Quantum algorithm solves matrix equations much faster than classical methods

Rolando D. Somma of Google Quantum AI and colleagues have devised a quantum algorithm that efficiently solves the Sylvester equation, a fundamental linear matrix equation used in fields from control theory to physics. The approach constructs a solution matrix using a technique, allowing for faster access to its properties than traditional methods of preparing a quantum state. The query and gate complexities of the quantum circuit that implements this block-encoding are almost linear in a condition number that depends on the input matrices and logarithmically with the problem's dimension and desired accuracy. The team demonstrates this circuit can efficiently tackle problems within the BQP class, suggesting a pathway toward practical…