# How do I construt a mixed state for an arbitrary symmetric matrix?

A symmetric matrix can be seen as a density matrix. If I have an arbitrary symmetrical matrix, can I use a quantum random access memory to construct a corresponding mixed state? What kind of quantum RAM do I need?

• Density matrices are usually Hermitian, these matrices are symmetric only in the case that the coefficients are real. Also not every symmetric matrix is a valid density matrix, you need postive-definite matrices with trace 1. Nov 23 at 14:55