Mapping a 50-spin-qubit network through correlated sensing

Solid-state defects with optically accessible spins offer a promising platform for advancing quantum technologies, including quantum simulation, quantum networks, and quantum sensing. Systems such as defects in diamond, silicon carbide, silicon, hexagonal boron nitride (hBN), and rare-earth ions are being explored. The electron spin serves as a high-fidelity qubit, enabling optical initialization and readout, and acting as a long-range photonic interface. Furthermore, the electron spin can be used to sense and control numerous surrounding nuclear spins, creating a qubit register for quantum information processing and a testbed for nanoscale magnetic resonance imaging (nano-MRI). Applications include quantum simulations of many-body physics, quantum networks using nuclear spins for quantum memory and entanglement, and error correction. Current experiments have imaged networks with up to 27 nuclear spins; however, mapping larger networks is crucial for more complex quantum simulations, a better understanding of noise, and potentially imaging more complex external systems. The main challenge in mapping larger networks is spectral crowding, where overlapping signals hinder the assignment of individual spins and their interactions.

Existing techniques for mapping spin networks often rely on isolating individual nuclear-nuclear interactions using spin-echo double resonance (SEDOR). Simultaneous echo pulses at specific frequencies preserve the interaction between selected spins while decoupling them from environmental noise. The resulting nuclear-spin polarization is mapped onto the NV electron spin and read optically. This yields pairwise correlations of frequencies and couplings. However, spectral crowding from finite spectral linewidths leads to ambiguities in assigning measured couplings to specific spins, particularly when multiple spins overlap in frequency. This makes it challenging to reconstruct the network's complete structure. Previous work has demonstrated imaging of networks containing up to 27 nuclear spins, but larger networks pose a significant challenge due to spectral overlap.

This research introduces correlated sensing sequences to measure both network connectivity and characteristic spin frequencies with high spectral resolution. The core concept involves concatenating double-resonance sequences to measure chains of coupled spins. Mapping these spin chains removes ambiguity arising from spectral overlap. The process starts by polarizing the spin network and using the electron spin to sense a nuclear spin, initiating the chain. A double-resonance sequence is performed, revealing strong connections through dips in the coherence signal. By iteratively extending the chain using additional double-resonance blocks, multiple spin frequencies and their couplings are correlated. This enables measuring couplings otherwise inaccessible due to weak interactions or spectral crowding. Additionally, a correlated double-echo spectroscopy scheme is used to improve the resolution of spin frequency measurements, further reducing spectral overlap. The entire network can be mapped by expanding and looping single chains; in practice, measuring limited-size chains suffices due to the non-uniform couplings. Chains are fused together based on overlapping sections to reconstruct the network. A 3D spatial image of the network is obtained by combining measured hyperfine shifts and dipolar couplings. A graph search algorithm is employed, assisted by a positioning algorithm that uses spatial constraints and measured hyperfine shifts to validate and refine the network map.

The researchers successfully mapped a 50-nuclear-spin network comprising 1225 spin-spin interactions near an NV center in diamond. They achieved high spectral resolution by using concatenated double-resonance sequences to identify and map spin chains. The method effectively addresses the spectral crowding problem, enabling the identification of individual spins and their couplings even when their frequencies overlap. The use of spin chains allows access to couplings that would be otherwise difficult to measure due to weak interactions or spectral congestion. High-resolution measurement of spin frequencies, achieved through electron-nuclear double-resonance, provided additional information for resolving ambiguous assignments. By combining spin-chain sensing and high-resolution frequency measurements, they were able to map a significantly larger network than previously possible. The reconstruction of the 50-spin network was validated by comparing the measured data with a 3D spatial model of the spin interactions, confirming the accuracy of the mapping. 249 interactions were measured through pairwise and chained measurements, and successfully fused to create a hypothesis for the network connectivity. A total of 1225 spin-spin couplings (including predictions for unmeasured couplings) were characterized for the 50-spin cluster. The high-resolution measurements of spin frequencies revealed linewidths significantly narrower than those obtained with conventional methods.

The development of correlated double-resonance sensing significantly advances the ability to characterize complex spin networks. The successful mapping of a 50-spin network demonstrates the power of the method to overcome the limitations of traditional approaches, particularly in the presence of spectral crowding. The increased size and complexity of accessible spin networks open up new possibilities for quantum simulations of many-body phenomena previously intractable. The precise characterization of the network provides crucial data for optimizing quantum control gates and studying coherence in solid-state spins. The method's applicability to various systems holds significant promise for future applications in nano-MRI of materials and biological samples, potentially enabling high-resolution imaging at the nanoscale.

This research presents a significant breakthrough in the mapping of large spin networks using correlated double-resonance sensing. The successful mapping of a 50-spin network demonstrates the effectiveness of the developed techniques in overcoming spectral crowding limitations. The method's high spectral resolution and ability to access previously inaccessible couplings have broad implications for quantum simulation, quantum control, and nanoscale imaging. Future work might explore machine learning techniques to enhance protocols, reduce acquisition times, and further scale up the mapping of even larger spin networks.

The current method is limited by the signal strength decreasing with increasing chain length. This limits the maximum effective chain length that can be used in practice. The resolution of the method is also dependent on the nuclear T2-time, which decreases for spins further away from the NV center. This ultimately limits the number of unique spins that can be reliably identified and added to the network map. While a 3D spatial model was used to validate the network reconstruction, there is always some uncertainty associated with such modeling. The spatial resolution of the reconstructed network map might be further improved by combining the measurements with other techniques, or by using higher magnetic fields to further separate the spectral regions.