Towards large-scale quantum optimization solvers with few qubits

TL;DR

This paper presents a quantum optimization method that efficiently solves large combinatorial problems with fewer qubits, demonstrating superior performance and mitigation of barren plateaus, and achieving high-quality solutions both numerically and experimentally.

Contribution

The authors introduce a qubit-efficient variational quantum solver with super-polynomial barren plateau mitigation, enabling large-scale combinatorial optimization on near-term quantum devices.

Findings

Numerical solutions for 7000 variables are competitive with classical solvers.

Experimental MaxCut approximation ratios exceed the hardness threshold.

The method significantly reduces barren plateau issues in quantum optimization.

Abstract

We introduce a variational quantum solver for combinatorial optimizations over $m=\mathcal{O}(n^k)$ binary variables using only $n$ qubits, with tunable $k>1$. The number of parameters and circuit depth display mild linear and sublinear scalings in $m$, respectively. Moreover, we analytically prove that the specific qubit-efficient encoding brings in a super-polynomial mitigation of barren plateaus as a built-in feature. This leads to unprecedented quantum-solver performances. For $m=7000$, numerical simulations produce solutions competitive in quality with state-of-the-art classical solvers. In turn, for $m=2000$, an experiment with $n=17$ trapped-ion qubits featured MaxCut approximation ratios estimated to be beyond the hardness threshold $0.941$. To our knowledge, this is the highest quality attained experimentally on such sizes. Our findings offer a novel heuristics for quantum-inspired solvers as well as a promising route towards solving commercially-relevant problems on near term quantum devices.