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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…
Quantum error correction is crucial for protecting quantum information against decoherence. Traditional codes like the surface code require substantial overhead, making them impractical for near-term, early fault-tolerant devices. We…
Noisy intermediate-scale quantum (NISQ) devices are spearheading the second quantum revolution. Of these, quantum annealers are the only ones currently offering real world, commercial applications on as many as 5000 qubits. The size of…
Quantum computers could solve problems beyond the reach of classical devices, but this potential depends on quantum error correction (QEC) to protect fragile quantum states from noise. A central challenge in QEC is decoding: inferring…
Quantum information is vulnerable to environmental noise and experimental imperfections, hindering the reliability of practical quantum information processors. Therefore, quantum error correction (QEC) that can protect quantum information…
The robustness of quantum memory against physical noises is measured by two methods: the exact and approximate quantum error correction (QEC) conditions for error recoverability, and the decoder-dependent error threshold which assesses if…
Recent work on approximate quantum error correction (QEC) has opened up the possibility of constructing subspace codes that protect information with high fidelity in scenarios where perfect error correction is impossible. Motivated by this,…
Quantum error mitigation (EM) is a family of hybrid quantum-classical methods for eliminating or reducing the effect of noise and decoherence on quantum algorithms run on quantum hardware, without applying quantum error correction (EC).…
Reducing errors is essential for reliable quantum computation. Quantum error mitigation (QEM) and quantum error correction (QEC) are two leading approaches for this task, each with challenges: QEM suffers from high sampling costs and cannot…
The use of analog classical systems for computation is generally thought to be a difficult proposition due to the susceptibility of these devices to noise and the lack of a clear framework for achieving fault-tolerance. We present…
Quantum computing has the potential to solve problems that are intractable for classical systems, yet the high error rates in contemporary quantum devices often exceed tolerable limits for useful algorithm execution. Quantum Error…
Continuous-time quantum error correction (CTQEC) is an approach to protecting quantum information from noise in which both the noise and the error correcting operations are treated as processes that are continuous in time. This chapter…
We present a unified approach to quantum error correction, called operator quantum error correction. This scheme relies on a generalized notion of noiseless subsystems that is not restricted to the commutant of the interaction algebra. We…
More than ten years ago a first step towards quantum error correction (QEC) was implemented [Phys. Rev. Lett. 81, 2152 (1998)]. The work showed there was sufficient control in nuclear magnetic resonance (NMR) to implement QEC, and…
As quantum computing advances toward fault-tolerant architectures, quantum error detection (QED) has emerged as a practical and scalable intermediate strategy in the transition from error mitigation to full error correction. By identifying…
Quantum error correction (QEC) is one of the central concepts in quantum information science and also has wide applications in fundamental physics. The capacity theorems provide solid foundations of QEC. We here provide a general and highly…
Quantum machine learning (QML) is an emerging field that promises advantages such as faster training, improved reliability and superior feature extraction over classical counterparts. However, its implementation on quantum hardware is…
Quantum error correction protects quantum information against environmental noise. When using qubits, a measure of quality of a code is the maximum number of errors that it is able to correct. We show that a suitable notion of ``number of…
The overhead of quantum error correction (QEC) poses a major bottleneck for realizing fault-tolerant computation. To reduce this overhead, we exploit the idea of erasure qubits, relying on an efficient conversion of the dominant noise into…
Characterizing and mitigating errors in current noisy intermediate-scale devices is important to improve performance of next generations of quantum hardware. In order to investigate the importance of the different noise mechanisms affecting…