On the Computational Viability of Quantum Optimization for PMU Placement

Using optimal phasor measurement unit placement as a prototypical problem, we assess the computational viability of the current generation D-Wave Systems 2000Q quantum annealer for power systems design problems. We reformulate minimum dominating set for the annealer hardware, solve the reformulation for a standard set of IEEE test systems, and benchmark solution quality and time to solution against the CPLEX optimizer and simulated annealing. For some problem instances the 2000Q outpaces CPLEX. For instances where the 2000Q underperforms with respect to CPLEX and simulated annealing, we suggest hardware improvements for the next generation of quantum annealers.

[1]  Michael J. Dinneen,et al.  Formulating graph covering problems for adiabatic quantum computers , 2017, ACSW.

[2]  Aidan Roy,et al.  A practical heuristic for finding graph minors , 2014, ArXiv.

[3]  Michael Jünger,et al.  Performance of a Quantum Annealer for Ising Ground State Computations on Chimera Graphs , 2019, ArXiv.

[4]  Ryan Babbush,et al.  What is the Computational Value of Finite Range Tunneling , 2015, 1512.02206.

[5]  D. McMahon Adiabatic Quantum Computation , 2008 .

[6]  M. Wache,et al.  Application of Synchrophasor Measurements for distribution networks , 2011, 2011 IEEE Power and Energy Society General Meeting.

[7]  John Preskill,et al.  Quantum Computing in the NISQ era and beyond , 2018, Quantum.

[8]  Lenwood S. Heath,et al.  The PMU Placement Problem , 2005, SIAM J. Discret. Math..

[9]  Stefan Zohren,et al.  Circuit design for multi-body interactions in superconducting quantum annealing systems with applications to a scalable architecture , 2016, 1603.09521.

[10]  Kin Cheong Sou,et al.  A branch-decomposition approach to power network design , 2015, 2016 American Control Conference (ACC).

[11]  H. Nishimori,et al.  Quantum annealing in the transverse Ising model , 1998, cond-mat/9804280.

[12]  Abhinav Verma,et al.  Power grid security analysis: an optimization approach , 2010 .

[13]  Catherine C. McGeoch,et al.  Quantum Annealing amid Local Ruggedness and Global Frustration , 2017, Journal of the Physical Society of Japan.

[14]  P. S. Georgilakis,et al.  Optimal placement of phasor measurement units: A literature review , 2011, 2011 16th International Conference on Intelligent System Applications to Power Systems.

[15]  Rupak Biswas,et al.  From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz , 2017, Algorithms.

[16]  Chung-Shou Liao,et al.  Hybrid search for the optimal PMU placement problem on a power grid , 2015, Eur. J. Oper. Res..

[17]  Andrey Bernstein,et al.  Autonomous Energy Grids , 2018, HICSS.

[18]  Kathryn M. Schumacher Optimization Algorithms for Power Grid Planning and Operational Problems. , 2014 .

[19]  H Neven,et al.  A blueprint for demonstrating quantum supremacy with superconducting qubits , 2017, Science.