Quantum Algorithms Database
HHL Algorithm
Solves systems of linear equations exponentially faster than classical methods, under specific conditions.
Year
2009
Inventor(s)
Harrow, Hassidim & Lloyd
Speedup Type
Exponential Speedup
Difficulty
★★★★★
The Problem
Solving a system of linear equations (Ax = b) — a problem underlying enormous amounts of scientific computing and machine learning.
How It Works
Encodes the linear system into a quantum state, uses quantum phase estimation to find eigenvalues, and inverts them to construct the solution — all without ever writing out the full solution vector classically.
Real-World Impact
Has significant caveats (requires the matrix to be 'sparse' and well-conditioned, and the output is a quantum state, not a classical answer), but is foundational to quantum machine learning research.