Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network: Toward quantum soft computing

TL;DR

This paper proposes a novel quantum computing approach using nonlinear oscillator networks that leverage bifurcation and quantum superposition to solve complex optimization problems, resembling neural networks in structure.

Contribution

It introduces a quantum adiabatic computation method based on nonlinear oscillators instead of qubits, offering a new paradigm for quantum and neural-inspired computing.

Findings

Numerical simulations show effective use of quantum superposition and fluctuations.

The approach can solve hard combinatorial optimization problems.

The system resembles neural networks, opening interdisciplinary research avenues.

Abstract

The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schr\"odinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence.