#### erek

##### Supreme [H]ardness

- Joined
- Dec 19, 2005

- Messages
- 4,410

"Combinatorial optimization by simulating adiabatic bifurcations in nonlinear Hamiltonian systems:

Combinatorial optimization problems are ubiquitous but difficult to solve. Hardware devices for these problems have recently been developed by various approaches, including quantum computers. Inspired by recently proposed quantum adiabatic optimization using a nonlinear oscillator network, we propose a new optimization algorithm simulating adiabatic evolutions of classical nonlinear Hamiltonian systems exhibiting bifurcation phenomena, which we call simulated bifurcation (SB). SB is based on adiabatic and chaotic (ergodic) evolutions of nonlinear Hamiltonian systems. SB is also suitable for parallel computing because of its simultaneous updating. Implementing SB with a field-programmable gate array, we demonstrate that the SB machine can obtain good approximate solutions of an all-to-all connected 2000-node MAX-CUT problem in 0.5 ms, which is about 10 times faster than a state-of-the-art laser-based machine called a coherent Ising machine. SB will accelerate large-scale combinatorial optimization harnessing digital computer technologies and also offer a new application of computational and mathematical physics.

In social life and industry, one often encounters problems for finding the best combination among an enormous number of candidates. These combinatorial optimization problems are mathematically formulated as minimization or maximization of certain functions of discrete variables, which are called objective functions or cost functions. These problems are notoriously difficult because of combinatorial explosion (1, 2). Thus, special-purpose hardware devices for these problems are expected to be useful. In particular, “Ising machines” designed for finding a ground state of the Ising spin model (3) have recently attracted much attention because many combinatorial optimization problems can be mapped to the Ising problem (4), including very-large-scale integrated circuit design (5), drug design (6), and financial portfolio management (7). These machines have been developed by various approaches: quantum computers based on quantum annealing (8, 9) or quantum adiabatic optimization (10–12) implemented with superconducting circuits (13, 14), coherent Ising machines (CIMs) implemented with laser pulses (15–20), and Ising machines based on simulated annealing (SA) (1, 21, 22) implemented with digital circuits such as field-programmable gate arrays (FPGAs) (23–29)."

"Combinatorial optimization by simulating adiabatic bifurcations in nonlinear Hamiltonian systems:

Combinatorial optimization problems are ubiquitous but difficult to solve. Hardware devices for these problems have recently been developed by various approaches, including quantum computers. Inspired by recently proposed quantum adiabatic optimization using a nonlinear oscillator network, we propose a new optimization algorithm simulating adiabatic evolutions of classical nonlinear Hamiltonian systems exhibiting bifurcation phenomena, which we call simulated bifurcation (SB). SB is based on adiabatic and chaotic (ergodic) evolutions of nonlinear Hamiltonian systems. SB is also suitable for parallel computing because of its simultaneous updating. Implementing SB with a field-programmable gate array, we demonstrate that the SB machine can obtain good approximate solutions of an all-to-all connected 2000-node MAX-CUT problem in 0.5 ms, which is about 10 times faster than a state-of-the-art laser-based machine called a coherent Ising machine. SB will accelerate large-scale combinatorial optimization harnessing digital computer technologies and also offer a new application of computational and mathematical physics.

In social life and industry, one often encounters problems for finding the best combination among an enormous number of candidates. These combinatorial optimization problems are mathematically formulated as minimization or maximization of certain functions of discrete variables, which are called objective functions or cost functions. These problems are notoriously difficult because of combinatorial explosion (1, 2). Thus, special-purpose hardware devices for these problems are expected to be useful. In particular, “Ising machines” designed for finding a ground state of the Ising spin model (3) have recently attracted much attention because many combinatorial optimization problems can be mapped to the Ising problem (4), including very-large-scale integrated circuit design (5), drug design (6), and financial portfolio management (7). These machines have been developed by various approaches: quantum computers based on quantum annealing (8, 9) or quantum adiabatic optimization (10–12) implemented with superconducting circuits (13, 14), coherent Ising machines (CIMs) implemented with laser pulses (15–20), and Ising machines based on simulated annealing (SA) (1, 21, 22) implemented with digital circuits such as field-programmable gate arrays (FPGAs) (23–29)."

https://www.tomshardware.com/news/toshiba-claims-new-algorithm-runs-faster-on-desktop-pcs-than-similar-algorithms-on-supercomputers