Solving the Optimal Trading Trajectory Problem Using a Quantum Annealer

Gili Rosenberg, Poya Haghnegahdar, Phil Goddard, Peter Carr, Kesheng Wu, Marcos López De Prado

Research output: Contribution to journalArticlepeer-review


We solve a multi-period portfolio optimization problem using D-Wave Systems' quantum annealer. We derive a formulation of the problem, discuss several possible integer encoding schemes, and present numerical examples that show high success rates. The formulation incorporates transaction costs (including permanent and temporary market impact), and, significantly, the solution does not require the inversion of a covariance matrix. The discrete multi-period portfolio optimization problem we solve is significantly harder than the continuous variable problem. We present insight into how results may be improved using suitable software enhancements and why current quantum annealing technology limits the size of problem that can be successfully solved today. The formulation presented is specifically designed to be scalable, with the expectation that as quantum annealing technology improves, larger problems will be solvable using the same techniques.

Original languageEnglish (US)
Article number7482755
Pages (from-to)1053-1060
Number of pages8
JournalIEEE Journal on Selected Topics in Signal Processing
Issue number6
StatePublished - Sep 2016


  • Optimal trading trajectory
  • portfolio optimization
  • quantum annealing

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering


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