Related papers: Anyon condensation and the color code
Concatenating quantum error correction codes scales error correction capability by driving logical error rates down double-exponentially across levels. However, the noise structure shifts under concatenation, making it hard to choose an…
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…
Scaling up quantum computers to attain substantial speedups over classical computing requires fault tolerance. Conventionally, protocols for fault-tolerant quantum computation demand excessive space overheads by using many physical qubits…
Topological color codes defined by the 4.8.8 semiregular lattice feature geometrically local check operators and admit transversal implementation of the entire Clifford group, making them promising candidates for fault-tolerant quantum…
Analyzing and developing new quantum error-correcting schemes is one of the most prominent tasks in quantum computing research. In such efforts, introducing time dynamics explicitly in both analysis and design of error-correcting protocols…
This dissertation reports our investigation into the existence of anyons, which interpolate between bosons and fermions, in light of the Symmetrization Postulate, which states that only the two extremes exist. The Symmetrization Postulate…
We show how to perform scalable fault-tolerant non-Clifford gates in two dimensions by introducing domain walls between the surface code and a non-Abelian topological code whose codespace is stabilized by Clifford operators. We formulate a…
Modular quantum computing architectures require error correction schemes that remain effective in the presence of noisy inter-processor operations. As such, minimizing the number of such operations on logical circuits partitioned across…
One of the most promising routes towards fault-tolerant quantum computation utilizes topological quantum error correcting codes, such as the $\mathbb{Z}_2$ surface code. Logical qubits can be encoded in a variety of ways in the surface…
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.…
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 $[[7,1,3]]$ Steane code and $[[23,1,7]]$ quantum Golay code have been identified as good candidates for fault-tolerant quantum computing via code concatenation. These two codes have transversal implementations of all Clifford gates, but…
We consider the $\mathbb{Z}_2$ toric code, surface code and Floquet code defined on a non-orientable surface, which can be considered as families of codes extending Shor's 9-qubit code. We investigate the fault-tolerant logical gates of the…
The emergence of non-Abelian anyons from large collections of interacting elementary particles is a conceptually beautiful phenomenon with important ramifications for fault-tolerant quantum computing. Over the last few decades the field has…
We show that quasicrystals exhibit anyonic behavior that can be used for topological quantum computing. In particular, we study a correspondence between the fusion Hilbert spaces of the simplest non-abelian anyon, the Fibonacci anyons, and…
Many current quantum error-correcting codes that achieve full fault tolerance suffer from having low ratios of logical to physical qubits and significant overhead. This makes them difficult to implement on current noisy intermediate-scale…
Twists are defects that are used to encode and process quantum information in topological codes like surface and color codes. Color codes can host three basic types of twists viz., charge-permuting, color-permuting and domino twists. In…
Anyon systems are studied in connection with several interesting applications including high $T_C$ superconductivity and topological quantum computing. In this work we show that these systems can be realized starting from directed polymers…
It is conjectured that quantum computers are able to solve certain problems more quickly than any deterministic or probabilistic computer. A quantum computer exploits the rules of quantum mechanics to speed up computations. However, it is a…
A universal quantum computing scheme, with a universal set of logical gates, is proposed based on networks of 1D quantum systems. The encoding of information is in terms of universal features of gapped phases, for which effective field…