Generalized parity measurements

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.

7 pages, 1 fig; updated to the published version

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Cited by in corpus (17)

• Deterministic Preparation of Dicke States
• Photonic two-qubit parity gate with tiny cross-Kerr nonlinearity
• Entanglement genesis under continuous parity measurement
• Approximating many-body quantum states with quantum circuits and measurements
• Multi-qubit entanglement engineering via projective measurements
• Quantum entanglement distribution with hybrid parity gate
• Preparing Dicke states in a spin ensemble using phase estimation
• On-chip generation and collectively coherent control of the superposition of the whole family of Dicke states
• Efficient detection of inhomogeneous magnetic fields from a single spin with Dicke states
• Hybrid quantum computing with ancillas
• A versatile source of polarization-entangled photons
• Quantum computation mediated by ancillary qudits and spin coherent states
• Efficient nonclassical state preparation via generalized parity measurement
• Efficient quantum algorithm to construct arbitrary Dicke states
• Quantum Probes Reduce Measurements: Application to Distributed Grover Algorithm
• Generalized Parity Measurements and Efficient Large Multi-component Cat State Preparation with Quantum Signal Processing
• An Optimum Algorithm for Quantum Search