Experimental Quantum Error Correction

Abstract

Quantum error correction is required to compensate for the fragility of the state of a quantum computer. We report the first experimental implementations of quantum error correction and confirm the expected state stabilization. In NMR computing, however, a net improvement in the signal-to-noise would require very high polarization. The experiment implemented the 3-bit code for phase errors in liquid state state NMR.

5 pages, three figures

References in corpus (3)

• Reliable Quantum Computers
• Effective Pure States for Bulk Quantum Computation
• NMR GHZ

Cited by in corpus (262)

• Decoherence, einselection, and the quantum origins of the classical
• Microwave photonics with superconducting quantum circuits
• NMR Techniques for Quantum Control and Computation
• Quantum computing with trapped ions
• State preservation by repetitive error detection in a superconducting quantum circuit
• Quantum strategies
• Josephson-Junction Qubits with Controlled Couplings
• Deterministic entanglement of two trapped ions
• Quantum error correction in a solid-state hybrid spin register
• Realization of Three-Qubit Quantum Error Correction with Superconducting Circuits
• Separability of very noisy mixed states and implications for NMR quantum computing
• Complete quantum teleportation using nuclear magnetic resonance
• Detecting arbitrary quantum errors via stabilizer measurements on a sublattice of the surface code
• Qudits and high-dimensional quantum computing
• Quantum Decoherence
• Universal control and error correction in multi-qubit spin registers in diamond
• Generation of Three-Qubit Entangled States using Superconducting Phase Qubits
• New class of quantum error-correcting codes for a bosonic mode
• Exponential suppression of bit or phase flip errors with repetitive error correction
• Implementation of a Toffoli Gate with Superconducting Circuits
• Repeated Quantum Error Detection in a Surface Code
• Realization of the quantum Toffoli gate with trapped ions
• Implementing the Quantum von Neumann Architecture with Superconducting Circuits
• Controlling the dynamics of an open many-body quantum system with localized dissipation
• Can One Trust Quantum Simulators?
• Experimental realization of quantum games on a quantum computer
• Implementation of the Quantum Fourier Transform
• Demonstration of quantum error correction and universal gate set on a binomial bosonic logical qubit
• Experimental Implementation of Discrete Time Quantum Random Walk on an NMR Quantum Information Processor
• Detecting bit-flip errors in a logical qubit using stabilizer measurements
• Experimental Implementation of the Quantum Random-Walk Algorithm
• Sophisticated quantum search without entanglement
• Design of Strongly Modulating Pulses to Implement Precise Effective Hamiltonians for Quantum Information Processing
• Quantum physics meets biology
• Quantum computation using electrons trapped by surface acoustic waves
• Quantum error correction with only two extra qubits
• Experimental demonstration of topological error correction
• Implementation of the Five Qubit Error Correction Benchmark
• Benchmarking quantum control methods on a 12-qubit system
• Error corrected quantum annealing with hundreds of qubits
• Quantum Computing with NMR
• Beating the break-even point with a discrete-variable-encoded logical qubit
• Quantum error correction with silicon spin qubits
• Quantum Simulations on a Quantum Computer
• High-Resolution Correlation Spectroscopy of 13C Spins Near a Nitrogen-Vacancy Center in Diamond
• Quantum Computers and Quantum Coherence
• Assessing the progress of trapped-ion processors towards fault-tolerant quantum computation
• Quantum simulation of a system with competing two- and three-body interactions
• Creating Decoherence-Free Subspaces with Strong and Fast Pulses
• Quantum computers in phase space
• Liquid State NMR as a Test-bed for Developing Quantum Control Methods
• Universal quantum gates for hybrid systems assisted by quantum dots inside double-sided optical microcavities
• Repeated multi-qubit readout and feedback with a mixed-species trapped-ion register
• Quantum computing with neutral atoms
• Entanglement-Assisted Quantum Networks: Mechanics, Enabling Technologies, Challenges, and Research Directions
• Quantum simulation of a three-body interaction Hamiltonian on an NMR quantum computer
• Noisy intermediate-scale quantum computers
• High-Fidelity Single-Shot Toffoli Gate via Quantum Control
• A CNOT gate between multiphoton qubits encoded in two cavities
• Measurement-based quantum computation with trapped ions
• Information preserving structures: A general framework for quantum zero-error information
• Physical Optimization of Quantum Error Correction Circuits
• Holographic tensor network models and quantum error correction: A topical review
• Heating and decoherence suppression using decoupling techniques
• The structure of preserved information in quantum processes
• Fast multi-qubit gates by adiabatic evolution in interacting excited state manifolds
• Asymptotic Improvements to Quantum Circuits via Qutrits
• Quantum Computation
• Higher Order Methods for Simulations on Quantum Computers
• Entanglement Stabilization using Parity Detection and Real-Time Feedback in Superconducting Circuits
• Fault tolerant architectures for superconducting qubits
• Quantum Logic Gates and Nuclear Magnetic Resonance Pulse Sequences
• Optimal control of entangling operations for trapped ion quantum computing
• Optimal Scheme for Quantum Metrology
• A conditional-phase switch at the single-photon level
• Experimental Implementation of the Quantum Baker's Map
• Demonstration of Quantum Error Correction using Linear Optics
• Designing High-Fidelity Single-Shot Three-Qubit Gates: A Machine Learning Approach
• Quantum Nonlinear Optics without Photons
• Scalable quantum computing with qudits on a graph
• Quantum logic and entanglement by neutral Rydberg atoms: methods and fidelity
• Five Two-Qubit Gates Are Necessary for Implementing Toffoli Gate
• Experimental quantum coding against photon loss error
• Demonstration of Controlled-Phase Gates between Two Error-Correctable Photonic Qubits
• Classical model for bulk-ensemble NMR quantum computation
• Fault-tolerant holonomic quantum computation
• Single-step implementation of high fidelity $n$-bit Toffoli gate
• Quantum gate learning in engineered qubit networks: Toffoli gate with always-on interactions
• Processing multi-photon state through operation on single photon: methods and applications
• Multipulse Control of Decoherence
• Compressed sensing quantum process tomography for superconducting quantum gates
• Deutsch, Toffoli, and CNOT Gates via Rydberg Blockade of Neutral Atoms
• Grover search with pairs of trapped ions
• Control Landscapes for Observable Preparation with Open Quantum Systems
• Robustness of dynamical decoupling sequences
• Generalized Toffoli gates using qudit catalysis
• Quantum Computation and Quantum Information
• Realization of efficient quantum gates with a superconducting qubit-qutrit circuit
• Scalable algorithm simplification using quantum AND logic
• Fault-Tolerant Operation of a Quantum Error-Correction Code
• Quantum optical coherence can survive photon losses: a continuous-variable quantum erasure correcting code
• Experimental implementation of encoded logical qubit operations in a perfect quantum error correcting code
• Fast three-qubit Toffoli quantum gate based on the three-body Förster resonances in Rydberg atoms
• Experimental Implementation of a Concatenated Quantum Error-Correcting Code
• Solid-State Nuclear Spin Quantum Computer Based on Magnetic Resonance Force Microscopy
• NMR quantum computation with indirectly coupled gates
• Experimental exploration of five-qubit quantum error correcting code with superconducting qubits
• Large-scale quantum networks based on graphs
• Realization of logically labeled effective pure states for bulk quantum computation
• Experimental Realization of A Two Bit Phase Damping Quantum Code
• Demonstration of sufficient control for two rounds of quantum error correction in a solid state ensemble quantum information processor
• Quantum Computing: An Overview Across the System Stack
• Nonlinear optics with less than one photon
• One-step implementation of a hybrid Fredkin gate with quantum memories and single superconducting qubit in circuit QED and its applications
• Continuous-variable and hybrid quantum gates
• Quantum Router with Network Coding
• A programmable three-qubit superconducting processor with all-to-all connectivity
• Nuclear Magnetic Resonance Implementation of a Quantum Clock Synchronization Algorithm
• Fault-tolerance thresholds for the surface code with fabrication errors
• Block synchronization for quantum information
• A taxonomy of small Markovian errors
• Implementation-independent sufficient condition of the Knill-Laflamme type for the autonomous protection of logical qudits by strong engineered dissipation
• Generalized Quantum Search with Parallelism
• NMR analogues of the quantum Zeno effect
• Protocol for a resonantly-driven three-qubit Toffoli gate with silicon spin qubits
• The Road From Classical to Quantum Codes: A Hashing Bound Approaching Design Procedure
• Realizing the quantum baker's map on an NMR quantum computer
• Exploring Noiseless Subsystems via Nuclear Magnetic Resonance
• Introduction to NMR Quantum Information Processing
• Quantum Error Correction with Quantum Autoencoders
• Resource-Efficient Quantum Computing by Breaking Abstractions
• Using error correction to determine the noise model
• Fault-tolerant protection of near-term trapped-ion topological qubits under realistic noise sources
• Efficient construction of three- and four-qubit quantum gates by global entangling gates
• Automated Error Correction in IBM Quantum Computer and Explicit Generalization
• Hadamard Products of Product Operators and the Design of Gradient-Diffusion Experiments for Simulating Decoherence by NMR Spectroscopy
• Gaussian error correction of quantum states in a correlated noisy channel
• A scalable solid-state quantum computer based on quantum dot pillar structures
• Quantum Logic with a Single Trapped Electron
• Universal quantum multi-qubit entangling gates with auxiliary spaces
• Implementing universal multi-qubit quantum logic gates in three and four-spin systems at room temperature
• Automatic Quantum Error Correction
• Introduction to Quantum Error Correction and Fault Tolerance
• Guaranteed recovery of quantum processes from few measurements
• Quantum processing with ensembles of rare earth ions in a stoichiometric crystal
• Tailored codes for small quantum memories
• Direct measurement of Bacon-Shor code stabilizers
• Supervised learning of time-independent Hamiltonians for gate design
• Decoherence control in microwave cavities
• Implementation of a Deutsch-like quantum algorithm utilizing entanglement at the two-qubit level, on an NMR quantum information processor
• A Study of Quantum Error Correction by Geometric Algebra and Liquid-State NMR Spectroscopy
• Loss-tolerant all-photonic quantum repeater with generalized Shor code
• An optically driven quantum dot quantum computer
• Time-optimal Unitary Operations in Ising Chains II: Unequal Couplings and Fixed Fidelity
• Spatially Encoded Pseudo-Pure States for NMR Quantum Information Processing
• Experimental Quantum Error Rejection for Quantum Communication
• Undoing a quantum measurement
• Simple implementation of high fidelity controlled-$i$SWAP gates and quantum circuit exponentiation of non-Hermitian gates
• Experimental quantum error correction with high fidelity
• Simulating nonnative cubic interactions on noisy quantum machines
• Demonstrating Quantum Error Correction that Extends the Lifetime of Quantum Information
• Effect of system level structure and spectral distribution of the environment on the decoherence rate
• Scheme for fault-tolerant holonomic computation on stabilizer codes
• Quantum error correction with the color-Gottesman-Kitaev-Preskill code
• Efficient experimental design of high-fidelity three-qubit quantum gates via genetic programming
• Designing High-Fidelity Zeno Gates for Dissipative Cat Qubits
• Simple quantum error detection and correction for superconducting qubits
• Error correcting Bacon-Shor code with continuous measurement of noncommuting operators
• Non-Markovian dynamics under time-translation symmetry
• Nonlocal Activation of Bound Entanglement via Local Quantum Zeno Dynamics
• Simulating Zeno physics by quantum quench with superconducting circuits
• Controlling NMR spin systems for quantum computation
• Quantum error correction via less noisy qubits
• Single-Step Parity Check Gate Set for Quantum Error Correction
• Scalable uniform construction of highly-conditional quantum gates
• Quantum state engineering by steering in the presence of errors
• High-rate quantum low-density parity-check codes assisted by reliable qubits
• A Cat-State Benchmark on a Seven Bit Quantum Computer
• An Introduction to Quantum Computing for Non-Physicists
• Implementation of three-qubit Toffoli gate in a single step
• A simple trapped-ion architecture for high-fidelity Toffoli gates
• Preparing pseudo-pure states with controlled-transfer gates
• Spectral investigation of the noise influencing multi-qubit states
• A Toffoli Gate Decomposition via Echoed Cross-Resonance Gates
• "Spectral Implementation" for creating a labeled pseudo-pure state and the Bernstein-Vazirani's algorithm in a four-qubit nuclear magnetic resonance quantum processor
• Implementation of a three-qubit quantum error correction code in a cavity-QED setup
• Implementation of the three-qubit phase-flip error correction code with superconducting qubits
• Bacon-Shor code with continuous measurement of non-commuting operators
• Errors due to Finite Rise/fall Times of Pulses in Superconducting Charge Qubits
• Quantum Error Correction with magnetic molecules
• Three-body Förster resonance of a new type in Rydberg atoms
• A simple Example of Definitions of Truth, Validity, Consistency, and Completeness in Quantum Mechanics
• Thermodynamic Analysis of Algorithmic Cooling Protocols: Efficiency Metrics and Improved Designs
• Quantifying the Performance of Quantum Codes
• Universal resource-efficient topological measurement-based quantum computation via color-code-based cluster states
• Testing a Quantum Error-Correcting Code on Various Platforms
• The Influence of Superpositional Wave Function Oscillations on Shor's Quantum Algorithm
• LILLIPUT: A Lightweight Low-Latency Lookup-Table Based Decoder for Near-term Quantum Error Correction
• Implementations of two-photon four-qubit Toffoli and Fredkin gates assisted by nitrogen-vacancy centers
• Energy spectra of three electrons in Si/SiGe single and vertically coupled double quantum dots
• Spin-dependent inter- and intra-valley electron-phonon scattering in germanium
• Broadband noise decoherence in solid-state complex architectures
• Quantum error correction under numerically exact open-quantum-system dynamics
• Toffoli gate based on a three-body fine-structure-state-changing Förster resonance in Rydberg atoms
• Low-temperature environments for quantum computation and quantum simulation
• Quantum error correction benchmarks for continuous weak parity measurements
• Gate-set evaluation metrics for closed-loop optimal control on nitrogen-vacancy center ensembles in diamond
• Experimental demonstration of switching entangled photons based on the Rydberg blockade effect
• One-step achievement of robust multipartite Greenberger-Horne-Zeilinger state and controlled-phase gate via Rydberg interaction
• Machine-learning-inspired quantum optimal control of nonadiabatic geometric quantum computation via reverse engineering
• A Quantum Computational Learning Algorithm
• Non-commutative graphs based on finite-infinite system couplings: quantum error correction for a qubit coupled to a coherent field
• Efficient separation of quantum from classical correlations for mixed states with a fixed charge
• Quantum correlations which imply causation
• Quantum Error Correction with Uniformly Mixed State Ancillae
• Integration of highly probabilistic sources into optical quantum architectures: perpetual quantum computation
• Stabilization of Discrete Time-Crystaline Response on a Superconducting Quantum Computer by increasing the Interaction Range
• Para-ortho transition of artificial H${}_2$ molecule in lateral quantum dots doped with magnetic impurities
• Demonstrating quantum error mitigation on logical qubits
• Subsystem Pseudo-pure States
• Experimental realization of a highly structured search algorithm
• Lightcone Bounds for Quantum Circuit Mapping via Uncomplexity
• SpinQ Gemini: a desktop quantum computer for education and research
• Exploring a Double Full-Stack Communications-Enabled Architecture for Multi-Core Quantum Computers
• Quantum error correction using weak measurements
• Reversible ternary logic with Laguerre-Gaussian modes
• Generalized Number-Phase Lattice Encoding of a Bosonic Mode for Quantum Error Correction
• Single-qubit rotation algorithm with logarithmic Toffoli count and gate depth
• Dynamics of a Quantum Control-Not Gate for an Ensemble of Four-Spin Molecules at Room Temperature
• Experimental realization of quantum non-Markovianity through the convex mixing of Pauli semigroups on an NMR quantum processor
• Fast Simulation of Magnetic Field Gradients for Optimization of Pulse Sequences
• Universal framework for simultaneous tomography of quantum states and SPAM noise
• Algorithms on Ensemble Quantum Computers
• Experimental replication of single-qubit quantum phase gates
• Long-range Ising interactions mediated by $\lambda {\varphi }^4$ fields: probing the renormalisation of sound in crystals of trapped ions
• High cooperativity coupling to nuclear spins on a circuit QED architecture
• Demonstration of a variational quantum eigensolver with a solid-state spin system under ambient conditions
• Quantum Codes for Controlling Coherent Evolution
• Robustness of Magic in the quantum Ising chain via Quantum Monte Carlo tomography
• Quantum control without quantum states
• Scalability and high-efficiency of an $(n+1)$-qubit Toffoli gate sphere via blockaded Rydberg atoms
• A unification of the coding theory and OAQEC perspective on hybrid codes
• Universal set of Dynamically Protected Gates for Bipartite Qubit Networks II: Soft Pulse Implementation of the [[5,1,3]] Quantum Error Correcting Code
• Simplify proposal for realizing multiqubit tunable phase gate in circuit QED
• Microwave-activated high-fidelity three-qubit gate scheme for fixed-frequency superconducting qubits
• Circuit-Noise-Resilient Virtual Distillation
• Error Correction with Euclidean Qubits
• Performance engineering of semiconductor spin qubit systems
• Break-even point of the quantum repetition code
• Principles and Demonstrations of Quantum Information Processing by NMR Spectroscopy
• Resurrection of Schrodinger Cat
• Implementing a Ternary Decomposition of the Toffoli Gate on Fixed-FrequencyTransmon Qutrits
• Semiclassical model for a memory dephasing channel
• Entanglement preservation in tripartite quantum systems under dephasing dynamics
• Stabilization of symmetry-protected long-range entanglement in stochastic quantum circuits
• Achieving ultimate noise tolerance in quantum communication
• Enhancing entanglement and total correlations dynamics via local unitaries
• Engineering long-range and multi-body interactions via global kinetic constraints
• Universal quantum gates for photon-atom hybrid systems assisted by bad cavities
• Practical implementation of Toffoli-based qubit rotation
• Experimental Quantum Error-Free Transmission
• Dephasing-Induced Distribution of Entanglement in Tripartite Quantum Systems