Related papers: Automorphism gadgets in homological product codes
Recent discoveries in asymptotically good quantum codes have intensified research on their application in quantum computation and fault-tolerant operations. This study focuses on the addressability problem within CSS codes: what circuits…
We introduce a differential geometric framework for describing families of quantum error-correcting codes and for understanding quantum fault tolerance. This work unifies the notion of topological fault tolerance with fault tolerance in…
The capacity to custom tailor the properties of quantum matter and materials is a central requirement for enlarging their range of possible functionalities. A particularly promising route is the use of driving protocols to engineer specific…
We define solvable quantum mechanical systems on a Hilbert space spanned by bipartite ribbon graphs with a fixed number of edges. The Hilbert space is also an associative algebra, where the product is derived from permutation group…
Topological quantum computing has recently proven itself to be a powerful computational model when constructing viable architectures for large scale computation. The topological model is constructed from the foundation of a error correction…
The design of decoding algorithms is a significant technological component in the development of fault-tolerant quantum computers. Often design of quantum decoders is inspired by classical decoding algorithms, but there are no general…
Logical gates constitute the building blocks of fault-tolerant quantum computation. While quantum error-corrected memories have been extensively studied in the literature, explicit constructions and detailed analyses of thresholds and…
Transversal gates are the ideal gates in a fault-tolerant scenario; relatively easy to implement, and minimally error propagating. Their availability will maximise fault tolerant thresholds, enabling universal quantum computation in a wider…
Homomorphic quantum error correction aims to protect quantum data against both unauthorized access and environmental noise during server-based processing. We investigate the algebraic compatibility between quantum homomorphic encryption and…
In this paper, we study groups of automorphisms of algebraic systems over a set of $p$-adic integers with different sets of arithmetic and coordinate-wise logical operations and congruence relations modulo $p^k,$ $k\ge 1.$ The main result…
The Variational Quantum Eigensolver approach to the electronic structure problem on a quantum computer involves measurement of the Hamiltonian expectation value. Formally, quantum mechanics allows one to measure all mutually commuting or…
Standard approaches to quantum error correction for fault-tolerant quantum computing are based on encoding a single logical qubit into many physical ones, resulting in asymptotically zero encoding rates and therefore huge resource…
Quantum random walks represent a powerful tool for the implementation of various quantum algorithms. We consider a convolution problem for the graphs which provide quantum and classical random walks. We suggest a new method for lattices and…
Fault-tolerant capacities quantify the ability of a quantum channel to reliably transmit information when every component of the encoding and decoding procedure is noisy. Earlier work analyzed achievable communication rates under such noise…
Quasi-Hermitian quantum systems, including $\mathcal{PT}$-symmetric ones, can be mapped to equivalent Hermitian systems via a similarity transformation that redefines the inner product with a positive-definite metric operator. Although an…
Voltage operations extend traditional geometric and combinatorial operations (such as medial, truncation, prism, and pyramid over a polytope) to operations on maniplexes, maps, polytopes, and hypertopes. In classical operations, the…
We generalise the implementation of logical quantum gates via Dehn twists from topological codes to the hypergraph and balanced products of cyclic codes. These generalised Dehn twists implement logical entangling gates with no additional…
Topological color codes are widely acknowledged as promising candidates for fault-tolerant quantum computing. Neither a two-dimensional nor a three-dimensional topology, however, can provide a universal gate set $\{$H, T, CNOT$\}$, with the…
Achieving reliable performance on early fault-tolerant quantum hardware will depend on protocols that manage noise without incurring prohibitive overhead. We propose a novel framework that integrates quantum computation with the…
The notion of homomorphism indistinguishability offers a combinatorial framework for characterizing equivalence relations of graphs, in particular equivalences in counting logics within finite model theory. That is, for certain graph…