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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…
We discuss methods of quantum state tomography for solid-state systems with a large nuclear spin $I=3/2$ in nanometer-scale semiconductors devices based on a quantum well. Due to quadrupolar interactions, the Zeeman levels of these…
Practical quantum computing will require error rates that are well below what is achievable with physical qubits. Quantum error correction offers a path to algorithmically-relevant error rates by encoding logical qubits within many physical…
Fault-tolerant quantum computing demands many qubits with long lifetimes to conduct accurate quantum gate operations. However, external noise limits the computing time of physical qubits. Quantum error correction codes may extend such…
Quantum error correction allows for faulty quantum systems to behave in an effectively error free manner. One important class of techniques for quantum error correction is the class of quantum subsystem codes, which are relevant both to…
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 correcting codes are designed to pinpoint exactly when and where errors occur in quantum circuits. This feature is the foundation of their primary task: to support fault-tolerant quantum computation. However, this feature…
Quantum error correction uses the measurement of syndromes and classical decoding algorithms to estimate the location and type of errors while protecting the encoded quantum bits. Here we consider how prior information and Bayesian updates…
Methods borrowed from the world of quantum information processing have lately been used to enhance the signal-to-noise ratio of quantum detectors. Here we analyze the use of stabilizer quantum error-correction codes for the purpose of…
We study numerically the process of nuclear spin measurement in a solid-state quantum computer of the type proposed by Kane by modeling the quantum dynamics of two coupled nuclear spins on $^{31}$P donors implanted in silicon. We estimate…
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…
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 have developed semiconductor point contact devices in which nuclear spins in a nanoscale region are coherently controlled by all-electrical methods. Different from the standard nuclear-magnetic resonance technique, the longitudinal…
Quantum sensors are expected to be a prominent use-case of quantum technologies, but in practice, noise easily degrades their performance. Quantum sensors can for instance be afflicted with erasure errors. Here, we consider using quantum…
Error mitigation has enabled quantum computing applications with over one hundred qubits and deep circuits. The most general error mitigation methods rely on a faithful characterization of the noise channels of the hardware. However,…
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…
Performing active quantum error correction to protect fragile quantum states highly depends on the correctness of error information--error syndromes. To obtain reliable error syndromes using imperfect physical circuits, we propose the idea…
Molecular Nanomagnets may enable the implementation of qudit-based quantum error-correction codes which exploit the many spin levels naturally embedded in a single molecule, a promising step towards scalable quantum processors. To fully…
Scalable quantum computing and communication requires the protection of quantum information from the detrimental effects of decoherence and noise. Previous work tackling this problem has relied on the original circuit model for quantum…
Quantum information can be protected from decoherence and other errors, but only if these errors are sufficiently rare. For quantum computation to become a scalable technology, practical schemes for quantum error correction that can…