Quantum annealing with a network of all-to-all connected, two-photon driven Kerr nonlinear oscillators

Abstract

Quantum annealing aims to solve combinatorial optimization problems mapped on to Ising interactions between quantum spins. A critical factor that limits the success of a quantum annealer is its sensitivity to noise, and intensive research is consequently focussed towards developing noise-resilient annealers. Here we propose a new paradigm for quantum annealing with a scalable network of all-to-all connected, two-photon driven Kerr-nonlinear resonators. Each of these resonators encode an Ising spin in a robust degenerate subspace formed by two coherent states of opposite phases. The fully-connected optimization problem is mapped onto local fields driving the resonators, which are themselves connected by local four-body interactions. We describe an adiabatic annealing protocol in this system and analyze its performance in the presence of photon loss. Numerical simulations indicate substantial resilience to this noise channel, making it a promising platform for implementing a large scale quantum Ising machine. Finally, we propose a realistic implementation of this scheme in circuit QED.

References in corpus (11)

• QuTiP 2: A Python framework for the dynamics of open quantum systems
• Network of Time-Multiplexed Optical Parametric Oscillators as a Coherent Ising Machine
• Engineering the quantum states of light in a Kerr-nonlinear resonator by two-photon driving
• Large-scale Ising spin network based on degenerate optical parametric oscillators
• Minor-embedding in adiabatic quantum computation: II. Minor-universal graph design
• Experimental implementation of an adiabatic quantum optimization algorithm
• Decoherence in adiabatic quantum computation
• Robust quantum optimizer with full connectivity
• Nonstoquastic Hamiltonians and Quantum Annealing of an Ising Spin Glass
• Exponential Enhancement of the Efficiency of Quantum Annealing by Non-Stochastic Hamiltonians
• Quantum annealing of the random-field Ising model by transverse ferromagnetic interactions

Cited by in corpus (106)

• Perspectives of quantum annealing: Methods and implementations
• The Kerr-Cat Qubit: Stabilization, Readout, and Gates
• Bias-preserving gates with stabilized cat qubits
• Nanomechanical Resonators: Toward Atomic Scale
• Quantum computing with rotation-symmetric bosonic codes
• Stabilized Cat in Driven Nonlinear Cavity: A Fault-Tolerant Error Syndrome Detector
• Quantum critical regime in a quadratically-driven nonlinear photonic lattice
• Quantum Computation Based on Quantum Adiabatic Bifurcations of Kerr-Nonlinear Parametric Oscillators
• Robust quantum optimizer with full connectivity
• Classical many-body time crystals
• Qubit-photon bound states in topological waveguides with long-range hoppings
• Effect of higher-order nonlinearities on amplification and squeezing in Josephson parametric amplifiers
• Noise-enhanced spatial-photonic Ising machine
• Spontaneous symmetry breaking in a quadratically-driven nonlinear photonic lattice
• Dissipative quantum bifurcation machine: Quantum heating of coupled nonlinear oscillators
• Symmetries and conserved quantities of boundary time crystals in generalized spin models
• Integrable time-dependent quantum Hamiltonians
• Mean-field validity in a dissipative critical system: Liouvillian gap, $\mathbb{PT}$-symmetric antigap, and permutational symmetry in the $XYZ$ model
• Observing quantum synchronization blockade in circuit quantum electrodynamics
• Boundary time crystals in collective $d$-level systems
• Interaction-induced time-symmetry breaking in driven quantum oscillators
• A quantum annealer with fully programmable all-to-all coupling via Floquet engineering
• Improving quantum annealing of the ferromagnetic $p$-spin model through pausing
• 3-Regular 3-XORSAT Planted Solutions Benchmark of Classical and Quantum Heuristic Optimizers
• The squeezed Kerr oscillator: spectral kissing and phase-flip robustness
• Field Theory of Many-Body Lindbladian Dynamics
• A Quantum Model for Coherent Ising Machines: Discrete-time Measurement Feedback Formulation
• Observation and manipulation of quantum interference in a superconducting Kerr parametric oscillator
• Reservoir Computing Approach to Quantum State Measurement
• High-accuracy Ising machine using Kerr-nonlinear parametric oscillators with local four-body interactions
• Scalable and Robust Photonic Integrated Unitary Converter
• Two-photon driven Kerr resonator for quantum annealing with three-dimensional circuit QED
• Squeezing and multimode entanglement of surface acoustic wave phonons
• Gaussian trajectory approach to dissipative phase transitions: the case of quadratically driven photonic lattices
• Quantum Gate for Kerr Nonlinear Parametric Oscillator Using Effective Excited States
• Dynamics of transient cat-states in degenerate parametric oscillation with and without nonlinear Kerr interactions
• Overcoming decoherence of cat-states formed in a cavity using squeezed-state inputs
• Simulated bifurcation assisted by thermal fluctuation
• Chaos in coupled Kerr-nonlinear parametric oscillators
• Controls of a superconducting quantum parametron under a strong pump field
• Simulated bifurcation for higher-order cost functions
• Variational optimization of the quantum annealing schedule for the Lechner-Hauke-Zoller scheme
• Dynamics of Many-Body Quantum Synchronisation
• Rapid flipping of parametric phase states
• On-Demand Generation of Traveling Cat States Using a Parametric Oscillator
• Towards long-distance quantum networks with superconducting processors and optical links
• High-fidelity dissipative engineering using parametric interactions
• Nonadiabatic dynamics of the excited states for the Lipkin-Meshkov-Glick model
• Correlated oscillations in Kerr parametric oscillators with tunable effective coupling
• Computational Overhead of Locality Reduction in Binary Optimization Problems
• Quantum state preparation for coupled period tripling oscillators
• Stabilization of multi-mode Schrodinger cat states via normal-mode dissipation engineering
• Blueprint for all-to-all connected superconducting spin qubits
• Simulating frustrated antiferromagnets with quadratically driven QED cavities
• Two-qubit gate using conditional driving for highly detuned Kerr-nonlinear parametric oscillators
• Controlled asymmetric Ising model implemented with parametric micromechanical oscillators
• Dynamics of inhomogeneous spin ensembles with all-to-all interactions: breaking permutational invariance
• Quantum Correlations in the Kerr Ising Model
• Classical critical dynamics in quadratically driven Kerr resonators
• Analog Coupled Oscillator Based Weighted Ising Machine
• Symmetries of the squeeze-driven Kerr oscillator
• Phase synchronization in coupled bistable oscillators
• Fast, Lifetime-Preserving Readout for High-Coherence Quantum Annealers
• Control of the $ZZ$ coupling between Kerr-cat qubits via transmon couplers
• Deterministic and stochastic sampling of two coupled Kerr parametric oscillators
• Effective spin models of Kerr-nonlinear parametric oscillators for quantum annealing
• Quantum annealing with twisted fields
• Photonic quantum metrology with variational quantum optical non-linearities
• Performance enhancement of quantum annealing under the Lechner-Hauke-Zoller scheme by non-linear driving of the constraint term
• Designing ground states of Hopfield networks for quantum state preparation
• Highly Versatile FPGA-Implemented Cyber Coherent Ising Machine
• Expressive Quantum Supervised Machine Learning using Kerr-nonlinear Parametric Oscillators
• Constructive plaquette compilation for the parity architecture
• Emerging unitary evolutions in dissipatively coupled systems
• Frustration Elimination and Excited State Search in Coherent Ising Machines
• Fast elementary gates for universal quantum computation with Kerr parametric oscillator qubits
• Proliferation of unstable states and their impact on stochastic out-of-equilibrium dynamics
• Search for optimal driving in finite quantum systems with precursors of criticality
• Spectroscopic estimation of the photon number for superconducting Kerr parametric oscillators
• Nonstoquastic catalyst for bifurcation-based quantum annealing of ferromagnetic $p$-spin model
• Unraveling the switching dynamics in a quantum double-well potential
• Decoherence-assisted quantum driving
• The failure of semiclassical approach in the dissipative fully-connected Ising model
• Analysis of the Hopfield Model with Discrete Coupling
• Edge-of-chaos enhanced quantum-inspired algorithm for combinatorial optimization
• Adiabatic evolution on a spatial-photonic Ising machine
• Non-linear-enabled localization in driven-dissipative photonic lattices
• Spectroscopic observation of the crossover from a classical Duffing oscillator to a Kerr parametric oscillator
• Decoherence of a tunable capacitively shunted flux qubit
• A scalable 2-local architecture for quantum annealing of Ising models with arbitrary dimensions
• Limits of Short-Time Evolution of Local Hamiltonians
• Quantum annealing in capacitively coupled Kerr parametric oscillators using frequency-chirped drives
• Suppression of effective noise in Hamiltonian simulations
• Excited-State Adiabatic Quantum Computation Started with Vacuum States
• High-performance conditional-driving gate for Kerr parametric oscillator qubits
• Neural networks with quantum states of light
• Four-body coupler for superconducting qubits based on Josephson parametric oscillators
• Flux-modulated tunable interaction regimes in two strongly nonlinear oscillators
• Minor embedding with Stuart-Landau oscillator networks
• Spin Model for Quantum Annealing with Kerr Parametric Oscillators
• Autonomous Quantum Error Correction in a Four-Photon Kerr Parametric Oscillator
• Theoretical study of reflection spectroscopy for superconducting quantum parametrons
• Validating multi-photon quantum interference with finite data
• Generation of all-to-all connections in a two-dimensional qubit array with two-body interactions
• Practical hybrid decoding scheme for parity-encoded spin systems
• Steady state distributions of network of degenerate optical parametric oscillators in solving combinatorial optimization problems