Related papers: Topological One-Way Quantum Computation on Verifie…
This paper proves the threshold result, which asserts that quantum computation can be made robust against errors and inaccuracies, when the error rate, $\eta$, is smaller than a constant threshold, $\eta_c$. The result holds for a very…
Fault-tolerant quantum computing based on surface codes has emerged as a popular route to large-scale quantum computers capable of accurate computation even in the presence of noise. Its popularity is, in part, because the fault-tolerance…
Fault-tolerant quantum computing in systems composed of both Majorana fermions and topologically unprotected quantum systems, e.g. superconducting circuits or quantum dots, is studied in this paper. Errors caused by topologically…
Topological error correction provides an effective method to correct errors in quantum computation. It allows quantum computation to be implemented with higher error threshold and high tolerating loss rates. We present a topological a error…
Proving threshold theorems for fault-tolerant quantum computation is a burdensome endeavor with many moving parts that come together in relatively formulaic but lengthy ways. It is difficult and rare to combine elements from multiple papers…
The concept of qudit (a d-level system) cluster state is proposed by generalizing the qubit cluster state (Phys. Rev. Lett. \textbf{86}, 910 (2001)) according to the finite dimensional representations of quantum plane algebra. We…
This article is a short introduction to and review of the cluster-state model of quantum computation, in which coherent quantum information processing is accomplished via a sequence of single-qubit measurements applied to a fixed quantum…
We show how to realize a general quantum circuit involving gates between arbitrary pairs of qubits by means of geometrically local quantum operations and efficient classical computation. We prove that circuit-level local stochastic noise…
Topological quantum computing is a way of allowing precise quantum computations to run on noisy and imperfect hardware. One implementation uses surface codes created by forming defects in a highly-entangled cluster state. Such a method of…
Current hardware for quantum computing suffers from high levels of noise, and so to achieve practical fault-tolerant quantum computing will require powerful and efficient methods to correct for errors in quantum circuits. Here, we explore…
In this paper, we estimate the errors of Gaussian transformations implemented using one-way quantum computations on cluster states of various configurations. From all possible cluster state configurations, we choose those that give the…
Recently Shor showed how to perform fault tolerant quantum computation when the error probability is logarithmically small. We improve this bound and describe fault tolerant quantum computation when the error probability is smaller than…
The preparation of a quantum state using a noisy quantum computer (gate noise strength $\delta$), will necessarily affect an O($\delta$)-fraction of the qubits, no matter which protocol is used. Here, we show that fault-tolerant quantum…
The highest current estimates for the amount of noise a quantum computer can tolerate are based on fault-tolerance schemes relying heavily on postselecting on no detected errors. However, there has been no proof that these schemes give even…
Topological subsystem codes proposed recently by Bombin are quantum error correcting codes defined on a two-dimensional grid of qubits that permit reliable quantum information storage with a constant error threshold. These codes require…
In this paper, we place bounds on when it is impossible to purify a noisy two-qubit state if all the gates used in the purification protocol are subject to adversarial local, independent, noise. It is found that the gate operations must be…
A major challenge in practical quantum computation is the ineludible errors caused by the interaction of quantum systems with their environment. Fault-tolerant schemes, in which logical qubits are encoded by several physical qubits, enable…
As there is no quantum error correction code with universal set of transversal gates, several approaches have been proposed which, in combination of transversal gates, make universal fault-tolerant quantum computation possible. Magic state…
Quantum computation promises applications that are thought to be impossible with classical computation. To realize practical quantum computation, the following three properties will be necessary: universality, scalability, and…
Continuous-variable (CV) cluster states are a universal quantum computing platform that has experimentally out-scaled qubit platforms by orders of magnitude. Room-temperature implementation of CV cluster states has been achieved with…