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Time-continuous quantum error correction, necessary to protect quantum information under time-dependent Hamiltonians, relies on weak continuous syndrome measurements. Implementing these measurements requires a continuous coupling among at…
Quantum error correction is an important ingredient for scalable quantum computing. Stabilizer codes are one of the most promising and straightforward ways to correct quantum errors, are convenient for logical operations, and improve…
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 introduce the notion of trace-norm isometric encoding and explore its implications for passive and active methods to protect quantum information against errors. Beside providing an operational foundations to the "subsystems principle"…
Quantum error correcting codes have a distance parameter, conveying the minimum number of single spin errors that could cause error correction to fail. However, the success thresholds of finite per-qubit error rate that have been proven for…
Qudits can be described by a state vector in a $q$-dimensional Hilbert space, enabling a more extensive encoding and manipulation of information compared to qubits. This implies that conducting fault-tolerant quantum computations using…
Conventional fault-tolerant quantum error-correction schemes require a number of extra qubits that grows linearly with the code's maximum stabilizer generator weight. For some common distance-three codes, the recent "flag paradigm" uses…
Quantum error correction plays a critical role in enabling fault-tolerant quantum computing by protecting fragile quantum information from noise. While general-purpose quantum error correction codes are designed to address a wide range of…
In order to use quantum error-correcting codes to actually improve the performance of a quantum computer, it is necessary to be able to perform operations fault-tolerantly on encoded states. I present a general theory of fault-tolerant…
In this work, we analyze a framework for constructing fault-tolerant measurement schedules of varying lengths by combining stabilizer generators, and prove results about the distance of such schedules by combining according to classical…
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…
Quantum error-correcting codes (QECCs) require high encoding rate in addition to high threshold unless a sufficiently large number of physical qubits are available. The many-hypercube (MHC) codes defined as the concatenation of the…
Quantum error-correcting codes are constructed that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of a system described by continuous quantum variables. These codes exploit the noncommutative geometry of…
Mid-circuit measurements used in quantum error correction are essential in quantum computer architecture, as they read out syndrome data and drive logic gates. Here, we use a heavy-hex code prepared on a superconducting qubit array to…
Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. The theory of quantum error-correcting codes has some close ties to and some striking differences…
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 correction (QEC) is considered a deciding component in enabling practical quantum computing. Stabilizer codes, and in particular topological surface codes, are promising candidates for implementing QEC by redundantly encoding…
We introduce a novel type of quantum error correcting code, called the spinor code, based on spaces defined by total spin. The code is a nonstabilizer code, and is also a nonlinear quantum error correcting code, meaning that quantum…
We generalize the construction of quantum error-correcting codes from GF(4)-linear codes by Calderbank et al. to p^m-state systems. Then we show how to determine the error from a syndrome. Finally we discuss a systematic construction of…
Continuous quantum error correction has been found to have certain advantages over discrete quantum error correction, such as a reduction in hardware resources and the elimination of error mechanisms introduced by having entangling gates…