Bell inequality violation in gate-defined quantum dots
Paul Steinacker, Tuomo Tanttu, Wee Han Lim, Nard Dumoulin Stuyck, MengKe Feng, Santiago Serrano, Ensar Vahapoglu, Rocky Y. Su, Jonathan Yinhao Huang, Cameron Jones, Kohei M. Itoh, Fay E. Hudson, Christopher C. Escott, Andrea Morello, André Saraiva, Chih Hwan Yang, Andrew S. Dzurak, Arne Laucht
Quantum computers leverage entanglement to achieve superior computational power. However, verifying that the entangled state does not follow the principle of local causality has proven difficult for spin qubits in gate-defined quantum dots, as it requires simultaneously high concurrence values and readout fidelities to break the classical bound imposed by Bell’s inequality. While low error rates for state preparation, control, and measurement have been independently demonstrated, a simultaneous demonstration remained challenging. We employ advanced protocols like heralded initialization and calibration via gate set tomography (GST), to push fidelities of the full 2-qubit gate set above 99%, including state preparation and measurement (SPAM). We demonstrate a 97.17% Bell state fidelity without correcting for readout errors and violate Bell’s inequality using direct parity readout with a Bell signal of S = 2.731. Our measurements exceed the classical limit even at 1.1 K or entanglement lifetimes of 100 μs. Violating Bell’s inequality in a silicon quantum dot qubit system is a key milestone, as it proves quantum entanglement, fundamental to achieving quantum advantage. Silicon-based spin qubits are promising candidates for a scalable quantum computer. Here the authors demonstrate the violation of Bell’s inequality in gate-defined quantum dots in silicon, marking a significant advancement that showcases the maturity of this platform.
Quantum computers leverage entanglement to achieve superior computational power. However, verifying that the entangled state does not follow the principle of local causality has proven difficult for spin qubits in gate-defined quantum dots, as it requires simultaneously high concurrence values and readout fidelities to break the classical bound imposed by Bell’s inequality. While low error rates for state preparation, control, and measurement have been independently demonstrated, a simultaneous demonstration remained challenging. We employ advanced protocols like heralded initialization and calibration via gate set tomography (GST), to push fidelities of the full 2-qubit gate set above 99%, including state preparation and measurement (SPAM). We demonstrate a 97.17% Bell state fidelity without correcting for readout errors and violate Bell’s inequality using direct parity readout with a Bell signal of S = 2.731. Our measurements exceed the classical limit even at 1.1 K or entanglement lifetimes of 100 μs. Violating Bell’s inequality in a silicon quantum dot qubit system is a key milestone, as it proves quantum entanglement, fundamental to achieving quantum advantage. Silicon-based spin qubits are promising candidates for a scalable quantum computer. Here the authors demonstrate the violation of Bell’s inequality in gate-defined quantum dots in silicon, marking a significant advancement that showcases the maturity of this platform.
Abstract Universal quantum computation will require qubit technology based on a scalable platform1, together with quantum error correction protocols that place strict limits on the maximum infidelities for one- and two-qubit gate operations2, 3. Although various qubit systems have shown high fidelities at the one-qubit level4–10, the only solid-state qubits manufactured using standard lithographic techniques that have demonstrated two-qubit fidelities near the fault-tolerance threshold6 have been in superconductor systems. Silicon-based quantum dot qubits are also amenable to large-scale fabrication and can achieve high single-qubit gate fidelities (exceeding 99.9 per cent) using isotopically enriched silicon11, 12. Two-qubit gates have now been demonstrated in a number of systems13–15, but as yet an accurate assessment of their fidelities using Clifford-based randomized benchmarking, which uses sequences of randomly chosen gates to measure the error, has not been achieved. Here, for qubits encoded on the electron spin states of gate-defined quantum dots, we demonstrate Bell state tomography with fidelities ranging from 80 to 89 per cent, and two-qubit randomized benchmarking with an average Clifford gate fidelity of 94.7 per cent and an average controlled-rotation fidelity of 98 per cent. These fidelities are found to be limited by the relatively long gate times used here compared with the decoherence times of the qubits. Silicon qubit designs employing fast gate operations with high Rabi frequencies16, 17, together with advanced pulsing techniques18, should therefore enable much higher fidelities in the near future.
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∗, to a time limited instead by 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.
Electron spins in silicon quantum dots are a promising platform for fault-tolerant quantum computing. Low-frequency noise, including nuclear spin fluctuations and charge noise, is a primary factor limiting gate fidelities. Suppressing this noise is crucial for high-fidelity qubit operations. Here, we report on a two-qubit quantum device in natural silicon with universal qubit control, designed to investigate the upper limits of gate fidelities in a non-purified Si/SiGe quantum dot device. By employing advanced device structures, qubit manipulation techniques, and optimization methods, we have achieved single-qubit gate fidelities exceeding 99% and a two-qubit controlled-Z (CZ) gate fidelity of 91%. Decoupled CZ gates are used to prepare Bell states with an average fidelity of 91%, typically exceeding previously reported values in natural silicon devices. These results underscore that even natural silicon has the potential to achieve high-fidelity gate operations, particularly with further optimization methods to suppress low-frequency noise.
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.
Scalable quantum processors require high-fidelity universal quantum logic operations in a manufacturable physical platform. Donors in silicon provide atomic size, excellent quantum coherence and compatibility with standard semiconductor processing, but no entanglement between donor-bound electron spins has been demonstrated to date. Here we present the experimental demonstration and tomography of universal one- and two-qubit gates in a system of two weakly exchange-coupled electrons, bound to single phosphorus donors introduced in silicon by ion implantation. We observe that the exchange interaction has no effect on the qubit coherence. We quantify the fidelity of the quantum operations using gate set tomography (GST), and we use the universal gate set to create entangled Bell states of the electrons spins, with fidelity 91.3 ± 3.0%, and concurrence 0.87 ± 0.05. These results form the necessary basis for scaling up donor-based quantum computers. Donors spins in silicon are coherent, high-performance qubits, but scale-up has been challenging. Here the authors present the first experimental demonstration of exchange-based, entangling two qubit gates between electrons bound to 31P donors in Si.
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.