Programmable Quantum Matter: Heralding Large Cluster States in Driven Inhomogeneous Spin Ensembles

Abstract

Atom-like emitters in solids have emerged as promising platforms for quantum sensing and information processing. Among the major challenges are inhomogeneities in emitter fine structure, which complicates quantum control. Here, we introduce a framework that leverages this emitter diversity to simplify the experimental resources needed to create optically heralded spin cluster states across N q emitters from the conventional order O ( N q ) to O ( 1 ) within ensembles of N q ∼ 10 – 100 . Specifically, the optimized pulse sequence simultaneously corrects parameter variations (pulse-length error and frequency detuning error), achieving single-qubit gate fidelities exceeding 99.99% for errors (normalized relative to Rabi-drive strength) up to 0.3, while maintaining fidelities above 99% even for errors as large as 0.4. Applying this optimized pulse sequence in the form of a Carr-Purcell-Meiboom-Gill (CPMG) based dynamical decoupling protocol to the dominant noise spectral density of silicon-vacancy centers in diamond, our approach enhances ensemble-average coherence times by more than a factor of 7 relative to interleaved bang-bang-based CPMG. For state-of-the-art dilution refrigeration systems, we further estimate sharply reduced heating when driving a global resonant optimal dynamical decoupling across N q silicon-vacancy spins, potentially resolving the current trade-off between spin coherence and scaling to N q ≫ 1 . We further introduce a modified single-photon entanglement protocol with an efficient algorithm for deterministic entanglement compilation. Depending on the decoupling window, our method yields order O ( 10 2 – 10 4 ) more entanglement links than bang-bang sequences, with theoretical guarantees of order Ω ( N q ) unique links—improvable via control-parameter tuning. Our approach thus offers enhanced fidelity, scalability, and robustness. Together, these techniques provide foundational tools—including global unitary control, phase denoising, remote entanglement, and compilation—for scalable quantum computing architectures based on heterogeneous spin ensembles.