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Nature Communications

Multiparticle entanglement of nuclear spins in silicon

Feng Xu, Yi Deng, Guangchong Hu, Kada Yang, Chunhui Li, Chao Wei, Shihang Zhang, Chunhui Zhang, Peng Du, Keji Shi, Meiling Duan, Tianluo Pan, Zhen Tian, Peihao Huang, Guanyong Wang, Song Liu, Dapeng Yu, Yu He, Tao Xin

Published Jun 25, 2026• 0 citations
Publisher

Abstract

Silicon spin qubits offer high-fidelity control and semiconductor manufacturing compatibility. However, the systematic generation and characterization of multiparticle entanglement, a core resource for quantum information science, remain elusive in such systems. Here, we demonstrate the complete preparation of all nine canonical families of four-qubit entanglement between donor spins in silicon, by designing hardware-efficient quantum circuits that use native multi-qubit operations. We employ advanced overlapping tomography and multifaceted verification to fully characterize these states. Our results confirm genuine multiparticle entanglement, resolve their entanglement structure, and assess their robustness under qubit loss. Moreover, we observe significant violations of multiparticle Bell-type inequalities for genuine four-qubit nonlocality. On the prepared Greenberger-Horne-Zeilinger state, we further uncover a noise-induced entanglement dynamics from distillable to bound and finally to separable, with bound entanglement unlocked via joint measurement. This work generates diverse entanglement resources alongside their complete characterization, establishing a foundation for entanglement-enabled quantum applications in silicon. Multiparticle entanglement in silicon spin qubits has been difficult to generate and fully characterize beyond three-qubit Greenberger-Horne-Zeilinger states. Here, the authors demonstrate complete preparation and verification of all nine canonical families of four qubit entanglement in donor spins in silicon.

DOI
10.1038/s41467-026-74491-1

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Silicon spin qubits offer high-fidelity control and semiconductor manufacturing compatibility. However, the systematic generation and characterization of multiparticle entanglement, a core resource for quantum information science, remain elusive in such systems. Here, we demonstrate the complete preparation of all nine canonical families of four-qubit entanglement between donor spins in silicon, by designing hardware-efficient quantum circuits that use native multi-qubit operations. We employ advanced overlapping tomography and multifaceted verification to fully characterize these states. Our results confirm genuine multiparticle entanglement, resolve their entanglement structure, and assess their robustness under qubit loss. Moreover, we observe significant violations of multiparticle Bell-type inequalities for genuine four-qubit nonlocality. On the prepared Greenberger-Horne-Zeilinger state, we further uncover a noise-induced entanglement dynamics from distillable to bound and finally to separable, with bound entanglement unlocked via joint measurement. This work generates diverse entanglement resources alongside their complete characterization, establishing a foundation for entanglement-enabled quantum applications in silicon. Multiparticle entanglement in silicon spin qubits has been difficult to generate and fully characterize beyond three-qubit Greenberger-Horne-Zeilinger states. Here, the authors demonstrate complete preparation and verification of all nine canonical families of four qubit entanglement in donor spins in silicon.
Nuclear spins were among the first physical platforms to be considered for quantum information processing1,2, because of their exceptional quantum coherence3 and atomic-scale footprint. However, their full potential for quantum computing has not yet been realized, owing to the lack of methods with which to link nuclear qubits within a scalable device combined with multi-qubit operations with sufficient fidelity to sustain fault-tolerant quantum computation. Here we demonstrate universal quantum logic operations using a pair of ion-implanted 31P donor nuclei in a silicon nanoelectronic device. A nuclear two-qubit controlled-Z gate is obtained by imparting a geometric phase to a shared electron spin4, and used to prepare entangled Bell states with fidelities up to 94.2(2.7)%. The quantum operations are precisely characterized using gate set tomography (GST)5, yielding one-qubit average gate fidelities up to 99.95(2)%, two-qubit average gate fidelity of 99.37(11)% and two-qubit preparation/measurement fidelities of 98.95(4)%. These three metrics indicate that nuclear spins in silicon are approaching the performance demanded in fault-tolerant quantum processors6. We then demonstrate entanglement between the two nuclei and the shared electron by producing a Greenberger-Horne-Zeilinger three-qubit state with 92.5(1.0)% fidelity. Because electron spin qubits in semiconductors can be further coupled to other electrons7-9 or physically shuttled across different locations10,11, these results establish a viable route for scalable quantum information processing using donor nuclear and electron spins.
Quantum error detection is essential in realizing large-scale universal quantum computation, especially for quantum error correction (QEC). However, key elements for FTQC have yet to be realized in silicon qubits. Here, we demonstrate quantum error detection on a donor-based silicon quantum processor comprising four-nuclear spin qubits and one electron spin as an auxiliary qubit. The entanglement capability of this system is validated through the establishment of two-qubit Bell state entanglement between the nuclear spins and the generation of a four-qubit Greenberger-Horne-Zeilinger (GHZ) state, achieving a GHZ state fidelity of 88.5(2.3)%. Furthermore, by executing a four-qubit error detection circuit with the stabilizers, we successfully detect arbitrary single-qubit errors. The encoded Bell state entanglement information is recovered by performing the Pauli-frame update (PFU) via postprocessing. Based on the detected errors, we identify strongly biased noise in our system. Our results mark a significant advance toward FTQC in silicon spin qubits.
Spin qubits in silicon-MOS (SiMOS) quantum dots have recently demonstrated compatibility with existing industry standard CMOS fabrication techniques. These devices have routinely achieved single- and two-qubit gate fidelities above 99% and demonstrated highly entangled two-qubit Bell states in isolated double quantum dot (DQD) unit cells, however coupling between unit cells has remained challenging. In this work, we present a two unit cell, four-qubit SiMOS processor with universal controllability and fully parallelised state initialisation and readout. We use this processor to generate maximally entangled three-qubit states, including the Greenberger-Horne-Zeilinger (GHZ) state, and certify multipartite entanglement through violation of the classical Mermin-witness bound. By using a fully symmetric dynamically decoupled gate sequence to create our entangled states, we are able to preserve the lifetime of the entanglement beyond T2∗T_2^*T2∗​, to a time limited instead by T2HahnT_2^\textrm{Hahn}T2Hahn​. These demonstrations pave a road to the scalable operation of larger SiMOS processors, and achieving high purity, long-lived multi-qubit entangled states in them.
Silicon-based spin qubits have emerged as a promising platform for scalable quantum computation due to their compatibility with advanced semiconductor fabrication and integration with classical CMOS electronics. As fabrication capabilities advance toward larger, higher-yield devices, the field is transitioning from academic prototypes toward processors ultimately requiring millions of qubits. This shift places increasing emphasis on developing operating techniques that scale with qubit number. In this thesis, a four qubit SiMOS processor is used to investigate three key aspects of multi-qubit operation for spin-based quantum computing. First, tuning and operation techniques for parallel double-quantum-dot unit cells are developed. Electron loading strategies enable four-qubit operation in an isolated charge configuration, and universal single- and two-qubit control is demonstrated. The native gate set is characterised using gate set tomography. The processor is operated as two unit cells that can be initialised and read out in parallel, providing two independent parity measurements per shot, without increasing operation time or degrading state preparation and measurement fidelity. Second, control techniques for generating multi-qubit entangled states and executing general quantum circuits are established. Three-qubit maximally entangled states, including cluster and Greenberger–Horne–Zeilinger states, are generated and measured with a maximum fidelity of 82.5%. A Mermin value of 3.14 is achieved, certifying genuine tripartite entanglement. A fully symmetric dynamically decoupled gate sequence is developed, extending the entanglement lifetime beyond T2* to a limit set by T2-Hahn. A workflow for compiling, executing, and analysing arbitrary circuits from OpenQASM is also demonstrated. Finally, the first mid-circuit measurements in a silicon spin-qubit system are presented. This capability is extended to feedforward control, including a novel “in-layer” method that performs conditional phase operations without routing information to the classical control layer. This approach leverages measurement-induced backaction as a control mechanism. Both in-layer and FPGA-enabled feedforward strategies are benchmarked, and their dominant error channels are identified.
We present a programmable silicon photonic four-qubit integrated circuit for the generation and manipulation of diverse quantum states. The silicon photonic chip integrates photon-pair sources, pump-reducing filters, wavelength-division-multiplexing filters, Mach–Zehnder interferometer switches, and single-qubit arbitrary gates, enabling versatile state preparation and tomography. We measure Hong–Ou–Mandel interference with an impressive 98% visibility using four-photon coincidence, laying the foundation for high-purity qubits. Our analysis involves estimating the fidelity and purity of distinct quantum states through maximum-likelihood estimation applied to tomographic measurements. In our experimental results, we showcase the following achievements: a heralded single qubit achieving 98.2% fidelity and 98.3% purity, a Bell state reaching 95.2% fidelity and 94.8% purity, and a four-qubit system with two simultaneous Bell states exhibiting 87.4% fidelity and 84.6% purity. Finally, a four-qubit Greenberger–Horne–Zeilinger (GHZ) state demonstrates 85.4% fidelity and 81.7% purity. In addition, we certify the entanglement of the four-photon GHZ state through Bell’s inequality violations and a negative entanglement witness.
Recent advances in coherent spin shuttling have made sparse semiconductor spin qubit arrays an appealing solid-state platform to realize quantum processors. The dynamic and long-range connectivity enabled by shuttling is also essential for many quantum error-correction (QEC) schemes. Here, we demonstrate a silicon spin-qubit device that comprises a shuttling bus for coherently transporting qubits that can interact at four isolated locations we call bus stops. We dynamically populate the array and tune all single- and two-qubit operations using shuttling and quantum non-demolition (QND) spin measurements, without access to charge sensing in most of the device. We achieve universal control of the effective five-qubit processor and select the connectivity required to form a surface-code stabilizer plaquette that supports X- and Z-type parity checks up to weight-four. We use the parity checks to generate multi-qubit entanglement between all qubit combinations in the array and report the genuine entanglement of a five-qubit Greenberger-Horne-Zeilinger (GHZ) state, constituting the largest such state ever constructed with gate-defined semiconductor spins. This work opens immediate opportunities to pursue QEC experiments with spin qubits, and the protocols developed here lay the groundwork for the modular calibration and operation of sparse spin qubit arrays.