Generalized parity measurements

Abstract

Measurements play an important role in quantum computing (QC), either by providing the nonlinearity required for two-qubit gates (linear optics QC), or by implementing a quantum algorithm using single-qubit measurements on a highly entangled initial state (cluster state QC). Parity measurements can be used as building blocks for preparing arbitrary stabilizer states, and, together with one-qubit gates, are universal for quantum computing. Here we generalize parity gates by using a higher-dimensional (qudit) ancilla. This enables us to go beyond the stabilizer or graph state formalism and prepare other types of multiparticle entangled states. The generalized parity module introduced here can prepare in one shot, heralded by the outcome of the ancilla, a large class of entangled states, including Greenberger-Home-Zeilinger states ${\mathrm{GHZ}}_{n}$, ${\mathrm{W}}_{n}$, Dicke states ${\mathcal{D}}_{n,k}$, and, more generally, certain sums of Dicke states, like ${G}_{n}$ states used in secret sharing. For ${\mathrm{W}}_{n}$ states it provides an exponential gain compared to linear-optics-based methods.