An electromechanical Ising Hamiltonian

The phonons localized in a mechanical resonator can be electrically manipulated to emulate the Ising Hamiltonian. Solving intractable mathematical problems in simulators composed of atoms, ions, photons, or electrons has recently emerged as a subject of intense interest. We extend this concept to phonons that are localized in spectrally pure resonances in an electromechanical system that enables their interactions to be exquisitely fashioned via electrical means. We harness this platform to emulate the Ising Hamiltonian whose spin 1/2 particles are replicated by the phase bistable vibrations from the parametric resonances of multiple modes. The coupling between the mechanical spins is created by generating two-mode squeezed states, which impart correlations between modes that can imitate a random, ferromagnetic state or an antiferromagnetic state on demand. These results suggest that an electromechanical simulator could be built for the Ising Hamiltonian in a nontrivial configuration, namely, for a large number of spins with multiple degrees of coupling.

• Publication year

  2015

• Venue

  Science Advances

• Publication date

  2015-05-11

• Fields of study

  Medicine, Physics

• Identifiers
  DOI 10.1126/sciadv.1600236arXiv 1505.02467PMID 28861469PMCID 5566114
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• No claims are published for this paper.

• No concepts are published for this paper.

• Splash, pop, sizzle: Information processing with phononic computing

  2015cited by this paper
• Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network

  2015cited by this paper
• Two-mode thermal-noise squeezing in an electromechanical resonator.

  2014influential reference
• Measurement-based control of a mechanical oscillator at its thermal decoherence rate

  2014cited by this paper
• Network of time-multiplexed optical parametric oscillators as a coherent Ising machine

  2014cited by this paper
• Josephson parametric phase-locked oscillator and its application to dispersive readout of superconducting qubits

  2014cited by this paper
• Coherent Ising machine based on degenerate optical parametric oscillators

  2013cited by this paper
• Quantum Simulators

  2013cited by this paper
• Generating entangled microwave radiation over two transmission lines.

  2012cited by this paper
• A nanomechanical mass sensor with yoctogram resolution.

  2012cited by this paper
• A Viewpoint on : Generating Entangled Microwave Radiation Over Two Transmission Lines

  2012cited by this paper
• Nonlinear damping in mechanical resonators made from carbon nanotubes and graphene.

  2011cited by this paper
• Observation of two-mode squeezing in the microwave frequency domain.

  2011cited by this paper
• Quantum annealing with manufactured spins

  2011cited by this paper
• Subject Areas: Nanophysics A Viewpoint on: Signal Amplification by Sensitive Control of Bifurcation Topology

  2011cited by this paper
• Laser cooling of a nanomechanical oscillator into its quantum ground state

  2011cited by this paper
• Sideband cooling of micromechanical motion to the quantum ground state

  2011cited by this paper
• Photon generation in an electromagnetic cavity with a time-dependent boundary.

  2010cited by this paper
• Two-mode correlation of microwave quantum noise generated by parametric down-conversion.

  2010cited by this paper
• A symmetry-breaking electromechanical detector

  2010cited by this paper
• Quantum ground state and single-phonon control of a mechanical resonator

  2010cited by this paper
• Optomechanics

  2009cited by this paper
• Quantum Simulators

  2009cited by this paper
• Phase-preserving amplification near the quantum limit with a Josephson ring modulator

  2009cited by this paper
• Switching-path distribution in multidimensional systems.

  2008cited by this paper
• Bit storage and bit flip operations in an electromechanical oscillator.

  2008influential reference
• Quantum interference in the classically forbidden region: A parametric oscillator

  2007cited by this paper
• Cavity opto-mechanics.

  2007cited by this paper
• Efficient and sensitive capacitive readout of nanomechanical resonator arrays.

  2007cited by this paper
• Resonant symmetry lifting in a parametrically modulated oscillator.

  2006cited by this paper
• Nanoelectromechanical systems

  2005cited by this paper
• Coherent signal amplification in bistable nanomechanical oscillators by stochastic resonance

  2005cited by this paper
• Noise-enabled precision measurements of a duffing nanomechanical resonator.

  2004cited by this paper
• Single spin detection by magnetic resonance force microscopy

  2004cited by this paper
• Theory of Quantum Annealing of an Ising Spin Glass

  2002cited by this paper
• Nanoelectromechanical systems face the future

  2001cited by this paper
• Nanoelectromechanical Systems

  2000cited by this paper
• Five parametric resonances in a microelectromechanical system

  1998cited by this paper
• Quantum annealing: A new method for minimizing multidimensional functions

  1994cited by this paper
• Mechanical parametric amplification and thermomechanical noise squeezing.

  1991cited by this paper
• Optimization by Simulated Annealing

  1983cited by this paper
• On the computational complexity of Ising spin glass models

  1982cited by this paper
• Fluctuations in a parametrically excited subharmonic oscillator

  1971cited by this paper

• Three Strongly Coupled Kerr Parametric Oscillators Forming a Boltzmann Machine.

  2025cites this paper
• Direct comparison of stochastic driven nonlinear dynamical systems for combinatorial optimization.

  2025cites this paper
• Finding independent sets in large-scale graphs with a coherent Ising machine

  2025cites this paper
• Programmable synthetic magnetism and chiral edge states in nano-optomechanical quantum Hall networks

  2025cites this paper
• Simultaneous generation and transfer of mechanical noise squeezing

  2025cites this paper
• Parametric instability landscape of coupled Kerr parametric oscillators

  2025cites this paper
• Self-Frequency Pumping for Chaotic Micromechanical Frequency Comb Generation via Multimodal Internal Resonance

  2025cites this paper
• Multimodal electromechanics with niobium vacuum gap capacitor membranes

  2025cites this paper
• A network of parametrically driven silicon nitride mechanical membranes

  2025cites this paper
• Quantum‐Enhanced Computing for the Antiferromagnetic J1−J2$J_1-J_2$ Heisenberg Model

  2025cites this paper
• Topologically Defective Lattice Potential‐Based Gain‐Dissipative Ising Annealer with Large Noise Margin

  2024cites this paper
• Performance of quantum annealing inspired algorithms for combinatorial optimization problems

  2024cites this paper
• Overdamped Ising machine with stochastic resonance phenomena in large noise condition

  2024cites this paper
• True Random Number Generator Based on Chaotic Oscillation of a Tunable Double-Well MEMS Resonator.

  2024cites this paper
• Acoustically driven single-frequency mechanical logic

  2024cites this paper
• Biased Ising Model Using Two Coupled Kerr Parametric Oscillators with External Force.

  2024cites this paper
• On-chip mechanical computing: status, challenges, and opportunities

  2023cites this paper
• Thermodynamic quantities of two-dimensional Ising models obtained by noisy mean-field annealing and a coherent Ising machine

  2023cites this paper
• Experimental Demonstration of Coupled Sub-Harmonic Injection Locked Oscillation in Micro-Electro-Mechanical Relays

  2023cites this paper
• Probing Linear to Nonlinear Damping in 2D Semiconductor Nanoelectromechanical Resonators toward a Unified Quality Factor Model.

  2023cites this paper
• Many-Valued Logic-Memory Elements Based on Nano-Scale Electromechanical Oscillators

  2023cites this paper
• Proliferation of unstable states and their impact on stochastic out-of-equilibrium dynamics in two coupled Kerr parametric oscillators.

  2023cites this paper
• A biased Ising model using two coupled Kerr parametric oscillators with external force

  2023cites this paper
• Numerical simulation of probabilistic computing to NP-complete number theory problems

  2023cites this paper
• Intermodal coupling spectroscopy of mechanical modes in microcantilevers

  2023cites this paper
• Scalable nanomechanical logic gate

  2022influential citation
• Deterministic and stochastic sampling of two coupled Kerr parametric oscillators

  2022cites this paper
• Quantum Analog Annealing of Gain‐Dissipative Ising Machine Driven by Colored Gaussian Noise

  2022cites this paper
• Memristive Ising Circuits

  2022cites this paper
• Observation of distinct phase transitions in a nonlinear optical Ising machine

  2022cites this paper
• Fundamental Physics and Applications of Skyrmions: A Review

  2022cites this paper
• Generation of phononic high-order sidebands via intra- and inter-mode couplings in interconnected electromechanical resonators

  2022cites this paper
• Deep Space Network Scheduling Using Quantum Annealing

  2022cites this paper
• Nanomechanical Resonators: Toward Atomic Scale

  2022cites this paper
• Ising Machine Based on Bistable Microelectromechanical Systems

  2022cites this paper
• Ising machines as hardware solvers of combinatorial optimization problems

  2022cites this paper
• Engineering Multiple GHz Mechanical Modes in Optomechanical Crystal Cavities

  2022cites this paper
• Mesoscopic physics of nanomechanical systems

  2022cites this paper
• A Kuramoto Network in a Single Nonlinear Microelectromechanical Device

  2022cites this paper
• Ising Machines—Quantum-Inspired Machines for Combinatorial Optimization—

  2022cites this paper
• Non-Hermitian chiral phononics through optomechanically induced squeezing

  2021cites this paper
• Generation and Propagation of Topological Solitons in a Chain of Coupled Parametric-Micromechanical-Resonator Arrays

  2021cites this paper
• Floquet Phonon Lasing in Multimode Optomechanical Systems.

  2021cites this paper
• Non-equilibrium quadratic measurement-feedback squeezing in a micromechanical resonator

  2021cites this paper
• Efficient sampling of ground and low-energy Ising spin configurations with a coherent Ising machine

  2021cites this paper
• Computational capabilities of nonlinear oscillator networks

  2021cites this paper
• Solving combinatorial optimisation problems using oscillator based Ising machines

  2021cites this paper
• Synthetic PT Symmetry and Nonreciprocal Amplification in Optomechanics

  2021cites this paper
• Engineering Reflective Metasurfaces with Ising Hamiltonian and Quantum Annealing

  2021cites this paper
• Potts model solver based on hybrid physical and digital architecture

  2021influential citation
• Creating electronic oscillator-based Ising machines without external injection locking

  2021cites this paper
• The challenges of modern computing and new opportunities for optics

  2021cites this paper
• Stochasticity of the magnon parametron

  2021cites this paper
• Scaling advantage of chaotic amplitude control for high-performance combinatorial optimization

  2021cites this paper
• Ising machines with strong bilinear coupling

  2021cites this paper
• Topological optomechanical amplifier in synthetic PT -symmetry

  2021cites this paper
• On computational capabilities of Ising machines based on nonlinear oscillators

  2021cites this paper
• Extracting the lifetime of a synthetic two-level system

  2021cites this paper
• Large-scale Ising emulation with four body interaction and all-to-all connections

  2020cites this paper
• On connection among quantum-inspired algorithms of the Ising model

  2020cites this paper
• Observation of binary phase states of time-multiplexed degenerate optical parametric oscillator pulses generated using a nonlinear fiber Sagnac loop.

  2020cites this paper
• Simulating Ising Spins in External Magnetic Fields with a Network of Degenerate Optical Parametric Oscillators

  2020cites this paper
• Adiabatic evolution on a spatial-photonic Ising machine

  2020cites this paper
• Noise-enhanced spatial-photonic Ising machine

  2020cites this paper
• Exact mapping between a laser network loss rate and the classical XY Hamiltonian by laser loss control

  2020cites this paper
• Novel Computing Paradigms using Oscillators

  2019cites this paper
• Phase Control of Self-Excited Parametric Resonators

  2019cites this paper
• Electro-optomechanical switch via tunable bistability and four-wave mixing

  2019cites this paper
• Weak signal enhancement by nonlinear resonance control in a forced nano-electromechanical resonator

  2019cites this paper
• Optoelectronics for refrigeration and analog circuits for combinatorial optimization

  2019cites this paper
• Spin Hall nano-oscillator arrays: towards GHz neuromorphics

  2019cites this paper
• Selective and switchable optical amplification with mechanical driven oscillators

  2019cites this paper
• Binary optimization by momentum annealing.

  2019cites this paper
• Optically probing Schwinger angular momenta in a micromechanical resonator

  2019cites this paper
• Large-Scale Photonic Ising Machine by Spatial Light Modulation.

  2019cites this paper
• Rapid Flipping of Parametric Phase States.

  2019cites this paper
• Gate-controlled phase switching in a parametron.

  2019cites this paper
• OIM: Oscillator-based Ising Machines for Solving Combinatorial Optimisation Problems

  2019cites this paper
• Interaction-induced time-symmetry breaking in driven quantum oscillators

  2018cites this paper
• Distributions of steady states in a network of degenerate optical parametric oscillators in solving combinatorial optimization problems

  2018cites this paper
• Bifurcation Generated Mechanical Frequency Comb.

  2018cites this paper
• Energy-efficient switching of nanomagnets for computing: straintronics and other methodologies

  2018cites this paper
• Estimation of π-π Electronic Couplings from Current Measurements.

  2017cites this paper
• Spin Order and Phase Transitions in Chains of Polariton Condensates.

  2017cites this paper
• Switching of localized surface plasmon resonance of gold nanoparticles using phase-change materials and implementation of computing functionality

  2017cites this paper
• Boltzmann sampling from the Ising model using quantum heating of coupled nonlinear oscillators

  2017cites this paper
• Oscillator-based Ising Machine

  2017cites this paper
• Phase shifter tuned by varying the spring constant of a nanomechanical cantilever

  2017cites this paper
• A coherent Ising machine for 2000-node optimization problems

  2016cites this paper
• Intrinsic optimization using stochastic nanomagnets

  2016cites this paper
• 10  GHz clock time-multiplexed degenerate optical parametric oscillators for a photonic Ising spin network.

  2016cites this paper
• Parametric Symmetry Breaking in a Nonlinear Resonator.

  2016cites this paper