Quantum gate arrays can be programmed to evaluate the expectation value of any operator
Juan Pablo Paz, Augusto J. Roncaglia · Physical Review A · 2003
A programmable gate array is a circuit whose action is controlled by input data. In this paper 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 $|\ensuremath{\Psi}(O){〉}_{P}$ 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.