Related papers: Quantum Codes on Graphs
PhD thesis investigating homological quantum codes derived from curved and higher dimensional geometries. In the first part we will consider closed surfaces with constant negative curvature. We show how such surfaces can be constructed and…
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…
Floquet codes are an intriguing generalisation of stabiliser and subsystem codes, which can provide good fault-tolerant characteristics while benefiting from reduced connectivity requirements in hardware. A recent question of interest has…
Graphs are closely related to quantum error-correcting codes: every stabilizer code is locally equivalent to a graph code, and every codeword stabilized code can be described by a graph and a classical code. For the construction of good…
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…
Floquet quantum error-correcting codes provide an operationally economical route to fault tolerance by dynamically generating stabilizer structures using only two-body Pauli measurements. But while it is well established that stabilizer…
Quantum information is fragile and must be protected by a quantum error-correcting code for large-scale practical applications. Recently, highly efficient quantum codes have been discovered which require a high degree of spatial…
We propose a new class of error-correcting dynamic codes in two and three dimensions that has no explicit connection to any parent subsystem code. The two-dimensional code, which we call the CSS honeycomb code, is geometrically similar to…
Quantum error correction would be a primitive for demonstrating quantum advantage in a realistic noisy environment. Floquet codes are a class of dynamically generated, stabilizer-based codes in which low-weight parity measurements are…
We describe a method for creating twist defects in the honeycomb Floquet code of Hastings and Haah. In particular, we construct twist defects at the endpoints of condensation defects, which are built by condensing emergent fermions along…
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.…
Deciding if a given family of quantum states is topologically ordered is an important but nontrivial problem in condensed matter physics and quantum information theory. We derive necessary and sufficient conditions for a family of graph…
The toric code can be constructed as a gauge theory of finite groups on oriented two dimensional lattices. Here we construct analogous models with the gauge fields belonging to groupoids, which are categories where every morphism has an…
Dynamical quantum error-correcting codes (QECC) offer wider possibilities in how one can protect logical quantum information from noise and perform fault-tolerant quantum computation compared to static QECCs. A family of dynamical QECCs…
A protocol called the "honeycomb code", or generically a "Floquet code", was introduced by Hastings and Haah in \cite{hastings_dynamically_2021}. The honeycomb code is a subsystem code based on the honeycomb lattice with zero logical qubits…
Floquet codes are a novel class of quantum error-correcting codes with dynamically generated logical qubits arising from a periodic schedule of non-commuting measurements. We utilize the interpretation of measurements in terms of…
Floquet codes define fault-tolerant protocols through periodic measurement sequences that drive a dynamically evolving stabilizer group. They provide a natural framework for hardware supporting two-qubit parity measurements but no unitary…
We introduce a new type of sparse CSS quantum error correcting code based on the homology of hypermaps. Sparse quantum error correcting codes are of interest in the building of quantum computers due to their ease of implementation and the…
We generalize a construction of non-binary quantum LDPC codes over $\F_{2^m}$ due to \cite{KHIS11a} and apply it in particular to toric codes. We obtain in this way not only codes with better rates than toric codes but also improve…
The Floquet code utilizes a periodic sequence of two-qubit measurements to realize the topological order. After each measurement round, the instantaneous stabilizer group can be mapped to a honeycomb toric code, explaining the topological…