semiregular lattice feature geometrically local check operators and admit transversal implementation of the entire Clifford group, making them promising candidates for fault-tolerant quantum…
A quantum error correcting code is a subspace $\mathcal{C}$ such that allowed errors acting on any state in $\mathcal{C}$ can be corrected. A quantum code for which state recovery is only required up to a logical rotation within…