Quantum Dueling: an Efficient Solution for Combinatorial Optimization

TL;DR

This paper introduces quantum dueling, a novel quantum algorithm for combinatorial optimization that uses dual qubit registers to achieve quadratic speedup and can be integrated into larger quantum algorithms.

Contribution

The paper proposes a new quantum dueling algorithm with a dual-register setup, enabling dynamic solution competition and quadratic speedup in combinatorial optimization.

Findings

Achieves quadratic speedup over classical methods.

Demonstrates effectiveness through classical simulation.

Can be integrated into larger quantum algorithms.

Abstract

In this paper, we present a new algorithm for generic combinatorial optimization, which we term quantum dueling. Traditionally, potential solutions to the given optimization problems were encoded in a ``register'' of qubits. Various techniques are used to increase the probability of finding the best solution upon measurement. Quantum dueling innovates by integrating an additional qubit register, effectively creating a ``dueling'' scenario where two sets of solutions compete. This dual-register setup allows for a dynamic amplification process: in each iteration, one register is designated as the 'opponent', against which the other register's more favorable solutions are enhanced through a controlled quantum search. This iterative process gradually steers the quantum state within both registers toward the optimal solution. With a quantitative contraction for the evolution of the state vector, classical simulation under a broad range of scenarios and hyper-parameter selection schemes shows that a quadratic speedup is achieved, which is further tested in more real-world situations. In addition, quantum dueling can be generalized to incorporate arbitrary quantum search techniques and as a quantum subroutine within a higher-level algorithm. Our work demonstrates that increasing the number of qubits allows the development of previously unthought-of algorithms, paving the way for advancement of efficient quantum algorithm design.