Related papers: Fault-Tolerant One-Bit Addition with the Smallest …

A method for the implementation of a universal set of fault-tolerant logical gates is presented using homological product codes. In particular, it is shown that one can fault-tolerantly map between different encoded representations of a…

Using transversal gates is a straightforward and efficient technique for fault-tolerant quantum computing. Since transversal gates alone cannot be computationally universal, they must be combined with other approaches such as magic state…

We present a set of efficiently implementable logical multi-qubit gates in concatenated quantum error correction codes using parity qubits. In particular, we show how fault-tolerant high-weight rotation gates of arbitrary angle can be…

Instead of a quantum computer where the fundamental units are 2-dimensional qubits, we can consider a quantum computer made up of d-dimensional systems. There is a straightforward generalization of the class of stabilizer codes to…

Majorana-based quantum computation in nanowires and neutral atoms has gained prominence as a promising platform to encode qubits and protect them against noise. In order to run computations reliably on such devices, a fully fault-tolerant…

Fault-tolerant quantum computation traditionally incurs substantial resource overhead, with both qubit and time overheads scaling polylogarithmically with the size of the computation. While prior work by Gottesman showed that constant qubit…

In this paper we demonstrate how data encoded in a five-qubit quantum error correction code can be converted, fault-tolerantly, into a seven-qubit Steane code. This is achieved by progressing through a series of codes, each of which…

Correcting errors is a vital but expensive component of fault tolerant quantum computation. Standard fault tolerant protocol assumes the implementation of error correction, via syndrome measurements and possible recovery operations, after…

Topological quantum error correction codes are currently among the most promising candidates for efficiently dealing with the decoherence effects inherently present in quantum devices. Numerically, their theoretical error threshold can be…

Constructing an efficient and robust quantum memory is central to the challenge of engineering feasible quantum computer architectures. Quantum error correction codes can solve this problem in theory, but without careful design it can…

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…

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 error correction and fault-tolerant quantum computation are two fundamental concepts which make quantum computing feasible. While providing a theoretical means with which to ensure the arbitrary accuracy of any quantum circuit,…

Steane code is one of the most widely studied quantum error-correction codes, which is a natural choice for fault-tolerant quantum computation (FTQC). However, the original Steane code is not fault-tolerant because the CNOT gates in an…

The study of holographic bulk-boundary dualities has led to the construction of novel quantum error correcting codes. Although these codes have shed new light on conceptual aspects of these dualities, they have widely been believed to lack…

I discuss how to perform fault-tolerant quantum computation with concatenated codes using local gates in small numbers of dimensions. I show that a threshold result still exists in three, two, or one dimensions when next-to-nearest-neighbor…

Attaining fault tolerance while maintaining low overhead is one of the main challenges in a practical implementation of quantum circuits. One major technique that can overcome this problem is the flag technique, in which high-weight errors…

Noise and errors are inevitable parts of any practical implementation of a quantum computer. As a result, large-scale quantum computation will require ways to detect and correct errors on quantum information. Here, we present such a quantum…

Quantum error correction methods use processing power to combat noise. The noise level which can be tolerated in a fault-tolerant method is therefore a function of the computational resources available, especially the size of computer and…

We propose a scheme that converts a stabilizer code into another stabilizer code in a fault tolerant manner. The scheme first puts both codes in specific forms, and proceeds the conversion from a source code to a target code by applying…