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Quantum error correction offers a promising path to suppress errors in quantum processors, but the resources required to protect logical operations from noise, especially non-Clifford operations, pose a substantial challenge to achieve…
We discuss how the presence of gauge sub-systems in the Bacon-Shor code [D. Bacon, Phys. Rev. A 73, 012340 (2006)] leads to remarkably simple and efficient methods for fault-tolerant error correction (FTEC). Most notably, FTEC does not…
We present a quantum circuit synthesis algorithm for implementing universal fault-tolerant quantum computing based on concatenated codes. To realize fault-tolerant quantum computing, the fault-tolerant quantum protocols should be…
We describe a quantum error correction scheme aimed at protecting a flow of quantum information over long distance communication. It is largely inspired by the theory of classical convolutional codes which are used in similar circumstances…
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…
We develop a measurement-based protocol for simultaneously purifying arbitrary logical states in multiple quantum error correcting codes with unit fidelity and finite probability, starting from arbitrary thermal states of each code. The…
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…
The strongly correlated systems we use to realise quantum error-correcting codes may give rise to high-weight, problematic errors. Encouragingly, we can expect local quantum error-correcting codes with no string-like logical operators $-$…
We compare the performance of quantum error correcting codes when memory errors are unitary with the more familiar case of dephasing noise. For a wide range of codes we analytically compute the effective logical channel that results when…
Fault-tolerant quantum computation with bosonic qubits often necessitates the use of noisy discrete-variable ancillae. In this work, we establish a comprehensive and practical fault-tolerance framework for such a hybrid system and…
In this paper, we derive optimized measurement-free protocols for quantum error correction and the implementation of a universal gate set optimized for an error model that is noise biased . The noise bias is adapted for neutral atom…
We give an introduction to the theory of quantum error correction using stabilizer codes that is geared towards the working computer scientists and mathematicians with an interest in exploring this area. To this end, we begin with an…
Fault tolerant quantum computing relies on the ability to detect and correct errors, which in quantum error correction codes is typically achieved by projectively measuring multi-qubit parity operators and by conditioning operations on the…
Quantum error correcting codes have a distance parameter, conveying the minimum number of single spin errors that could cause error correction to fail. However, the success thresholds of finite per-qubit error rate that have been proven for…
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…
The scheme of entanglement-assisted quantum error-correcting (EAQEC) codes assumes that the ebits of the receiver are error-free. In practical situations, errors on these ebits are unavoidable, which diminishes the error-correcting ability…
We present and analyze protocols for fault-tolerant quantum computing using color codes. We present circuit-level schemes for extracting the error syndrome of these codes fault-tolerantly. We further present an integer-program-based…
Reliable qubits are difficult to engineer, but standard fault-tolerance schemes use seven or more physical qubits to encode each logical qubit, with still more qubits required for error correction. The large overhead makes it hard to…
The essential insight of quantum error correction was that quantum information can be protected by suitably encoding this quantum information across multiple independently erred quantum systems. Recently it was realized that, since the most…
Most quantum error correcting codes are predicated on the assumption that there exists a reservoir of qubits in the state $\ket{0}$, which can be used as ancilla qubits to prepare multi-qubit logical states. In this report, we examine the…