Graph Search Using Adiabatic Bifurcation for Arbitrage Cycles
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Solution Overview
Problem
Existing technologies are inefficient in quickly detecting optimal paths or cycles in directed graphs for arbitrage opportunities and other combinatorial optimization problems, such as the Ising problem, which require faster and more effective solutions.
Innovation Solution
A search device and method that utilize a 0-1 optimization problem formulation and simulate adiabatic bifurcations in nonlinear Hamiltonian systems to numerically solve the classical equations of motion using symplectic Euler method, integrating particle positions and momenta over time to find optimal paths or cycles in directed graphs.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If conventional optimization algorithms are used to solve combinatorial optimization problems, then the solution can be obtained, but the computation time is too long and efficiency is low
Solution Approach 1:
The patent replaces conventional digital computer-based optimization algorithms with a physical system that naturally evolves toward optimal solutions through simulated adiabatic bifurcations. The system uses physical laws (Hamiltonian dynamics) to perform optimization computations, substituting mechanical/digital computation with physical process evolution, thereby achieving faster solution times for combinatorial optimization problems.
Solution Approach 2:
The patent changes the computational approach by transforming the optimization problem into a physical system with specific parameters (Hamiltonian, adiabatic parameter γ). By adjusting these physical parameters and allowing the system to evolve adiabatically, the computation is performed through physical evolution rather than iterative digital algorithms, significantly reducing computation time.
2Reliability
If existing search methods are applied to detect arbitrage opportunities in directed graphs, then arbitrage paths can be identified, but the detection speed is insufficient
Solution Approach 1:
The patent formulates the arbitrage detection problem as a combinatorial optimization problem (finding maximum weight cycles) and solves it using a physical system based on simulated adiabatic bifurcations. This replaces conventional graph search algorithms with a physical optimization process that naturally converges to optimal cycles, achieving both high accuracy and fast detection speed.
3Measurement precision
If classical optimization algorithms are used for Ising problem solving, then the ground state can be found, but the calculation efficiency is insufficient
Solution Approach 1:
The patent transforms the Ising problem into a continuous optimization problem by introducing a parameter γ that interpolates between the discrete Ising Hamiltonian and a continuous form. By solving the continuous version through simulated adiabatic bifurcations and then mapping back to discrete spin values, the system achieves both precise ground state identification and high calculation efficiency.
Data Source
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AI summary
A search device (10) updates positions and momentums of a plurality of virtual particles, for each unit time from an initial time to an end time. The search device (10), for each unit time, calculates, for each of the particles, a position at a target time of a corresponding particle, calculates, for each of a plurality of nodes, a first accumulative value by cumulatively adding positions at the target time of two or more particles corresponding to outgoing two or more directed edges, calculates, for each of the nodes, a second accumulative value by cumulatively adding positions at the target time of two or more particles corresponding to incoming two or more directed edges, and calculates, for each of the particles, a momentum at the target time of a corresponding particle based on the first accumulative value and the second accumulative value.