Related papers: Asymptotically Optimal Topological Quantum Compili…
A fundamental question in the theory of quantum computation is to understand the ultimate space-time resource costs for performing a universal set of logical quantum gates to arbitrary precision. Here we demonstrate that non-Abelian anyons…
A class of anyonic models for universal quantum computation based on weakly-integral anyons has been recently proposed. While universal set of gates cannot be obtained in this context by anyon braiding alone, designing a certain type of…
In a topological quantum computer, universal quantum computation is performed by dragging quasiparticle excitations of certain two dimensional systems around each other to form braids of their world lines in 2+1 dimensional space-time. In…
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…
Finding physical realizations of topologically ordered states in experimental settings, from condensed matter to artificial quantum systems, has been the main challenge en route to utilizing their unconventional properties. We show how to…
The Fibonacci topological order is the prime candidate for the realization of universal topological quantum computation. We devise minimal quantum circuits to demonstrate the non-Abelian nature of the doubled Fibonacci topological order, as…
Fibonacci anyons are attractive for use in topological quantum computation because any unitary transformation of their state space can be approximated arbitrarily accurately by braiding. However there is no known braid that entangles two…
Fibonacci anyons are non-Abelian particles for which braiding is universal for quantum computation. Reichardt has shown how to systematically generate nontrivial braids for three Fibonacci anyons which yield unitary operations with…
In a topological quantum computer, braids of non-Abelian anyons in a (2+1)-dimensional space-time form quantum gates, whose fault tolerance relies on the topological, rather than geometric, properties of the braids. Here we propose to…
Quantum gates in topological quantum computation are performed by braiding non-Abelian anyons. These braiding processes can presumably be performed with very low error rates. However, to make a topological quantum computation architecture…
Topological quantum computation (TQC) is one of the most striking architectures that can realize fault-tolerant quantum computers. In TQC, the logical space and the quantum gates are topologically protected, i.e., robust against local…
Non-Abelian topological order (TO) enables topologically protected quantum computation with its anyonic quasiparticles. Recently, TO with $S_3$ gauge symmetry was identified as a sweet spot -- simple enough to emerge from finite-depth…
In seminal work (arxiv:quant-ph/9707021) Alexei Kitaev proposed topological quantum computing (arXiv:cond-mat/0010440, arxiv:quant-ph/9707021, arXiv:quant-ph/0001108, arXiv:0707.1889), whereby logic gates of a quantum computer are conducted…
Fibonacci anyons provide the simplest possible model of non-Abelian fusion rules: [1] x [1] = [0] + [1]. We propose a conformal field theory construction of topological quantum registers based on Fibonacci anyons realized as quasiparticle…
Harnessing non-abelian statistics of anyons to perform quantum computational tasks is getting closer to reality. While the existence of universal anyons by braiding alone such as the Fibonacci anyon is theoretically a possibility,…
We introduce AQCtensor, a novel algorithm to produce short-depth quantum circuits from Matrix Product States (MPS). Our approach is specifically tailored to the preparation of quantum states generated from the time evolution of quantum…
We review the q-deformed spin network approach to topological quantum field theory and apply these methods to produce unitary representations of the braid groups that are dense in the unitary groups. The simplest case of these models is the…
Majorana-based quantum gates are not complete for performing universal topological quantum computation while Fibonacci-based gates are difficult to be realized electronically and hardly coincide with the conventional quantum circuit models.…
A method, termed controlled-injection, is proposed for compiling three-qubit controlled gates within the non-abelian Fibonacci anyon model. Building on single-qubit compilation techniques with three Fibonacci anyons, the approach showcases…
Universal compilation is a training process that compiles a trainable unitary into a target unitary and it serves vast potential applications from quantum dynamic simulations to optimal circuits with deep-compressing, device benchmarking,…