Introduction to Quantum Error Correction and Fault Tolerance
arXiv:2111.08894 · doi:10.21468/SciPostPhysLectNotes.70
Abstract
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 with bits and qubits, and with continuous variable systems (harmonic oscillators). The focus on the latter will be on practical examples that can be realized today or in the near future with a modular architecture based on superconducting electrical circuits and microwave photons. The goal and vision is 'hardware-efficient' quantum error correction that does not require exponentially large hardware overhead in order to achieve practical and useful levels of fault tolerance and circuit depth.
arXiv commentSubmitted to SciPost Lecture Notes. To appear in 'Quantum Information Machines; Lecture Notes of the Les Houches Summer School 2019,' eds. M. Devoret, B. Huard, and I. Pop. Update v4 consists of final post-refereeing edits
References in corpus (98)
- Fault-tolerant quantum computation by anyons
- Non-Abelian Anyons and Topological Quantum Computation
- Mixed State Entanglement and Quantum Error Correction
- Quantum information with continuous variables
- Surface codes: Towards practical large-scale quantum computation
- Cavity quantum electrodynamics for superconducting electrical circuits: an architecture for quantum computation
- Introduction to Quantum Noise, Measurement and Amplification
- Encoding a qubit in an oscillator
- Improved Simulation of Stabilizer Circuits
- Quantum Error Correction for Quantum Memories
- Quantum computation over continuous variables
- Suppressing quantum errors by scaling a surface code logical qubit
- Quantum computation with ions in thermal motion
- Reliable Quantum Computers
- A Theory of Fault-Tolerant Quantum Computation
- State preservation by repetitive error detection in a superconducting quantum circuit
- Stabilizer Codes and Quantum Error Correction
- Realizing Repeated Quantum Error Correction in a Distance-Three Surface Code
- Deterministic entanglement of two trapped ions
- Dynamically protected cat-qubits: a new paradigm for universal quantum computation
- Quantum error correction in a solid-state hybrid spin register
- Realization of Three-Qubit Quantum Error Correction with Superconducting Circuits
- Experimental Quantum Error Correction
- Confining the state of light to a quantum manifold by engineered two-photon loss
- Simple Quantum Error Correcting Codes
- Quantum Algorithms for Quantum Field Theories
- Instantaneous non-local computation of low T-depth quantum circuits
- The Heisenberg Representation of Quantum Computers
- Macroscopically distinct quantum superposition states as a bosonic code for amplitude damping
- The Kerr-Cat Qubit: Stabilization, Readout, and Gates
- Quantum error correction of a qubit encoded in grid states of an oscillator
- Universal control and error correction in multi-qubit spin registers in diamond
- Qubit-photon interactions in a cavity: Measurement induced dephasing and number splitting
- Efficient Classical Simulation of Continuous Variable Quantum Information Processes
- Real-time quantum error correction beyond break-even
- New class of quantum error-correcting codes for a bosonic mode
- Encoding a qubit in a trapped-ion mechanical oscillator
- Resilient Quantum Computation: Error Models and Thresholds
- Realization of an Error-Correcting Surface Code with Superconducting Qubits
- A No-Go Theorem for Gaussian Quantum Error Correction
- Engineering the quantum states of light in a Kerr-nonlinear resonator by two-photon driving
- Performance and structure of single-mode bosonic codes
- Hardware-efficient autonomous quantum error correction
- Demonstration of quantum error correction and universal gate set on a binomial bosonic logical qubit
- Cooling the Collective Motion of Trapped Ions to Initialize a Quantum Register
- Deterministic teleportation of a quantum gate between two logical qubits
- The XZZX Surface Code
- Repeated quantum error correction on a continuously encoded qubit by real-time feedback
- Exponential suppression of bit-flips in a qubit encoded in an oscillator
- On-demand quantum state transfer and entanglement between remote microwave cavity memories
- Approximate quantum error correction can lead to better codes
- Bosonic Quantum Codes for Amplitude Damping
- Implementation of the Five Qubit Error Correction Benchmark
- Cavity State Manipulation Using Photon-Number Selective Phase Gates
- Erasure conversion for fault-tolerant quantum computing in alkaline earth Rydberg atom arrays
- Error correction for continuous quantum variables
- Bosonic quantum error correction codes in superconducting quantum circuits
- Bias-preserving gates with stabilized cat qubits
- Beating the break-even point with a discrete-variable-encoded logical qubit
- Fast Universal Control of an Oscillator with Weak Dispersive Coupling to a Qubit
- Universal Control of an Oscillator with Dispersive Coupling to a Qubit
- Fault-tolerant bosonic quantum error correction with the surface-GKP code
- Repetition Cat Qubits for Fault-Tolerant Quantum Computation
- Digitization of Scalar Fields for Quantum Computing
- Fault-tolerant detection of a quantum error
- An Introduction to Quantum Error Correction and Fault-Tolerant Quantum Computation
- Protecting a Bosonic Qubit with Autonomous Quantum Error Correction
- Stabilized Cat in Driven Nonlinear Cavity: A Fault-Tolerant Error Syndrome Detector
- Quantum information processing with bosonic qubits in circuit QED
- Entangling Bosonic Modes via an Engineered Exchange Interaction
- Quantum Error Correction with the Toric-GKP Code
- Towards Scalable Bosonic Quantum Error Correction
- Quantum Error Correction with the Gottesman-Kitaev-Preskill Code
- Encoding a Qubit into a Cavity Mode in Circuit-QED using Phase Estimation
- A CNOT gate between multiphoton qubits encoded in two cavities
- Quantum control of bosonic modes with superconducting circuits
- Understanding Quality Factor Degradation in Superconducting Niobium Cavities at Low Microwave Field Amplitudes
- Error-transparent operations on a logical qubit protected by quantum error correction
- Density-matrix simulation of small surface codes under current and projected experimental noise
- Stabilization of Finite-Energy Gottesman-Kitaev-Preskill States
- Fault tolerant architectures for superconducting qubits
- Pair-cat codes: autonomous error-correction with low-order nonlinearity
- High-fidelity measurement of qubits encoded in multilevel superconducting circuits
- Demonstration of Quantum Error Correction using Linear Optics
- An Introduction to Quantum Error Correction
- Demonstration of Controlled-Phase Gates between Two Error-Correctable Photonic Qubits
- Climbing Mount Scalable: Physical-Resource Requirements for a Scalable Quantum Computer
- Experimental Implementation of a Concatenated Quantum Error-Correcting Code
- Error Rates and Resource Overheads of Repetition Cat Qubits
- Demonstration of sufficient control for two rounds of quantum error correction in a solid state ensemble quantum information processor
- Stabilizer quantum error correction toolbox for superconducting qubits
- Encoding qubits in multimode grid states
- Implementing and characterizing precise multi-qubit measurements
- Linear independence of nearest neighbor valence bond states on the kagome lattice and construction of SU(2)-invariant spin-1/2-Hamiltonian with a Sutherland-Rokhsar-Kivelson quantum liquid ground state
- Robust readout of bosonic qubits in the dispersive coupling regime
- Optimized Tomography of Continuous Variable Systems Using Excitation Counting
- Enhancing qubit readout through dissipative sub-Poissonian dynamics
- Autonomous quantum error correction and quantum computation
Cited by in corpus (17)
- Error-Tolerant Amplification and Simulation of the Ultrastrong-Coupling Quantum Rabi Model
- Hybrid Oscillator-Qubit Quantum Processors: Instruction Set Architectures, Abstract Machine Models, and Applications
- Simultaneous Discovery of Quantum Error Correction Codes and Encoders with a Noise-Aware Reinforcement Learning Agent
- Quantum spherical codes
- Neural Network-Based Design of Approximate Gottesman-Kitaev-Preskill Code
- Thermal Area Law for Lattice Bosons
- Noise-aware variational eigensolvers: a dissipative route for lattice gauge theories
- Quantum process tomography of continuous-variable gates using coherent states
- Exact results on finite size corrections for surface codes tailored to biased noise
- Quantum Error Channels in High Energetic Photonic Systems
- Dispersive Qubit Readout with Intrinsic Resonator Reset
- Safeguarding Oscillators and Qudits with Distributed Two-Mode Squeezing
- Automated discovery and optimization of autonomous quantum error correction codes for a general open quantum system
- Reshaping quantum device noise via repetition code circuits
- Unfolding the Toric Code Model with Emergent Qubits
- CDJ-Pontryagin Optimal Control for General Continuously Monitored Quantum Systems
- Quantum Error Correction with Superpositions of Squeezed Fock States