Quantum information is vulnerable to environmental noise and experimental imperfections,
hindering the reliability of practical quantum information processors. Therefore, quantum …

Bosonic modes have wide applications in various quantum technologies, such as optical
photons for quantum communication, magnons in spin ensembles for quantum information …

The unique features of quantum theory offer a powerful new paradigm for information
processing. Translating these mathematical abstractions into useful algorithms and …

The Gottesman-Kitaev-Preskill (GKP) code was proposed in 2001 by Daniel Gottesman,
Alexei Kitaev, and John Preskill as a way to encode a qubit in an oscillator. The GKP …

The design of quantum hardware that reduces and mitigates errors is essential for practical
quantum error correction (QEC) and useful quantum computation. To this end, we introduce …

Quantum computing offers a powerful new paradigm of information processing that has the
potential to transform a wide range of industries. In the pursuit of the tantalizing promises of …

We propose to create and stabilize long-lived macroscopic quantum superposition states in
atomic ensembles. We show that using a fully quantum parametric amplifier can cause the …

Quantum computers have the potential to efficiently solve problems in logistics, drug and
material design, finance, and cybersecurity. However, millions of qubits will be necessary for …

To reach their full potential, quantum computers need to be resilient to noise and
decoherence. In such a fault-tolerant quantum computer, errors must be corrected in real …

These lecture notes from the 2019 Les Houches Summer School on" Quantum Information
Machines" are intended to provide an introduction to classical and quantum error correction …