Related papers: Gauge Structures: From Stabilizer Codes to Continu…
Dynamical stabilizer codes (DSCs) have recently emerged as a powerful generalization of static stabilizer codes for quantum error correction, replacing a fixed stabilizer group with a sequence of non-commuting measurements. This dynamical…
The encoding of lattice gauge theories onto quantum computers requires a discretization of the gauge field's Hilbert space on each link, which presents errors with respect to the Kogut--Susskind limit. In the electric basis, Hilbert space…
High-rate bivariate bicycle (BB) codes are promising low-overhead quantum memories, but their stabilizer checks typically have weight $6$ or higher, making syndrome extraction challenging. We introduce subsystem bivariate bicycle (SBB)…
We prove that on any two-dimensional lattice of qudits of a prime dimension, every translation invariant Pauli stabilizer group with local generators and with code distance being the linear system size, is decomposed by a local Clifford…
There are several models of quantum computation which exhibit shared fundamental fault-tolerance properties. This article makes commonalities explicit by presenting these different models in a unifying framework based on the ZX calculus. We…
The stabilizer formalism for quantum error-correcting codes has been, without doubt, the most successful at producing examples of quantum codes with strong error-correcting properties. In this paper, we discuss strong automorphism groups of…
We introduce quantum pin codes: a class of quantum CSS codes. Quantum pin codes are a generalization of quantum color codes and Reed-Muller codes and share a lot of their structure and properties. Pin codes have gauge operators, an…
The persistence barcode is a topological descriptor of data that plays a fundamental role in topological data analysis. Given a filtration of data, the persistence barcode tracks the evolution of its homology groups. In this paper, we…
Linear lattice gauge theory is based on link variables that are arbitrary complex or real $N\times N$ matrices, in distinction to the usual (non-linear) formulation with unitary or orthogonal matrices. For a large region in parameter space…
This work proposes a model-reduction methodology that preserves Lagrangian structure (equivalently Hamiltonian structure) and achieves computational efficiency in the presence of high-order nonlinearities and arbitrary parameter dependence.…
In superconductors, and in other systems with a local U(1) gauge invariance, there are two mechanisms that form topological defects in phase transitions. In addition to the standard Kibble mechanism, thermal fluctuations of the magnetic…
Lur'e systems are feedback interconnection of a linear time-invariant subsystem in the forward path and a memoryless nonlinear one in the feedback path, which have many physical representatives. In this paper, some classical theorems about…
Iterative methods play an important role in science and engineering applications, with uses ranging from linear system solvers in finite element methods to optimization solvers in model predictive control. Recently, a new computational…
Protection of quantum information from noise is a massive challenge. One avenue people have begun to explore is reducing the number of particles needing to be protected from noise and instead use systems with more states, so called qudit…
Gauge theories appear broadly in physics, ranging from the standard model of particle physics to long-wavelength descriptions of topological systems in condensed matter. However, systems with sign problems are largely inaccessible to…
We demonstrate that it is possible to construct operators that stabilize the constraint-satisfying subspaces of computational problems in their Ising representations. We provide an explicit recipe to construct unitaries and associated…
Nonlinear gauge theory is a gauge theory based on a nonlinear Lie algebra (finite W algebra) or a Poisson algebra, which yields a canonical star product for deformation quantization as a correlator on a disk. We pursue nontrivial…
We propose a unifying paradigm for analyzing and constructing topological quantum error correcting codes as dynamical circuits of geometrically local channels and measurements. To this end, we relate such circuits to discrete fixed-point…
Quantum subsystem codes have been shown to improve error-correction performance, ease the implementation of logical operations on codes, and make stabilizer measurements easier by decomposing stabilizers into smaller-weight gauge operators.…
We construct lattice gauge theories in which the elements of the link matrices are represented by non-commuting operators acting in a Hilbert space. These quantum link models are related to ordinary lattice gauge theories in the same way as…