Lucas, A. Ising formulations of many NP problems. Front. Phys. 2 (2014). Yoshimura, C. et al. Uncertain behaviours of integrated circuits improve computational performance. Sci. Rep. 5, 16213 (2015). Article CAS ADS Google Scholar Johnson, M. W. et al. Quantum annealing with manufacture...
Lucas, A. Ising formulations of many NP problems. Front. Phys. 2, 5 (2014). Article Google Scholar Takata, K. et al. A 16-bit coherent Ising machine for one-dimensional ring and cubic graph problems. Sci. Rep. 6, 34089 (2016). Article ADS Google Scholar Inagaki, T. et al. La...
Ising formulations of some graph-theoretic problems in psychological research: models and methodsIt is well known that many NP-hard and NP-complete graph-theoretic problems can be formulated and solved as Ising spin models. We discuss several problems that have a particular history in mathematical ...
Lucas, A. Ising formulations of many NP problems. Front. Phys. 2, 5 (2014). Google Scholar Mohseni, N., McMahon, P. L. & Byrnes, T. Ising machines as hardware solvers of combinatorial optimization problems. Nat. Rev. Phys. 4, 363–379 (2022). Google Scholar Romera, M. et al...
Many problems in mathematics, statistical mechanics, and computer science are computationally hard but can often be mapped onto a ground-state-search problem of the Ising model and approximately solved by artificial spin-networks of coupled degenerate op
The number of different terms in (2) can be exponentially large asHIcan have arbitraryk-local terms that couplekspins directly with different coefficientsa{k}. Allowing only binary couplings in (2), this already includes NP-complete problems5,6,7,8, which means that many important QA problems...
Ising machines based on nonlinear analog systems are a promising method to accelerate computation of NP-hard optimization problems. Yet, their analog nature is also causing amplitude inhomogeneity which can deteriorate the ability to find optimal solutions. Here, we investigate how the system’s nonlin...
Lucas, A. Ising formulations of many NP problems. Front. Phys. 2014, 2, 5. [Google Scholar] [CrossRef] [Green Version] Rosenberg, G.; Haghnegahdar, P.; Goddard, P.; Carr, P.; Wu, K.; De Prado, M.L. Solving the optimal trading trajectory problem using a quantum annealer. IEEE...
Lucas, A. Ising formulations of many NP problems. Front. Phys. 2014, 2, 5. [Google Scholar] [CrossRef] [Green Version] Rosenberg, G.; Haghnegahdar, P.; Goddard, P.; Carr, P.; Wu, K.; De Prado, M.L. Solving the optimal trading trajectory problem using a quantum annealer. IEEE...
The Ising model is defined by an objective function using a quadratic formula of qubit variables. The problem of an Ising model aims to determine the qubit values of the variables that minimize the objective function, and many optimization problems can b