Grover Adaptive Search with Spin Variables

TL;DR

This paper introduces a spin-variable reformulation of Grover adaptive search that reduces quantum circuit complexity, making the algorithm more scalable for larger quantum problems.

Contribution

The paper proposes a novel spin-based quantum dictionary subroutine for GAS, significantly reducing CNOT gate requirements and improving scalability.

Findings

Reduces CNOT gates from exponential to polynomial in certain problems

Simplifies the quantum algorithm through spin variable reformulation

Enhances potential for larger-scale quantum optimization

Abstract

This paper presents a novel approach to Grover adaptive search (GAS) for a combinatorial optimization problem whose objective function involves spin variables. While the GAS algorithm with a conventional design of a quantum dictionary subroutine handles a problem associated with an objective function with binary variables $\{0,1\}$, we reformulate the problem using spin variables $\{+1,-1\}$ to simplify the algorithm. Specifically, we introduce a novel quantum dictionary subroutine that is designed for this spin-based formulation. A key benefit of this approach is the substantial reduction in the number of CNOT gates required to construct the quantum circuit. We theoretically demonstrate that, for certain problems, our proposed approach can reduce the gate complexity from an exponential order to a polynomial order, compared to the conventional binary-based approach. This improvement has the potential to enhance the scalability and efficiency of GAS, particularly in larger quantum computations.