SamBa-GQW Solves Binary combinatorial Optimization problems
SamBa-GQW New Quantum Algorithm “SamBa-GQW” Solves Difficult Optimisation Problems Without Classical Techniques
French academics have developed a quantum algorithm that handles binary combinatorial optimisation problems without employing classical optimisation methods used in most hybrid quantum systems. A proposed non-variational technique, SamBa-GQW, overcomes significant quantum computing barriers and may accelerate the realisation of a useful quantum advantage.
Ugo Nzongani, Dylan Laplace Mermoud, Giuseppe Di Molfetta, and colleagues from Aix-Marseille Université and the CNRS submitted the paper, which proposes a revolutionary technique to solve problems that challenge even the most powerful classical and quantum computers. Smarter, Guided Quantum Walk SamBa-GQW relies on a continuous-time quantum walk, a quantum random walk. A quantum “walker” searches a wide graph of alternative solutions to find the optimum arrangement that minimises a problem's cost function. Quantum computing targets combinatorial optimisation problems, which involve choosing the best solution from many choices. The algorithm's key innovation is “offline” classical sampling, which occurs before quantum computation. This pre-processing stage examines the Hamiltonian to learn about the problem's structure and energy spectrum. This data is used to produce a time-dependent “hopping rate” that intelligently guides the quantum walker to better options. SamBa-GQW distinguishes itself from hybrid quantum-classical techniques like the Quantum Approximate Optimisation Algorithm by avoiding “barren plateaus” and scalability issues that could hinder variational algorithms. Excellent Performance on Complex Issues
The study team tested SamBa-GQW on several difficult optimisation problems and found it effective. The approach performed well on quadratic problems like MaxCut and portfolio optimisation as well as higher-order polynomial problems like maximal independent set, MAX-SAT, and a quartic reformulation of the travelling salesperson problem. Empirical results are promising. SamBa-GQW produced high-quality approximate solutions for issues up to 20 qubits by sampling only n² of the 2ⁿ total possible states. The approach often outperformed QAOA and other guided quantum walks. By eliminating the classical optimiser during main computing, the team lowered execution time by at least one order of magnitude compared to the original Guided Quantum Walk (GQW). Making Quantum Advantage Practical SamBa-GQW's suitability for current and future quantum computers is crucial. Due to its polynomial depth scaling with qubits, the researchers transformed the continuous-time quantum walk into a gate-based quantum circuit that can be implemented on existing hardware. The investigation also revealed optimal answers without completing the quantum walkthrough. Solution recovery and premature measurement are possible when the quantum state representing the solution becomes well-localized early on. By eliminating classical optimisers and streamlining the process, SamBa-GQW advances quantum algorithm development. It provides a consistent, non-variational solution to complex computer problems. SamBa-GQW is a promising new path for quantum's promise, however performance depends on classical sampling precision and needs more investigation.
