Tight bound for estimating expectation values from a system of linear equations
Tight bound for estimating expectation values from a system of linear equations
The system of linear equations problem (SLEP) is specified by a complex invertible matrix $A$, the condition number $\ensuremath{\kappa}$ of $A$, a vector $\mathbit{b}$, a Hermitian matrix $M$, and an accuracy $\ensuremath{\epsilon}$, and the task is to estimate ${\mathbit{x}}^{\ifmmode\dagger\else\textdagger\fi{}}M\mathbit{x}$, where $\mathbit{x}$ is the solution vector to the equation $A\mathbit{x}=\mathbit{b}$. We …