Related papers: Quantum Codes, CFTs, and Defects
Quantum error correction is the art of protecting fragile quantum information through suitable encoding and active interventions. After encoding $k$ logical qubits into $n>k$ physical qubits using a stabilizer code, this amounts to…
We introduce a high-level graphical framework for designing and analysing quantum error correcting codes, centred on what we term the coherent parity check (CPC). The graphical formulation is based on the diagrammatic tools of the…
A quantum field theory is referred to as bosonic (non-spin) if its physical quantities are independent of the spacetime spin structure, and as fermionic (spin) if they depend on it. We explore fermionic conformal field theories (CFTs) that…
Conformal field theories (CFTs) with $U(m)\times U(n)$ global symmetry in $d=3$ dimensions have been studied for years due to their potential relevance to the chiral phase transition of quantum chromodynamics (QCD). In this work such CFTs…
Quantum error correction is an important ingredient for scalable quantum computing. Stabilizer codes are one of the most promising and straightforward ways to correct quantum errors, are convenient for logical operations, and improve…
Quantum error correction and symmetry arise in many areas of physics, including many-body systems, metrology in the presence of noise, fault-tolerant computation, and holographic quantum gravity. Here we study the compatibility of these two…
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…
It is known that a large class of characters of 2d conformal field theories (CFTs) can be written in the form of a Nahm sum. In \cite{Zagier:2007knq}, D. Zagier identified a list of Nahm sum expressions that are modular functions under a…
We investigate a novel class of quantum error correcting codes to correct errors on both qubits and higher-state quantum systems represented as qudits. These codes arise from an original graph-theoretic representation of sets of quantum…
Some mathematical questions relating to Coset Conformal Field Theories (CFT) are considered in the framework of Algebraic Quantum Field Theory as developed previously by us. We consider the issue of fixed point resolution in the diagonal…
We establish the emergence of a conformal field theory (CFT) in a (1+1)-dimensional hybrid quantum circuit right at the measurement-driven entanglement transition by revealing space-time conformal covariance of entanglement entropies and…
We construct Narain CFTs from self-dual codes on the finite field $F_p$ through even self-dual lattices for any prime $p>2$. Using this correspondence, we can relate the spectral gap and the partition function of the CFT to the error…
The disjointness of a stabilizer code is a quantity used to constrain the level of the logical Clifford hierarchy attainable by transversal gates and constant-depth quantum circuits. We show that for any positive integer constant $c$, the…
We study conformal field theories (CFTs) on curved spaces including both orientable and unorientable manifolds possibly with boundaries. We first review conformal transformations on curved manifolds. We then compute the identity components…
We consider chiral fermionic conformal field theories (CFTs) constructed from lattices and investigate their orbifolds under reflection and shift $\mathbb{Z}_2$ symmetries. For lattices based on binary error-correcting codes, we show the…
We investigate various aspects of operator quantum error-correcting codes or, as we prefer to call them, subsystem codes. We give various methods to derive subsystem codes from classical codes. We give a proof for the existence of subsystem…
Quantum computers have the potential to provide exponential speedups over their classical counterparts. Quantum principles are being applied to fields such as communications, information processing, and artificial intelligence to achieve…
Graph states are generalized from qubits to collections of $n$ qudits of arbitrary dimension $D$, and simple graphical methods are used to construct both additive and nonadditive quantum error correcting codes. Codes of distance 2…
In this work we extend the connection between Quantum Error Correction (QEC) and Lattice Gauge Theories (LGTs) by showing that a $\mathbb{Z}_N$ gauge theory with prime dimension $N$ coupled to dynamical matter can be expressed as a qudit…
One formidable difficulty in quantum communication and computation is to protect information-carrying quantum states against undesired interactions with the environment. In past years, many good quantum error-correcting codes had been…