Related papers: Flag fault-tolerant error correction with arbitrar…
A quantum error correcting code protects encoded logical information against errors. Transversal gates are a naturally fault-tolerant way to manipulate logical qubits but cannot be universal themselves. Protocols such as magic state…
We design flexible fault tolerant gate gadgets that allow the data and the ancilla to be encoded using different codes. By picking a stabilizer code for the ancilla we are able to perform both Clifford and non-Clifford gates fault…
Quantum error correction is necessary to perform large-scale quantum computations in the presence of noise and decoherence. As a result, several aspects of quantum error correction have already been explored. These have been primarily…
We study the implementation of fault-tolerant logical Clifford gates on stabilizer quantum error correcting codes based on their symmetries. Our approach is to map the stabilizer code to a binary linear code, compute its automorphism group,…
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…
The surface code is one of the most promising candidates for combating errors in large scale fault-tolerant quantum computation. A fault-tolerant decoder is a vital part of the error correction process---it is the algorithm which computes…
Motivated by limitations and capabilities of neutral atom qubits, we examine whether measurement-free error correction can produce practical error thresholds. We show that this can be achieved by extracting redundant syndrome information,…
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…
Whether it is at the fabrication stage or during the course of the quantum computation, e.g. because of high-energy events like cosmic rays, the qubits constituting an error correcting code may be rendered inoperable. Such defects may…
The performance of quantum error correction can be significantly improved if detailed information about the noise is available, allowing to optimize both codes and decoders. It has been proposed to estimate error rates from the syndrome…
Quantum error correction offers a promising path for performing quantum computations with low errors. Although a fully fault-tolerant execution of a quantum algorithm remains unrealized, recent experimental developments, along with…
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…
Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. The theory of quantum error-correcting codes has some close ties to and some striking differences…
A scalable and programmable quantum computer holds the potential to solve computationally intensive tasks that classical computers cannot accomplish within a reasonable time frame, achieving quantum advantage. However, the vulnerability of…
Quantum error correction (QEC) is essential for realizing scalable quantum computation. However, when evaluating its benefits, most analyses assume idealized components, overlooking the imperfections inherent in realistic fault-tolerant…
Controlling operational errors and decoherence is one of the major challenges facing the field of quantum computation and other attempts to create specified many-particle entangled states. The field of quantum error correction has developed…
The theory of stabilizer quantum error correction allows us to actively stabilize quantum states and simulate ideal quantum operations in a noisy environment. It is critical is to correctly diagnose noise from its syndrome and nullify it…
Quantum error-correcting codes, such as subspace, subsystem, and Floquet codes, are typically constructed within the stabilizer formalism, which does not fully capture the idea of fault-tolerance needed for practical quantum computing…
This paper explores a new approach to fault-tolerant quantum computing (FTQC), relying on quantum polar codes. We consider quantum polar codes of Calderbank-Shor-Steane type, encoding one logical qubit, which we refer to as $\mathcal{Q}_1$…
We report new construction of nine-qubit error-correcting code, which introduces two new nine-qubit codes and one new three-qubit code. Because both the new two nine-qubit codes have the normal logical operators, as opposed to the…