Related papers: Fault-Tolerant Preparation of Quantum Polar Codes …
In the early years of fault-tolerant quantum computing (FTQC), it is expected that the available code distance and the number of magic states will be restricted due to the limited scalability of quantum devices and the insufficient…
Practical quantum computation heavily relies on the ability to perform quantum error correction in a fault-tolerant manner. Fault-tolerant encoding is a critical first step, and careful consideration of the error correction cycle that…
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…
We explore the effect of Shor state construction methods on logical state encoding and quantum error correction for the [[7,1,3]] Calderbank-Shor-Steane quantum error correction code in a nonequiprobable error environment. We determine the…
Quantum error correction (QEC) protects quantum systems against inevitable noises and control inaccuracies, providing a pathway towards fault-tolerant (FT) quantum computation. Stabilizer codes, including surface code and color code, have…
With gate error rates in multiple technologies now below the threshold required for fault-tolerant quantum computation, the major remaining obstacle to useful quantum computation is scaling, a challenge greatly amplified by the huge…
The realization of quantum error correction is an essential ingredient for reaching the full potential of fault-tolerant universal quantum computation. Using a range of different schemes, logical qubits can be redundantly encoded in a set…
An important approach to the fault-tolerant quantum computation is protecting the logical information using the quantum error correction. Usually, the logical information is in the form of logical qubits, which are encoded in physical…
Fault-tolerant quantum error correction provides a strategy to protect information processed by a quantum computer against noise which would otherwise corrupt the data. A fault-tolerant universal quantum computer must implement a universal…
In order to use quantum error-correcting codes to actually improve the performance of a quantum computer, it is necessary to be able to perform operations fault-tolerantly on encoded states. I present a general theory of fault-tolerant…
Practical quantum computing will require error rates that are well below what is achievable with physical qubits. Quantum error correction offers a path to algorithmically-relevant error rates by encoding logical qubits within many physical…
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 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.…
Quantum error correction (QEC) is essential for quantum computers to perform useful algorithms, but large-scale fault-tolerant computation remains out of reach due to demanding requirements on operation fidelity and the number of…
When storing encoded qubits, if single faults can be corrected and double faults postselected against, logical errors only occur due to at least three faults. At current noise rates, having to restart when two errors are detected prevents…
Fault-tolerant quantum computation (FTQC) is expected to address a wide range of computational problems. To realize large-scale FTQC, it is essential to encode logical qubits using quantum error-correcting codes. High-rate concatenated…
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…
A major challenge in fault-tolerant quantum computation (FTQC) is to reduce both space overhead -- the large number of physical qubits per logical qubit -- and time overhead -- the long physical gate sequences per logical gate. We prove…
The promise of quantum computers hinges on the ability to scale to large system sizes, e.g., to run quantum computations consisting of more than 100 million operations fault-tolerantly. This in turn requires suppressing errors to levels…
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…