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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…
I present a fault-tolerant quantum computing method for 2D architectures that is particularly appealing for photonic qubits. It relies on a crossover of techniques from topological stabilizer codes and measurement based quantum computation.…
Braiding defects in topological stabiliser codes has been widely studied as a promising approach to fault-tolerant quantum computing. Here, we explore the potential and limitations of such schemes in codes of all spatial dimensions. We…
The color code has been invaluable for the development of the theory of fault-tolerant logic gates using transversal rotations. Three-dimensional examples of the color code have shown us how its structure, specifically the intersection of…
The constituent parts of a quantum computer are inherently vulnerable to errors. To this end we have developed quantum error-correcting codes to protect quantum information from noise. However, discovering codes that are capable of a…
Motivated by their central role in fault-tolerant quantum computation, we study the sets of gates of the third-level of the Clifford hierarchy and their distinguished subsets of `nearly diagonal' semi-Clifford gates. The Clifford hierarchy…
Color code is a promising topological code for fault-tolerant quantum computing. Insufficient research on the color code has delayed its practical application. In this work, we address several key issues to facilitate practical…
The paradigm behind digital quantum computing inherits the idea of using binary information processing. Nature in fact gives much more rich structures of physical objects that can be used for encoding information, which is especially…
We show that higher-dimensional versions of qubits, or qudits, can be encoded into spin systems and into harmonic oscillators, yielding important advantages for quantum computation. Whereas qubit-based quantum computation is adequate for…
We present and analyze protocols for fault-tolerant quantum computing using color codes. We present circuit-level schemes for extracting the error syndrome of these codes fault-tolerantly. We further present an integer-program-based…
A fundamental problem of fault-tolerant quantum computation with quantum low-density parity-check (qLDPC) codes is the tradeoff between connectivity and universality. It is widely believed that in order to perform native logical…
Quantum error-correcting codes are essential to the implementation of fault-tolerant quantum computation. Homological products of classical codes offer a versatile framework for constructing quantum error-correcting codes with desirable…
Qudits can be described by a state vector in a $q$-dimensional Hilbert space, enabling a more extensive encoding and manipulation of information compared to qubits. This implies that conducting fault-tolerant quantum computations using…
Quantum gates are the building blocks of quantum circuits, which in turn are the cornerstones of quantum information processing. In this work, we theoretically investigate a single-step implementation of both a universal two- (CNOT) and…
Bivariate bicycle codes are promising candidates for high-threshold, low-overhead fault-tolerant quantum memories. Meanwhile, color codes are the most prominent self-dual CSS codes, supporting transversal Clifford gates that have been…
Recently, Bravyi and K\"onig have shown that there is a tradeoff between fault-tolerantly implementable logical gates and geometric locality of stabilizer codes. They consider locality-preserving operations which are implemented by a…
Two-dimensional color codes are a promising candidate for fault-tolerant quantum computing, as they have high encoding rates, transversal implementation of logical Clifford gates, and resource-efficient magic state preparation schemes.…
Qubits, which are quantum counterparts of classical bits, are used as basic information units for quantum information processing, whereas underlying physical information carriers, e.g. (artificial) atoms or ions, admit encoding of more…
We present an architecture for early fault-tolerant quantum computers based on the smallest interesting colour code (Earl Campbell, 2016). It realizes a universal logical gate set consisting of single-qubit measurements and preparations in…
Surface codes describe quantum memory stored as a global property of interacting spins on a surface. The state space is fixed by a complete set of quasi-local stabilizer operators and the code dimension depends on the first homology group…