Generalized parity measurements

TL;DR

This paper introduces a generalized parity measurement technique using higher-dimensional ancillas, enabling efficient preparation of various multi-particle entangled states beyond stabilizer states, with significant advantages in certain cases.

Contribution

It extends parity gates to qudits, allowing the creation of diverse entangled states beyond stabilizer formalism, enhancing quantum state preparation capabilities.

Findings

Can prepare GHZ, W, Dicke, and G states in one shot

Provides exponential efficiency gain for W states over linear optics methods

Enables preparation of states beyond stabilizer/graph states

Abstract

Measurements play an important role in quantum computing (QC), by either 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 1-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/graph state formalism and prepare other types of multi-particle 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 GHZ_n, W_n, Dicke states D_{n,k}, and, more generally, certain sums of Dicke states, like G_n states used in secret sharing. For W_n states it provides an exponential gain compared to linear optics based methods.