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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…
Realizing the full potential of quantum computation requires Quantum Error Correction (QEC). QEC reduces error rates by encoding logical information across redundant physical qubits, enabling errors to be detected and corrected. A common…
Noise and errors are inevitable parts of any practical implementation of a quantum computer. As a result, large-scale quantum computation will require ways to detect and correct errors on quantum information. Here, we present such a quantum…
Arbitrarily long quantum computations require quantum memories that can be repeatedly measured without being corrupted. Here, we preserve the state of a quantum memory, notably with the additional use of flagged error events. All error…
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…
Performing experiments on small-scale quantum computers is certainly a challenging endeavor. Many parameters need to be optimized to achieve high-fidelity operations. This can be done efficiently for operations acting on single qubits as…
Quantum error correction plays an important role in fault-tolerant quantum information processing. It is usually difficult to experimentally realize quantum error correction, as it requires multiple qubits and quantum gates with high…
A fault-tolerant quantum computer will be supported by a classical decoding system interfacing with quantum hardware to perform quantum error correction. It is important that the decoder can keep pace with the quantum clock speed, within…
Quantum technologies have the potential to solve certain computationally hard problems with polynomial or super-polynomial speedups when compared to classical methods. Unfortunately, the unstable nature of quantum information makes it prone…
Analysis of quantum error correcting codes is typically done using a stochastic, Pauli channel error model for describing the noise on physical qubits. However, it was recently found that coherent errors (systematic rotations) on physical…
Quantum error correction protocols will play a central role in the realisation of quantum computing; the choice of error correction code will influence the full quantum computing stack, from the layout of qubits at the physical level to…
The minimum weight perfect matching (MWPM) decoder is the standard decoding strategy for quantum surface codes. However, it suffers a harsh decrease in performance when subjected to biased or non-identical quantum noise. In this work, we…
Topological error correcting codes, and particularly the surface code, currently provide the most feasible roadmap towards large-scale fault-tolerant quantum computation. As such, obtaining fast and flexible decoding algorithms for these…
The complexity of the error correction circuitry forces us to design quantum error correction codes capable of correcting a single error per error correction cycle. Yet, time-correlated error are common for physical implementations of…
Certain physical aspects of quantum error correction are discussed for a quantum computer (n-qubit register) in contact with a decohering environment. Under rather plausible assumptions upon the form of the computer-environment interaction,…
We describe a simple quantum error correcting code built out of a time-dependent transverse field Ising model. The code is similar to a repetition code, but has two advantages: an $N$-qubit code can be implemented with a finite-depth…
Quantum error correction (QEC) is an essential concept for any quantum information processing device. Typically, QEC is designed with minimal assumptions about the noise process; this generic assumption exacts a high cost in efficiency and…
Quantum error correction codes (QECCs) are critical for realizing reliable quantum computing by protecting fragile quantum states against noise and errors. However, limited research has analyzed the noise resilience of QECCs to help select…
Concatenating quantum error correction codes scales error correction capability by driving logical error rates down double-exponentially across levels. However, the noise structure shifts under concatenation, making it hard to choose an…
Quantum error correction works effectively only if the error rate of gate operations is sufficiently low. However, some rare physical mechanisms can cause a temporary increase in the error rate that affects many qubits; examples include…