Solving the Optimal Trading Trajectory Problem Using Simulated Bifurcation

  title={Solving the Optimal Trading Trajectory Problem Using Simulated Bifurcation},
  author={Kyle Steinhauer and Takahisa Fukadai and Shotaro Yoshida},
  journal={Bioengineering eJournal},
We use an optimization procedure based on simulated bifurcation (SB) to solve the integer portfolio and trading trajectory problem with an unprecedented computational speed. The underlying algorithm is based on a classical description of quantum adiabatic evolutions of a network of non-linearly interacting oscillators. This formulation has already proven to beat state of the art computation times for other NP-hard problems and is expected to show similar performance for certain portfolio… 
1 Citations
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