Quantum speedup and limitations on matroid property problems

Quantum computers show advantages over classical computers in some problems, such as unordered data base searching and prime factorization. Finding more problems that can take quantum speedup has become one of the focus problems in quantum computing. Before this, there is no research work on the quantum query complexity and quantum algorithm for matroid problems. It is interesting and meaningful to search for structures that can take quantum advantage in matroid problems.
In order to study the possibility and limitation of acceleration of quantum computing in matroid problems, a research team led by Lvzhou LI published their new research on 15 August 2024 in Frontiers of Computer Science co-published by Higher Education Press and Springer Nature.
The team investigates the quantum query complexity of some basic matroid problems and presents asymptotically optimal quantum algorithms for some of them.
In the research, they apply a technique called the quantum adversary method to prove the lower bound of the quantum query complexity of these matroid problems. The quantum adversary method is a versatile method for proving lower bounds on quantum algorithms. For some of these problems, they give asymptotically optimal quantum algorithms based on the quantum search algorithm (Grover’s algorithm). These results show that for these fundamental matroid problems quantum speedup is possible.
Future work can focus on finding the structure of matroid problems with more quantum speedup and matroid problems for the Noisy intermediate scale quantum (NISQ) era to demonstrate quantum dominance.
DOI: 10.1007/s11704-023-3130-9