Violating Bell's inequality in gate-defined quantum dots

The superior computational power promised by quantum computers utilises the fundamental quantum mechanical principle of entanglement. However, achieving entanglement and verifying that the generated 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 of these metrices has been challenging. Here we employ advanced operational protocols for spin qubits in silicon, such as heralded initialization and calibration via gate set tomography (GST) [1-3], to reduce all relevant errors and push the fidelities of the full 2-qubit gate set above 99%. We demonstrate a 97.17% Bell state fidelity without correcting for readout errors and violate Bell's inequality with a Bell signal of S = 2.731 close to the theoretical maximum of 2√2. Our measurements exceed the classical limit even at elevated temperatures of 1.1 K or entanglement lifetimes of 100 μs. The demonstration of a violation of Bell’s inequality is a major milestone for every qubit platform, as it requires high fidelity across all metrices, including readout.

[1] R. Blume-Kohout et al., Nat. Comm. 8, 14485 (2016)

[2] E. Nielsen et al., Quantum 5, 557 (2021)

[3] T. Tanttu, et al., Nat. Phys. (2024)