Related papers: Fault-Tolerant High Level Quantum Circuits: Form, …
The so-called "threshold" theorem says that, once the error rate per qubit per gate is below a certain value, indefinitely long quantum computation becomes feasible, even if all of the qubits involved are subject to relaxation processes,…
Quantum systems, in general, output data that cannot be simulated efficiently by a classical computer, and hence is useful for solving certain mathematical problems and simulating quantum many-body systems. This also implies, unfortunately,…
Achieving scalable, fault-tolerant quantum computation requires quantum memory architectures that minimize error correction overhead while preserving coherence. This work presents a framework for high-dimensional qudit memory in…
We present a method of concatenated quantum error correction in which improved classical processing is used with existing quantum codes and fault-tolerant circuits to more reliably correct errors. Rather than correcting each level of a…
It is not so well-known that measurement-free quantum error correction protocols can be designed to achieve fault-tolerant quantum computing. Despite the potential advantages of using such protocols in terms of the relaxation of accuracy,…
These lecture notes from the 2019 Les Houches Summer School on 'Quantum Information Machines' are intended to provide an introduction to classical and quantum error correction with bits and qubits, and with continuous variable systems…
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…
In this introduction we motivate and explain the ``decoding'' and ``subsystems'' view of quantum error correction. We explain how quantum noise in QIP can be described and classified, and summarize the requirements that need to be satisfied…
It is conjectured that quantum computers are able to solve certain problems more quickly than any deterministic or probabilistic computer. A quantum computer exploits the rules of quantum mechanics to speed up computations. However, it is a…
Standard approaches to quantum error correction for fault-tolerant quantum computing are based on encoding a single logical qubit into many physical ones, resulting in asymptotically zero encoding rates and therefore huge resource…
Fault-tolerant (FT) computation by using quantum error correction (QEC) is essential for realizing large-scale quantum algorithms. Devices are expected to have enough qubits to demonstrate aspects of fault tolerance in the near future.…
This is an expository article aiming to introduce the reader to the underlying mathematics and geometry of quantum error correction. Information stored on quantum particles is subject to noise and interference from the environment. Quantum…
Modular architectures offer a scalable path toward fault-tolerant quantum computing by interconnecting smaller quantum processing units (QPUs) provided that high-rate, fault-tolerant interfaces can be realized across modules. We present a…
Geometric quantum computation offers a practical strategy toward robust quantum computation due to its inherently error tolerance. However, the rigorous geometric conditions lead to complex and/or error-disturbed quantum controls,…
Quantum error correction codes are usually designed to correct errors regardless of their physical origins. In large-scale devices, this is an essential feature. In smaller-scale devices, however, the main error sources are often…
Quantum error correction (QEC) is considered a deciding component in enabling practical quantum computing. Stabilizer codes, and in particular topological surface codes, are promising candidates for implementing QEC by redundantly encoding…
Quantum computing is entering a period in which progress will be shaped as much by advances in computer science as by improvements in hardware. The central thesis of this report is that early fault-tolerant quantum computing shifts many of…
Over the past decade, research in quantum computing has tended to fall into one of two camps: near-term intermediate scale quantum (NISQ) and fault-tolerant quantum computing (FTQC). Yet, a growing body of work has been investigating how to…
Scalable quantum computing can only be achieved if qubits are manipulated fault-tolerantly. Topological error correction - a novel method which combines topological quantum computing and quantum error correction - possesses the highest…
In order to achieve fault-tolerant quantum computation, we need to repeat the following sequence of four steps: First, perform 1 or 2 qubit quantum gates (in parallel if possible). Second, do a syndrome measurement on a subset of the…