3 présentations

• 
  15h45 - 16h10

  Quantum-Inspired Optimization for Index Tracking in Financial Portfolios

  • David Escobar Vargas, prés., InfinityQ Technology Inc.
  • Brian Mao, InfinityQ Technology Inc.
  • Saavan Patel, InfinityQ Technology Inc.

  This work presents a quantum-inspired method that achieves significant computational speedups for the index tracking problem, a key challenge in financial portfolio management. Index tracking involves constructing and dynamically managing a portfolio to closely mirror the performance of a designated market index, such as the S&P 500 or FTSE 100, while minimizing tracking error and transaction costs. This problem is central to passive investment strategies, notably index funds and exchange-traded funds (ETFs), which seek to replicate index returns with high fidelity. We formulate the index tracking problem as a Mixed-Integer Quadratic Constrained Quadratic Program (MIQCQP). Solving this NP-hard problem with commercial solvers becomes computationally prohibitive, especially when considering real-world constraints and large asset universes. The primary computational challenge stems from the non-linearity introduced by tracking error minimization in the objective function, the usage of integer variables to model integer lot sizes and quadratic constraints for risk minimization. To address this, we evaluate our quantum-inspired solver through extensive numerical experiments on benchmark datasets, such as the S&P 500. Our results demonstrate up to a 1200X speedup over solvers such as CPLEX and Gurobi, without compromising solution quality. This enhanced computational efficiency directly improves portfolio management, enabling more frequent and precise index tracking. Our study highlights the potential of quantum-inspired methods in finance, which paves the way for broader applications in large-scale financial decision-making.

• 
  16h10 - 16h35

  Solving the Low Autocorrelation Binary Sequences (LABS) Problem using Quantum-Inspired Techniques

  • Brian Mao, InfinityQ Technology Inc.
  • Kevin Jordan, prés., InfinityQ Technology Inc.
  • Ethan Wang, InfinityQ Technology Inc.
  • Saavan Patel, InfinityQ Technology Inc.

  The Low Autocorrelation Binary Sequences (LABS) problem, also known as the Bernasconi model in statistical physics, is a classically intractable problem with many practical applications such as communications engineering, radar and sonar. The complexity of the LABS problem grows rapidly with optimal solutions only known for N≤66. In this work, a novel probabilistic quantum-inspired approach for this problem was formulated and solved. The Metropolis Hastings sampling algorithm was used in conjunction with Parallel Tempering facilitating exploration and exploitation of the state space. This work represents the first demonstration of a GPU accelerated solution to the LABS problem, creating a 1500% improvement in speed over a CPU only version. Low-level system design optimizations such as dynamic mixed precision allowed full device utilization for this compute-bound problem. This approach yielded time-to-solution scaling of 1.229^N and number of calls scaling of 1.187^N, whereas the best-known classical heuristic, memetic tabu search yielded a number of calls scaling of 1.35^N. It also performed similarly to true quantum methods, such as QAOA+QMF, with regards to scaling constant, and considerably better in terms of wall clock time. All LABS problems of size N≤66 were solved to optimality while directly handling higher order polynomials of the fourth order. Additionally, speed improvements of over 150,000x were demonstrated against both Gurobi and CPLEX.

• 
  16h35 - 17h00

  Unit Commitment Problem: A Siemens Energy Case Study by InfinityQ

  • Patrick St-Louis, prés., InfinityQ Technology Inc.
  • Saavan Patel, InfinityQ Technology
  • Brian Mao, InfinityQ Technology Inc.
  • David Escobar Vargas, InfinityQ Technology Inc.
  • Matthew Lang, Siemens Energy
  • Nigel Gwilliam, Siemens Energy
  • Lovish Chopra, Siemens Energy
  • Antonella Navarro, Siemens Energy
  • Éloi Vincent-Légaré, Siemens Energy

  Planning the energy production of a network of power plants is a difficult endeavor which can be mathematically modeled as a unit commitment problem. Projects must consider costs related to purchasing, installing, operating, and maintaining the required infrastructure for various energy providers (Solar panels, Wind turbines, Battery systems, Natural gas generators, etc.). In addition, due to the recent focus on green energy production, projects must also consider costs and measures of green energy as a cost per kg of CO2 emissions. These objectives are a key part of Siemens Energy solutions, which offer great support for CAPEX, OPEX, and Green Scoring in all their Battery Energy Storage Systems (BESS). In partnership with InfinityQ, a flexible mathematical model was designed to make tactical decisions on the number of units to purchase and install at various sites. The use of integer variables, such as the decisions on the number of units, and binary variables, to take into account activation, ramping, and uptime/downtime constraints, causes this problem to become NP-Hard. Therefore, it becomes difficult to handle for most solvers when a planning horizon of several months or years is required. We demonstrate how TitanQ, a quantum inspired solver, performs on real life unit commitment instances and explain how these approaches make use of probabilistic computing to find good quality solutions to non-linear non-convex problems.