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Quantum systems can be used to measure various quantities in their environment with high precision. Often, however, their sensitivity is limited by the decohering effects of this same environment. Dynamical decoupling schemes are widely…
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…
In measurement-based quantum computing an algorithm is performed by measurements on highly-entangled resource states. To date, several implementations were demonstrated, all of them assuming perfect noise-free environments. Here we consider…
Quantum error correction (QEC) is an essential element of physical quantum information processing systems. Most QEC efforts focus on extending classical error correction schemes to the quantum regime. The input to a noisy system is embedded…
Quantum information processing offers dramatic speedups, yet is famously susceptible to decoherence, the process whereby quantum superpositions decay into mutually exclusive classical alternatives, thus robbing quantum computers of their…
Protecting information against decoherence in open quantum systems remains a central challenge for quantum computing. In particular, passive error correction schemes have so far been limited to static memories rather than dynamical qubits.…
Quantum circuits with local particle number conservation (LPNC) restrict the quantum computation to a subspace of the Hilbert space of the qubit register. In a noiseless or fault-tolerant quantum computation, such quantities are preserved.…
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…
The main ideas of quantum error correction are introduced. These are encoding, extraction of syndromes, error operators, and code construction. It is shown that general noise and relaxation of a set of 2-state quantum systems can always be…
Active quantum error correction using qubit stabilizer codes has emerged as a promising, but experimentally challenging, engineering program for building a universal quantum computer. In this review we consider the formalism of qubit…
We study the effectiveness of quantum error correction against coherent noise. Coherent errors (for example, unitary noise) can interfere constructively, so that in some cases the average infidelity of a quantum circuit subjected to…
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…
We provide rigorous bounds for the error of the adiabatic approximation of quantum mechanics under four sources of experimental error: perturbations in the initial condition, systematic time-dependent perturbations in the Hamiltonian,…
We describe the smallest quantum error correcting (QEC) code to correct for amplitude-damping (AD) noise, namely, a 3-qubit code that corrects all the single-qubit damping errors. We generalize this construction to a family of codes that…
We investigate the limits of quantum error correction (QEC) in neutral-atom processors approaching high-fidelity gates and fast cycle times. We show that shorter QEC cycles amplify platform-specific errors, notably Rydberg excitation…
The demonstration of quantum error correction (QEC) is one of the most important milestones in the realization of fully-fledged quantum computers. Toward this, QEC experiments using the surface codes have recently been actively conducted.…
Characterizing noisy quantum processes is important to quantum computation and communication (QCC), since quantum systems are generally open. To date, all methods of characterization of quantum dynamics (CQD), typically implemented by…
Bosonic codes, leveraging infinite-dimensional Hilbert spaces for redundancy, offer great potential for encoding quantum information. However, the realization of a practical continuous-variable bosonic code that can simultaneously correct…
The storage and processing of quantum information are susceptible to external noise, resulting in computational errors that are inherently continuous A powerful method to suppress these effects is to use quantum error correction. Typically,…
In a recent study [Rohde et al., quant-ph/0603130 (2006)] of several quantum error correcting protocols designed for tolerance against qubit loss, it was shown that these protocols have the undesirable effect of magnifying the effects of…