Solving Linear Systems of Equations using HHL

HHL

• Quantum algorithm to estimate function of solution with running time complexity

The HHL algorithm
Assume b and x to be normalised and map them to the respective quantum states |b⟩ and |x⟩
Focus on the rescaled problem A|x⟩ = |b⟩

1. Load data |b⟩ ∈ C^N => perform the transformation |0⟩nb -> |b⟩nb
2. Apply QPE
3. Add an ancilla qubit and apply a rotation conditioned on |λj⟩
4. Apply QPE† and ignore possible errors from QPE
5. Measure ancilla qubit in computational basis