Implementation of a general single-qubit positive operator-valued measure on a circuit-based quantum computer

Abstract

We derive a deterministic protocol to implement a general single-qubit positive operator-valued measure (POVM) on near-term circuit-based quantum computers. The protocol has a modular structure such that an $n$-element POVM is implemented as a sequence of $(n\ensuremath{-}1)$ circuit modules. Each module performs a two-element POVM. Two variations of the protocol are suggested---one optimal in terms of number of ancilla qubits, the other optimal in terms of number of qubit gate operations and quantum circuit depth. We use the protocol to implement two- and three-element POVMs on two publicly available quantum computing devices. The results we obtain suggest that implementing nontrivial POVMs could be within the reach of the current noisy quantum computing devices.