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This article reports on SamBa-GQW, a non-variational quantum algorithm that solves binary combinatorial optimization problems using continuous-time quantum walks without classical optimizers. The method effectively handles instances up to 30 qubits by sampling polynomial states, offering a viable alternative to QAOA for addressing challenges like MaxCut and portfolio optimization on current NISQ hardware.

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A quantum walk finds good solutions with only 30 qubits

Quantum ZeitgeistOctober 13, 20265 min read

SamBa-GQW is a novel quantum algorithm for solving binary combinatorial optimization problems of arbitrary degree, without using a classical optimizer. The algorithm uses a continuous-time quantum walk and finds high quality approximate solutions on problems up to a size of $n=30$ qubits by sampling poly($n$) states among $2^n$ possible decisions.

Ugo Nzongani and colleagues have developed SamBa-GQW, a new quantum algorithm that efficiently tackles complex optimization problems. The researchers demonstrate solutions for problems reaching a size of 30 qubits by sampling only a polynomial number of states among the 2n possibilities, a marked gain in efficiency. SamBa-GQW successfully addresses challenges including MaxCut, portfolio optimization and a quartic reformulation of the travelling salesperson problem. This work positions the algorithm as a promising heuristic for tackling combinatorial problems beyond current quantum computer limitations. SamBa-GQW, a new quantum algorithm, demonstrates effective problem-solving capabilities up to a scale of 30 qubits, a notable achievement…

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