Related papers: Universal Fault-Tolerant Quantum Computing with St…
Fault-tolerant logic gates will consume a large proportion of the resources of a two-dimensional quantum computing architecture. Here we show how to perform a fault-tolerant non-Clifford gate with the surface code; a quantum…
The implementation of fault-tolerant quantum gates on encoded logic qubits is considered. It is shown that transversal implementation of logic gates based on simple geometric control ideas is problematic for realistic physical systems…
This is a comprehensive review on fault-tolerant topological quantum computation with the surface codes. The basic concepts and useful tools underlying fault-tolerant quantum computation, such as universal quantum computation, stabilizer…
The standard approach to universal fault-tolerant quantum computing is to develop a general purpose quantum error correction mechanism that can implement a universal set of logical gates fault-tolerantly. Given such a scheme, any quantum…
Recently, Bravyi and K\"onig have shown that there is a tradeoff between fault-tolerantly implementable logical gates and geometric locality of stabilizer codes. They consider locality-preserving operations which are implemented by a…
A long-standing challenge in quantum error correction is the infeasibility of universal transversal gates, as shown by the Eastin-Knill theorem. We obtain a necessary and sufficient condition for a quantum code to have universal transversal…
A long-standing open problem in fault-tolerant quantum computation has been to find a universal set of transversal gates. As three of us proved in arXiv: 0706.1382, such a set does not exist for binary stabilizer codes. Here we generalize…
Fault-tolerant quantum computing (FTQC) is essential for achieving large-scale practical quantum computation. Implementing arbitrary FTQC requires the execution of a universal gate set on logical qubits, which is highly challenging.…
In this perspective article, we revisit and critically evaluate prevailing viewpoints on the capabilities and limitations of near-term quantum computing and its potential transition toward fully fault-tolerant quantum computing. We examine…
Conventional approaches to fault-tolerant quantum computing realize logical circuits gate-by-gate, synthesizing each gate independently on one or more code blocks. This incurs excess overhead and doesn't leverage common structures in…
Quantum computers will require encoding of quantum information to protect them from noise. Fault-tolerant quantum computing architectures illustrate how this might be done but have not yet shown a conclusive practical advantage. Here we…
Active quantum error correction using qubit stabilizer codes has emerged as a promising, but experimentally challenging, engineering program for building a universal quantum computer. In this review we consider the formalism of qubit…
To achieve scalable universal quantum computing, we need to implement a universal set of logical gates fault-tolerantly, for which the main difficulty lies with non-Clifford gates. We demonstrate that several characteristic features of the…
In this paper we present a new unified theoretical framework that describes the full dynamics of quantum computation. Our formulation allows any questions pertaining to the physical behavior of a quantum computer to be framed, and in…
Fault-tolerant quantum computation is a technique that is necessary to build a scalable quantum computer from noisy physical building blocks. Key for the implementation of fault-tolerant computations is the ability to perform a universal…
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…
Usual scenarios of fault-tolerant computation are concerned with the fault-tolerant realization of quantum algorithms that compute classical functions, such as Shor's algorithm for factoring. In particular, this means that input and output…
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…
Fault-tolerant logical operations for qubits encoded by CSS codes are discussed, with emphasis on methods that apply to codes of high rate, encoding k qubits per block with k>1. It is shown that the logical qubits within a given block can…
Designing encoding and decoding circuits to reliably send messages over many uses of a noisy channel is a central problem in communication theory. When studying the optimal transmission rates achievable with asymptotically vanishing error…