Researchers set a lower bound for quantum equation solving

Researchers at Quantinuum K.K., the National University of Singapore, and RIKEN have established a lower bound on the complexity of solving linear systems with quantum computers. Published August 4, 2026, in Quantum Science and Technology, the work defines a concrete limit to quantum speedup for this specific task, moving beyond theoretical possibility to measurable constraints. The team proved a lower bound of Ω(κ sqrt(s)) for quantum algorithms solving linear systems with constant error, where κ represents the condition number and s denotes the sparsity of the system. This study utilized no new data creation or analysis, representing a purely theoretical advancement in understanding quantum computational limits. Researchers have demonstrated that quantum computers face inherent complexity when solving linear systems of…