Related papers: Quantum Error Correction and Detection for Quantum…
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…
Quantum error correction (QEC) aims to protect logical qubits from noises by utilizing the redundancy of a large Hilbert space, where an error, once it occurs, can be detected and corrected in real time. In most QEC codes, a logical qubit…
We develop a generalized theory of quantum error correction (QEC) that applies to any linear map, in particular maps that are not completely positive (CP). This theory describes entanglement-assisted QEC for invertible noise maps, which we…
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…
Quantum error correction (QEC) is a key concept in quantum computation as well as many areas of physics. There are fundamental tensions between continuous symmetries and QEC. One vital situation is unfolded by the Eastin--Knill theorem,…
In the era of noisy intermediate-scale quantum (NISQ) devices, the number of controllable hardware qubits is insufficient to implement quantum error correction (QEC). As an alternative, quantum error mitigation (QEM) can suppress errors in…
Quantum error mitigation is expected to play a crucial role in the practical applications of quantum machines for the foreseeable future. Thus it is important to put the numerous quantum error mitigation schemes proposed under a coherent…
Quantum machine learning is a rapidly growing field at the intersection of quantum technology and artificial intelligence. This review provides a two-fold overview of several key approaches that can offer advancements in both the…
Quantum effect enables enhanced estimation precision in metrology, with the Heisenberg limit (HL) representing the ultimate limit allowed by quantum mechanics. Although the HL is generally unattainable in the presence of noise, quantum…
The rapid advancement of quantum computing (QC) and machine learning (ML) has given rise to the burgeoning field of quantum machine learning (QML), aiming to capitalize on the strengths of quantum computing to propel ML forward. Despite its…
Quantum error mitigation (QEM) and quantum error correction (QEC) are two research areas that are often considered as distinct entities, and the problem of combining the two approaches in a non-trivial way has only recently started to be…
Quantum error correcting (QEC) codes protect quantum information from decoherence, as long as error rates fall below critical error thresholds. In general, obtaining thresholds implies simulating the QEC procedure using, in general,…
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…
Large-scale quantum computers promise transformative speedups, but their viability hinges on fast and reliable quantum error correction (QEC). At the center of QEC are decoders-classical algorithms running on hardware such as FPGAs, GPUs,…
In this introduction we motivate and explain the ``decoding'' and ``subsystems'' view of quantum error correction. We explain how quantum noise in QIP can be described and classified, and summarize the requirements that need to be satisfied…
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…
Quantum machine learning (QML) is emerging as an application of quantum computing with the potential to deliver quantum advantage, but its realisation for practical applications remains impeded by challenges. Amongst those, a key barrier is…
Quantum machine learning (QML) is rapidly transitioning from theoretical promise to practical relevance across data-intensive scientific domains. In this Review, we provide a structured overview of recent advances that bridge foundational…
Significant challenges remain with the development of macroscopic quantum computing, hardware problems of noise, decoherence, and scaling, software problems of error correction, and, most important, algorithm construction. Finding truly…
Quantum error correction (QEC) is an essential tool for quantum computing that enables reliable information processing in the presence of noise. Syndrome measurements play a central role in QEC, making it possible to unambiguously identify…