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Proposals for quantum computing devices are many and varied. They each have unique noise processes that make none of them fully reliable at this time. There are several error correction/avoidance techniques which are valuable for reducing…
For planar architectures surface code-based quantum error correction is one of the most promising approaches to fault-tolerant quantum computation. This is partially due to the variety of fault-tolerant logical protocols that can be…
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…
Topological stabilizer codes with different spatial dimensions have complementary properties. Here I show that the spatial dimension can be switched using gauge fixing. Combining 2D and 3D gauge color codes in a 3D qubit lattice,…
We introduce a unary coding of bosonic occupation states based on the famous "balls and walls" counting for the number of configurations of $N$ indistinguishable particles on $L$ distinguishable sites. Each state is represented by an…
Bosonic encodings of quantum information offer hardware-efficient, noise-biased approaches to quantum error correction relative to qubit register encodings. Implementations have focused in particular on error correction of stored, idle…
The first generation of multi-qubit quantum technologies will consist of noisy, intermediate-scale devices for which active error correction remains out of reach. To exploit such devices, it is thus imperative to use passive error…
Physical-level noise on traveling bosonic modes remains a critical bottleneck for scalable quantum information processing. We show that for any single-mode bosonic code (qumode) corrupted by thermal or Gaussian displacement noise at loss…
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…
A convenient way to represent quantum optical states is through the quadrature basis of single-modes of the field. This framework provides intuitive definitions for quasi-classical states, their phase-space representations, and enables the…
Bosonic codes allow the encoding of a logical qubit in a single component device, utilizing the infinitely large Hilbert space of a harmonic oscillator. In particular, the Gottesman-Kitaev-Preskill code has recently been demonstrated to be…
We show how good quantum error-correcting codes can be constructed using generalized concatenation. The inner codes are quantum codes, the outer codes can be linear or nonlinear classical codes. Many new good codes are found, including both…
Encoding in a high-dimensional Hilbert space improves noise resilience in quantum information processing. This approach, however, may result in cross-mode coupling and detection complexities, thereby reducing quantum cryptography…
Quantum error correction plays an important role in fault-tolerant quantum information processing. It is usually difficult to experimentally realize quantum error correction, as it requires multiple qubits and quantum gates with high…
In this paper, we address the problem of state communication in finite-level quantum systems through noise-affected channels. Our approach is based on a self-consistent theory of decoding inner products associated with the code and error…
Quantum error correction has recently emerged as a tool to enhance quantum sensing under Markovian noise. It works by correcting errors in a sensor while letting a signal imprint on the logical state. This approach typically requires a…
Noise and errors are inevitable parts of any practical implementation of a quantum computer. As a result, large-scale quantum computation will require ways to detect and correct errors on quantum information. Here, we present such a quantum…
Quantum error correction is a crucial technology for fault tolerant quantum computing. On superconducting platforms, hardware defects in large scale quantum processors can disrupt the regular lattice structure of topological codes and…
The most general method for encoding quantum information is not to encode the information into a subspace of a Hilbert space, but to encode information into a subsystem of a Hilbert space. Recently this notion has led to a more general…
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…