3 présentations

• 
  08h30 - 08h52

  Reformulations and Decomposition for Quantum Discrete Optimization: Applications in Optimal Power Flow

  • David E. Bernal Neira, prés., Purdue University

  Quantum computing has the potential to accelerate specific challenging computational tasks compared to classical computers. In particular, given the Ising spin model to quadratic unconstrained binary optimization (QUBO) equivalence, methods have been proposed to tackle discrete optimization through quantum methods. We present a series of tools that allow reformulating discrete nonlinear optimization problems into QUBO and solving them using current quantum computers.
  Given its quadratic formulation, Alternate Current Optimal Power Flow (ACOPF) appears to be a promising candidate for quantum computers. Nevertheless, the standard reformulations into a quantum system were found costly, with small networks requiring thousands of qubits. By analyzing individual constraints, we developed problem-specific strategies for reducing qubit requirements that are still beyond current-era quantum computer capabilities.
  Final perspectives of problem decomposition are presented as alternatives to exploit current quantum devices when aiming for practical discrete optimization applications.

• 
  08h52 - 09h14

  Optimizing Multi-level Magic State Factories for Fault-Tolerant Quantum Architectures

  • Pooya Ronagh, prés., 1QBit

  We propose a novel technique for optimizing a modular fault-tolerant quantum computing (FTQC) architecture, taking into account any desired space--time trade-offs between the number of physical qubits and the fault-tolerant execution time of a quantum algorithm. We consider an FTQC micro-architecture comprising dedicated zones for various FTQC procedures, forming a supply chain network for production and consumption of resource states. We then solve the multi-objective optimization problem of minimizing space and time subject to a user-defined error budget for the success of the computation, taking the physical noise profile of the quantum computer into account. As an application, we show that physical quantum resource estimation of utility-scale quantum algorithms reduces to a simple model involving a small number of key parameters, namely, the circuit volume, the error suppression rates of various FTQC protocols, and a slowdown factor for the computer.

• 
  09h14 - 09h36

  Graph clustering with Boltzmann machines

  • Pierre Miasnikof, prés., Université Laval
  • Mohammad Bagherbeik, University of Toronto
  • Ali Sheikholeslami, University of Toronto

  Graph clustering is the process of labeling nodes so that nodes sharing common labels form densely connected subgraphs with sparser connections to the remaining vertices. In this work, we extend the recent binary quadratic K-medoids formulation to graph clustering. We also generalize a quadratic formulation originally designed for partitioning complete graphs. Because binary quadratic optimization is an NP-hard problem, we obtain numerical solutions for these formulations using two novel Boltzmann machine meta-heuristics. For benchmarking purposes, we compare solution quality and computational performances to those obtained using a commercial solver, Gurobi. We also compare clustering quality to the clusters obtained using the popular Louvain modularity maximization method.

  *This talk is based on Miasnikof, Bagherbeik & Sheikholeslami (2024), “Graph clustering with Boltzmann machines”