Quantum algorithm for linear systems of equations

Harrow, Hassidim, and Lloyd give a quantum algorithm for sparse, well-conditioned linear systems. The output is a quantum state encoding the solution. Cited from the HHL algorithm for the runtime in Appendix A.1, the error bound in Theorem 1, and Theorems 4 and 6 on the condition number and on estimating an expectation. Also cited from linear systems and from the condition number entry.