Progress towards Analytically Optimal Angles in Quantum Approximate Optimisation

Daniil Rabinovich, Richik Sengupta, Ernesto Campos, Vishwanathan Akshay and Jacob Biamonte
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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

Mathematics, 2022, vol. 10, issue 15, 1-9

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.

Keywords: variatonal algorithms; QAOA; quantum circuit optimization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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