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Progress towards Analytically Optimal Angles in Quantum Approximate Optimisation

Author

Listed:
  • Daniil Rabinovich

    (Laboratory of Quantum Algorithms for Machine Learning and Optimisation, Skolkovo Institute of Science and Technology, 3 Nobel Street, 121205 Moscow, Russia)

  • Richik Sengupta

    (Laboratory of Quantum Algorithms for Machine Learning and Optimisation, Skolkovo Institute of Science and Technology, 3 Nobel Street, 121205 Moscow, Russia)

  • Ernesto Campos

    (Laboratory of Quantum Algorithms for Machine Learning and Optimisation, Skolkovo Institute of Science and Technology, 3 Nobel Street, 121205 Moscow, Russia)

  • Vishwanathan Akshay

    (Laboratory of Quantum Algorithms for Machine Learning and Optimisation, Skolkovo Institute of Science and Technology, 3 Nobel Street, 121205 Moscow, Russia)

  • Jacob Biamonte

    (Laboratory of Quantum Algorithms for Machine Learning and Optimisation, Skolkovo Institute of Science and Technology, 3 Nobel Street, 121205 Moscow, Russia)

Abstract

The quantum approximate optimisation algorithm is a p layer, time variable split operator method executed on a quantum processor and driven to convergence by classical outer-loop optimisation. The classical co-processor varies individual application times of a problem/driver propagator sequence to prepare a state which approximately minimises the problem’s generator. Analytical solutions to choose optimal application times (called parameters or angles) have proven difficult to find, whereas outer-loop optimisation is resource intensive. Here we prove that the optimal quantum approximate optimisation algorithm parameters for p = 1 layer reduce to one free variable and in the thermodynamic limit, we recover optimal angles. We moreover demonstrate that conditions for vanishing gradients of the overlap function share a similar form which leads to a linear relation between circuit parameters, independent of the number of qubits. Finally, we present a list of numerical effects, observed for particular system size and circuit depth, which are yet to be explained analytically.

Suggested Citation

  • Daniil Rabinovich & Richik Sengupta & Ernesto Campos & Vishwanathan Akshay & Jacob Biamonte, 2022. "Progress towards Analytically Optimal Angles in Quantum Approximate Optimisation," Mathematics, MDPI, vol. 10(15), pages 1-9, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2601-:d:871812
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    Cited by:

    1. Fernando L. Pelayo & Mauro Mezzini, 2022. "Preface to the Special Issue on “Quantum Computing Algorithms and Computational Complexity”," Mathematics, MDPI, vol. 10(21), pages 1-3, October.

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