Related papers: Qudit Stabilizer Codes, CFTs, and Topological Surf…
While stabilizer tableaus have proven useful as a descriptive tool for additive quantum codes, they otherwise offer little guidance for concrete constructions or algorithm analysis. We introduce a representation of stabilizer codes as…
The Pauli stabilizer formalism is perhaps the most thoroughly studied means of procuring quantum error-correcting codes, whereby the code is obtained through commutative Pauli operators and ``stabilized'' by them. In this work we will show…
In this paper we define homological stabilizer codes which encompass codes such as Kitaev's toric code and the topological color codes. These codes are defined solely by the graphs they reside on. This feature allows us to use properties of…
Graph states are widely used in quantum information theory, including entanglement theory, quantum error correction, and one-way quantum computing. Graph states have a nice structure related to a certain graph, which is given by either a…
We use the 3D SymTFT approach to study the generalized symmetries and partition functions of 2D CFTs in various orbifolded and fermionic phases. These phases can be realized by the sandwich construction in the associated 3D SymTFTs with…
The two-dimensional color code is an alternative to the toric code that encodes more logical qubits while maintaining crucial features of the $\mathbb{Z}_2\times\mathbb{Z}_2$ toric code in the long wavelength limit. However its short range…
In this work we establish lower bounds on the size of Clifford circuits that measure a family of commuting Pauli operators. Our bounds depend on the interplay between a pair of graphs: the Tanner graph of the set of measured Pauli…
The study of Riemann surfaces with parametrized boundary components was initiated in conformal field theory (CFT). Motivated by general principles from Teichmueller theory, and applications to the construction of CFT from vertex operator…
We present a family of simple three-dimensional stabilizer codes, called the chiral color codes, that realize fermionic and chiral topological orders. In the qubit case, the code realizes the topological phase of a single copy of the…
We consider Chern-Simons theory on 3-manifold $M$ that is the total space of a circle bundle over a 2d base $\Sigma$. We show that this theory is equivalent to a new 2d TQFT on the base, which we call Caloron BF theory, that can be obtained…
The Pauli groups are ubiquitous in quantum information theory because of their usefulness in describing quantum states and operations and their readily understood symmetry properties. In addition, the most well-understood quantum error…
Twist defects in surface codes can be used to encode more logical qubits, improve the code rate, and implement logical gates. In this work we provide a rigorous formalism for constructing surface codes with twists generalizing the…
We consider correlation functions in symmetric product orbifold CFTs on the sphere, focusing on the case where all operators are single-cycle twists, and the covering surface is also a sphere. We directly construct the general class of…
The fixed area states are constructed by gravitational path integrals in previous studies.In this paper we show the dual of the fixed area states in conformal field theories (CFTs).These CFT states are constructed by using spectrum…
Symmetry Topological Field Theory (SymTFT) is a framework to capture universal features of quantum many-body systems by viewing them as a boundary of topological order in one higher dimension. This has yielded numerous insights in static…
We extend the TFT construction of CFT correlators of [arXiv:hep-th/0204148] to so-called finite logarithmic CFTs for which the algebraic input data is no longer semisimple but still finite. More specifically, starting from the data of a…
We introduce a graphical representation of stabilizer states and translate the action of Clifford operators on stabilizer states into graph operations on the corresponding stabilizer-state graphs. Our stabilizer graphs are constructed of…
We undertake a study of the notion of a quantum graph over arbitrary finite-dimensional $C^*$-algebras $B$ equipped with arbitrary faithful states. Quantum graphs are realised principally as either certain operators on $L^2(B)$, the quantum…
We consider design of the quantum stabilizer codes via a two-step, low-complexity approach based on the framework of codeword-stabilized (CWS) codes. In this framework, each quantum CWS code can be specified by a graph and a binary code.…
We identify a categorical structure of the set of all CFTs. In particular, we show that the set of all CFTs has a natural monoidal strict $2$-category structure with the $1$-morphisms being sequences of deformations and $2$-morphisms…