Related papers: Magic and Non-Clifford Gates in Topological Quantu…
A fundamental problem in fault-tolerant quantum computation is the tradeoff between universality and dimensionality, exemplified by the the Bravyi-K\"onig bound for $n$-dimensional topological stabilizer codes. In this work, we extend…
In fault-tolerant quantum computing with the surface code, non-Clifford gates are crucial for universal computation. However, implementing these gates using methods like magic state distillation and code switching requires significant…
Topological matter provides natural platforms for robust, non-local information storage, central to quantum error correction. Yet, while the relation between entanglement and topology is well established, little is known about the role of…
Topological quantum computation may provide a robust approach for encoding and manipulating information utilizing the topological properties of anyonic quasi-particle excitations. We develop an efficient means to map between dense and…
We study the emergence of complexity in deep random $N$-qubit $T$-gate doped Clifford circuits, as reflected in their spectral properties and in magic generation, characterized by the stabilizer R\'enyi entropy distribution and the…
We introduce the magic hierarchy, a quantum circuit model that alternates between arbitrary-sized Clifford circuits and constant-depth circuits with two-qubit gates ($\textsf{QNC}^0$). This model unifies existing circuit models, such as…
Fault-tolerant quantum computation requires minimizing non-Clifford gates, whose implementation via magic state distillation dominates the resource costs. While $T$-count minimization is well-studied, dedicated $CCZ$ factories shift the…
We give a general proof for the existence and realizability of Clifford gates in the Ising topological quantum computer. We show that all quantum gates that can be implemented by braiding of Ising anyons are Clifford gates. We find that the…
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…
Non-Clifford gates are frequently exclusively implemented on fault-tolerant architectures by first distilling magic states in specialised magic-state factories. In the rest of the architecture, the computational space, magic states can then…
Clifford gates play a role in the optimisation of Clifford+T circuits. Reducing the count and the depth of Clifford gates, as well as the optimal scheduling of T gates, influence the hardware and the time costs of executing quantum…
We address the circuit-design problem of maximizing quantum magic in early fault-tolerant quantum computing (early FTQC), where logical dynamics natively take the form of alternating Clifford layers and diagonal non-Clifford layers. To…
Quantum gates built out of braid group elements form the building blocks of topological quantum computation. They have been extensively studied in $SU(2)_k$ quantum group theories, a rich source of examples of non-Abelian anyons such as the…
The Clifford hierarchy is a fundamental structure in quantum computation, classifying unitary operators based on their commutation relations with the Pauli group. Despite its significance, the mathematical structure of the hierarchy is not…
Gauge theories are important descriptions for many physical phenomena and systems in quantum computation. Automorphism of gauge group naturally gives global symmetries of gauge theories. In this work we study such symmetries in gauge…
We introduce group surface codes, which are a natural generalization of the $\mathbb{Z}_2$ surface code, and equivalent to quantum double models of finite groups with specific boundary conditions. We show that group surface codes can be…
We show that states obtained from deep random Clifford circuits doped with non-Clifford phase gates (including T-gates and $\sqrt{\mathrm{T}}$-gates) can be disentangled completely, provided the number of non-Clifford gates is smaller or…
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…
Classical simulation of quantum circuits is a pivotal part of the quantum computing landscape, specially within the NISQ era, where the constraints imposed by available hardware are unavoidable. The Gottesman-Knill theorem further motivates…
The gate version of quantum computation exploits several quantum key resources as superposition and entanglement to reach an outstanding performance. In the way, this theory was constructed adopting certain supposed processes imitating…