Complexity continuum within Ising formulation of NP problems

  title={Complexity continuum within Ising formulation of NP problems},
  author={Kirill P. Kalinin and Natalia G. Berloff},
A promising approach to achieve computational supremacy over the classical von Neumann architecture explores classical and quantum hardware as Ising machines. The minimisation of the Ising Hamiltonian is known to be NP-hard problem for certain interaction matrix classes, yet not all problem instances are equivalently hard to optimise. We propose to identify computationally simple instances with an `optimisation simplicity criterion'. Such optimisation simplicity can be found for a wide range of… 

Figures from this paper

Overleaf Example
This work develops a general analytical framework that describes injection locking of spin Hall oscillators with large precession angles, and integrates this analytical model into a versatile VerilogA device that can emulate the coupled dynamics of spinHall oscillators in circuit simulators.
All-optical scalable spatial coherent Ising machine
This work proposes an all-optical scalable CIM with fully-programmable coupling, paving the way towards the realization of size-independent ultrafast optical hardware for large-scale computation purposes.
Suppressing amplitude inhomogeneity enhances computational performance of Ising machines: why the choice of nonlinearity matters
This work investigates if the shape of the system’s nonlinear transfer function can mitigate amplitude inhomogeneity and improve computational performance, and reports order-of-magnitude improvements in the time-to-solution compared to conventional polynomial models.
Large-scale Sustainable Search on Unconventional Computing Hardware
It is demonstrated that special-purpose optical machines such as networks of optical parametric oscillators, lasers, and gain-dissipative condensates, may aid in accelerating the reliable reconstruction of principal eigenvectors of real-life web graphs.
Order-of-magnitude differences in computational performance of analog Ising machines induced by the choice of nonlinearity
This work investigates how the choice of nonlinear transfer functions partly suppresses errors caused by analog amplitude inhomogeneity, which leads to order-of-magnitude differences in the computation time.
Collective and synchronous dynamics of photonic spiking neurons
The experimental results show that the effective change causes spontaneous modification of the spiking modes and firing rates of clustered neurons, and such collective dynamics can be utilized to realize efficient heuristics for solving NP-hard combinatorial optimization problems.


Polaritonic XY-Ising machine
It is argued that the proposed architecture for the remote coupling control offers an improvement over geometrically coupled condensates in both accuracy and stability as well as increases versatility, range, and connectivity of spin Hamiltonians that can be simulated with polariton networks.
A fully programmable 100-spin coherent Ising machine with all-to-all connections
A scalable optical processor with electronic feedback that can be realized at large scale with room-temperature technology is presented and is able to find exact solutions of, or sample good approximate solutions to, a variety of hard instances of Ising problems.
A coherent Ising machine for 2000-node optimization problems
It is shown that an optical processing approach based on a network of coupled optical pulses in a ring fiber can be used to model and optimize large-scale Ising systems, and a coherent Ising machine outperformed simulated annealing in terms of accuracy and computation time for a 2000-node complete graph.
A 16-bit Coherent Ising Machine for One-Dimensional Ring and Cubic Graph Problems
Experimental and numerical results indicate that gradual pumping of the network combined with multiple spectral and temporal modes of the femtosecond pulses can improve the computational performance of the Ising machine, offering a new path for tackling larger and more complex instances.
Large-Scale Photonic Ising Machine by Spatial Light Modulation.
It is shown that light propagation can be tailored to minimize an Ising Hamiltonian with spin couplings set by input amplitude modulation and a feedback scheme, which opens the route to classical and quantum photonic Ising machines that exploit light spatial degrees of freedom for parallel processing of a vast number of spins with programmable couplings.
Experimental investigation of performance differences between coherent Ising machines and a quantum annealer
The difference in performance between the sparsely connected D-Wave machine and the fully-connected CIMs provides strong experimental support for efforts to increase the connectivity of quantum annealers.
A single shot coherent Ising machine based on a network of injection-locked multicore fiber lasers
An analog all-optical implementation of a coherent Ising machine (CIM) based on a network of injection-locked multicore fiber lasers using spatial light modulators (SLMs) to solve several Ising Hamiltonians.
Heuristic recurrent algorithms for photonic Ising machines
This work presents the Photonic Recurrent Ising Sampler (PRIS), a heuristic method tailored for parallel architectures allowing fast and efficient sampling from distributions of arbitrary Ising problems, and suggests speedups in heuristic methods via photonic implementations of the PRIS.
Realizing the classical XY Hamiltonian in polariton simulators.
The potential of polariton graphs are investigated as an efficient analogue simulator for finding the global minimum of the XY model and provide a route to study unconventional superfluids, spin liquids, Berezinskii-Kosterlitz-Thouless phase transition, and classical magnetism, among the many systems described by the XY Hamiltonian.