Towards Scalable Bosonic Quantum Error Correction

Abstract

We review some of the recent efforts in devising and engineering bosonic qubits for superconducting devices, with emphasis on the Gottesman-Kitaev-Preskill (GKP) qubit. We present some new results on decoding repeated GKP error correction using finitely-squeezed GKP ancilla qubits, exhibiting differences with previously studied stochastic error models. We discuss circuit-QED ways to realize CZ gates between GKP qubits and we discuss different scenario's for using GKP and regular qubits as building blocks in a scalable superconducting surface code architecture.

arXiv comment54 pages; 18 Figs; 3 Appendices; invited topical review for Quantum Science & Technology. v2 has a few corrections and some additional references. v3 has a few additional corrections and references

References in corpus (71)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Charge insensitive qubit design derived from the Cooper pair box
• Cavity quantum electrodynamics for superconducting electrical circuits: an architecture for quantum computation
• Encoding a qubit in an oscillator
• Quantum Error Correction for Quantum Memories
• The Magnus expansion and some of its applications
• Fluxonium: single Cooper pair circuit free of charge offsets
• Dynamically protected cat-qubits: a new paradigm for universal quantum computation
• Roads towards fault-tolerant universal quantum computation
• Schrieffer-Wolff transformation for quantum many-body systems
• Confining the state of light to a quantum manifold by engineered two-photon loss
• Squeezing as an irreducible resource
• Macroscopically distinct quantum superposition states as a bosonic code for amplitude damping
• New class of quantum error-correcting codes for a bosonic mode
• Encoding a qubit in a trapped-ion mechanical oscillator
• A quantum memory with near-millisecond coherence in circuit QED
• Black-box superconducting circuit quantization
• 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
• Rapid high-fidelity multiplexed readout of superconducting qubits
• The high-coherence fluxonium qubit
• Exponential suppression of bit-flips in a qubit encoded in an oscillator
• Granular aluminum: A superconducting material for high impedance quantum circuits
• 3-Wave Mixing Josephson Dipole Element
• Bosonic Quantum Codes for Amplitude Damping
• Cavity State Manipulation Using Photon-Number Selective Phase Gates
• Reaching 10 ms single photon lifetimes for superconducting aluminum cavities
• Scalable quantum circuit and control for a superconducting surface code
• A fast, low-leakage, high-fidelity two-qubit gate for a programmable superconducting quantum computer
• Fault-tolerant bosonic quantum error correction with the surface-GKP code
• All-Gaussian universality and fault tolerance with the Gottesman-Kitaev-Preskill code
• Repetition Cat Qubits for Fault-Tolerant Quantum Computation
• Progress towards practical qubit computation using approximate Gottesman-Kitaev-Preskill codes
• Quantum computing with rotation-symmetric bosonic codes
• Fault-tolerant detection of a quantum error
• Coherent oscillations inside a quantum manifold stabilized by dissipation
• Stabilized Cat in Driven Nonlinear Cavity: A Fault-Tolerant Error Syndrome Detector
• Entangling Bosonic Modes via an Engineered Exchange Interaction
• Quantum Error Correction with the Toric-GKP Code
• Generating Grid States From Schrödinger Cat States without Post-Selection
• Schrodinger's catapult: Launching multiphoton quantum states from a microwave cavity memory
• Single-Mode Displacement Sensor
• Non-degenerate, three-wave mixing with the Josephson ring modulator
• Circuit QED with fluxonium qubits: theory of the dispersive regime
• Encoding a Qubit into a Cavity Mode in Circuit-QED using Phase Estimation
• Tailoring surface codes for highly biased noise
• Parametric resonance in tunable superconducting cavities
• Simulation of Many-Body Hamiltonians using Perturbation Theory with Bounded-Strength Interactions
• Density-matrix simulation of small surface codes under current and projected experimental noise
• Error Analysis For Encoding A Qubit In An Oscillator
• Phase Structure of the Random-Plaquette Z_2 Gauge Model: Accuracy Threshold for a Toric Quantum Memory
• Quantum error correction against photon loss using NOON states
• Universal Gate Set for Continuous-Variable Quantum Computation with Microwave Circuits
• Quantum error correction against photon loss using multi-component cat states
• Wigner Function Evolution of Quantum States in Presence of Self-Kerr Interaction
• Protecting quantum entanglement from leakage and qubit errors via repetitive parity measurements
• Fault-tolerant preparation of approximate GKP states
• Universal Quantum Computing with Arbitrary Continuous-Variable Encoding
• Leakage detection for a transmon-based surface code
• Superconducting Quantum Simulator for Topological Order and the Toric Code
• Quantum control of an oscillator using stimulated nonlinearity
• Permutation-invariant constant-excitation quantum codes for amplitude damping
• Hardware-Efficient Bosonic Quantum Error-Correcting Codes Based on Symmetry Operators
• Implementing and characterizing precise multi-qubit measurements
• Quantum-limited Parametric Amplification with Josephson Circuits in the Regime of Pump Depletion
• Exact location of the multicritical point for finite-dimensional spin glasses: A conjecture
• Realizing modular quadrature measurements via a tunable photon-pressure coupling in circuit-QED
• Effective Hamiltonians for interacting superconducting qubits -- local basis reduction and the Schrieffer-Wolff transformation
• Error tolerance of topological codes with independent bit-flip and measurement errors

Cited by in corpus (112)

• Circuit Quantum Electrodynamics
• Real-time quantum error correction beyond break-even
• Blueprint for a Scalable Photonic Fault-Tolerant Quantum Computer
• Bosonic quantum error correction codes in superconducting quantum circuits
• Protecting a Bosonic Qubit with Autonomous Quantum Error Correction
• Quantum information processing with bosonic qubits in circuit QED
• Quantum Error Correction with the Gottesman-Kitaev-Preskill Code
• Noisy intermediate-scale quantum computers
• Quantum control of bosonic modes with superconducting circuits
• A fault-tolerant continuous-variable measurement-based quantum computation architecture
• Stabilization of Finite-Energy Gottesman-Kitaev-Preskill States
• A perspective on hybrid quantum opto- and electromechanical systems
• Low overhead fault-tolerant quantum error correction with the surface-GKP code
• Calibrated decoders for experimental quantum error correction
• Quantum error correction using squeezed Schrödinger cat states
• Tight bounds on the simultaneous estimation of incompatible parameters
• Cavity magnomechanical storage and retrieval of quantum states
• A critical Schrödinger cat qubit
• Crosstalk Suppression for Fault-tolerant Quantum Error Correction with Trapped Ions
• Fast parametric two-qubit gates with suppressed residual interaction using a parity-violated superconducting qubit
• Quantum Error Correction of Qudits Beyond Break-even
• Building a large-scale quantum computer with continuous-variable optical technologies
• Hardware-Encoding Grid States in a Non-Reciprocal Superconducting Circuit
• Measurement-free fault-tolerant quantum error correction in near-term devices
• Finite Rate QLDPC-GKP Coding Scheme that Surpasses the CSS Hamming Bound
• Architecture and noise analysis of continuous-variable quantum gates using two-dimensional cluster states
• Quantum Error Correction with Quantum Autoencoders
• Quantifying Qubit Magic Resource with Gottesman-Kitaev-Preskill Encoding
• Advances in Bosonic Quantum Error Correction with Gottesman-Kitaev-Preskill Codes: Theory, Engineering and Applications
• Introduction to Quantum Error Correction and Fault Tolerance
• Twirling and Hamiltonian Engineering via Dynamical Decoupling for GKP Quantum Computing
• Hybrid Oscillator-Qubit Quantum Processors: Instruction Set Architectures, Abstract Machine Models, and Applications
• Cubic phase gates are not suitable for non-Clifford operations on GKP states
• Unconditional preparation of squeezed vacuum from Rabi interactions
• Stabilizer subsystem decompositions for single- and multi-mode Gottesman-Kitaev-Preskill codes
• Free-electron interactions with photonic GKP states: universal control and quantum error correction
• Resolving nonclassical magnon composition of a magnetic ground state via a qubit
• Phase-space methods for representing, manipulating, and correcting Gottesman-Kitaev-Preskill qubits
• Fault-tolerant quantum computation by hybrid qubits with bosonic cat-code and single photons
• Boosting the Quantum State of a Cavity with Floquet Driving
• Designing High-Fidelity Zeno Gates for Dissipative Cat Qubits
• Gottesman-Kitaev-Preskill state preparation using periodic driving
• Estimation of Gaussian random displacement using non-Gaussian states
• Quantum communication on the bosonic loss-dephasing channel
• Closest lattice point decoding for multimode Gottesman-Kitaev-Preskill codes
• The $2T$-qutrit, a two-mode bosonic qutrit
• Error Correction Using Squeezed Fock States
• Ground state nature and nonlinear squeezing of Gottesman-Kitaev-Preskill states
• Resonant Multilevel Amplitude Damping Channels
• Qubit-oscillator concatenated codes: decoding formalism & code comparison
• Squeezed comb states
• Dynamical gauge fields with bosonic codes
• Bosonic Quantum Error Correction with Neutral Atoms in Optical Dipole Traps
• Neural Network-Based Design of Approximate Gottesman-Kitaev-Preskill Code
• Gaussian conversion protocol for heralded generation of qunaught states
• Improved readout of qubit-coupled Gottesman-Kitaev-Preskill states
• Homological Quantum Rotor Codes: Logical Qubits from Torsion
• Adaptive variational low-rank dynamics for open quantum systems
• Engineering Arbitrary Hamiltonians in Phase Space
• Lecture Notes on Quantum Electrical Circuits
• Two-qubit operations for finite-energy Gottesman-Kitaev-Preskill encodings
• Quantum error-correcting codes with a covariant encoding
• Quantum tomography of magnons using Brillouin light scattering
• Dissipative protection of a GKP qubit in a high-impedance superconducting circuit driven by a microwave frequency comb
• Analysis of loss correction with the Gottesman-Kitaev-Preskill code
• Autonomous Stabilization of Fock States in an Oscillator against Multiphoton Losses
• Good Gottesman-Kitaev-Preskill codes from the NTRU cryptosystem
• Quantum memories for squeezed and coherent superpositions in a driven-dissipative nonlinear oscillator
• Perturbative Framework for Engineering Arbitrary Floquet Hamiltonian
• Photonic counterdiabatic quantum optimization algorithm
• Trade-offs on number and phase shift resilience in bosonic quantum codes
• Passive environment-assisted quantum communication with GKP states
• Non-commutative graphs based on finite-infinite system couplings: quantum error correction for a qubit coupled to a coherent field
• Geometric correspondence of noisy quantum dynamics and universal robust quantum gates
• Exponential convergence of a dissipative quantum system towards finite-energy grid states of an oscillator
• Generalized squeezing as a witness
• On Quantum Steering and Wigner Negativity
• Bosonic quantum error correction using squeezed Fock states
• Incoherent Gaussian equivalence of $m-$mode Gaussian states
• Error suppression in multicomponent cat codes with photon subtraction and teleamplification
• Quantum error mitigation for rotation symmetric bosonic codes with symmetry expansion
• Quantum process tomography of continuous-variable gates using coherent states
• Fault-tolerant quantum computing with the parity code and noise-biased qubits
• Engineering Bosonic Codes with Quantum Lattice Gates
• Unifying non-Markovian characterisation with an efficient and self-consistent framework
• Adaptive Non-Gaussian Quantum State Engineering
• Husimi phase distribution in non-Gaussian operations
• Logical channel for heralded and pure loss with the Gottesman-Kitaev-Preskill code
• Practical quantum error correction with the XZZX code and Kerr-cat qubits
• Continuous-variable designs and design-based shadow tomography from random lattices
• Linear optical quantum computing with a hybrid squeezed cat code
• Toward a physically motivated notion of Gaussian complexity geometry
• Safeguarding Oscillators and Qudits with Distributed Two-Mode Squeezing
• Linear-optical approach to encoding qubits into harmonic-oscillator modes via quantum walks
• Chasing shadows with Gottesman-Kitaev-Preskill codes
• A Mathematical Structure for Amplitude-Mixing Error-Transparent Gates for Binomial Codes
• Logical channels in approximate Gottesman-Kitaev-Preskill error correction
• Arbitrary high-fidelity binomial codes from multiphoton spin-boson interactions
• Three-qubit encoding in ytterbium-171 atoms for simulating 1+1D QCD
• Quantum error correction beyond $SU(2)$: spin, bosonic, and permutation-invariant codes from convex geometry
• Autonomous Quantum Error Correction in a Four-Photon Kerr Parametric Oscillator
• Environment-Assisted Generation of Non-Gaussian Wavepacket Quantum States
• Cavity cooling using ultrafast electrons
• Incoherent Approximation of Leakage in Quantum Error Correction
• Deterministic Gaussian conversion protocols for non-Gaussian single-mode resources
• Quantum Error Correction with Superpositions of Squeezed Fock States
• Quantum sensing magnonic number states using a bosonic mode as the probe
• Fault-Tolerant Non-Clifford GKP Gates using Polynomial Phase Gates and On-Demand Noise Biasing
• Generalized Conditional Displacement
• Tunable anisotropic quantum Rabi model via a magnon--spin-qubit ensemble
• Gottesman-Kitaev-Preskill codes: A lattice perspective
• Engineering Strong Beamsplitter Interaction between Bosonic Modes via Quantum Optimal Control Theory