A quantum gate array can be programmed to evaluate the expectation value of any operator

Abstract

A programmable gate array is a circuit whose action is controlled by input data. In this letter we describe a special--purpose quantum circuit that can be programmed to evaluate the expectation value of any operator $O$ acting on a space of states of $N$ dimensions. The circuit has a program register whose state $|Ψ(O)>_P$ encodes the operator $O$ whose expectation value is to be evaluated. The method requires knowledge of the expansion of $O$ in a basis of the space of operators. We discuss some applications of this circuit and its relation to known instances of quantum state tomography.