Experimental Demonstration of the Harrow-Hassidim-Lloyd Algorithm on a 4-Qubit Spin Register in Silicon

Spin qubits in silicon have rapidly advanced in recent years, moving from a single-qubit testbed to small multi-qubit processors. However, demonstrations of small-scale quantum algorithms have been limited to three qubits in part due to the limited qubit connectivity in spin qubit processors. Spin registers hosted by phosphorus atoms in silicon natively support all-to-all connectivity and have recently demonstrated single- and two-qubit gate fidelities above 99 % [1]. Here, we implement the 4-qubit HHL algorithm [2] on a spin register in silicon. We explore two versions of the algorithm: a simplified version in which key states are directly encoded into the circuit, and a complete version where all subroutines are fully implemented. We characterize both versions using quantum process tomography and achieve fidelities of 93.4(5) % and 89.1(5) %, respectively. The slight reduction in fidelity emphasizes the benefits of running quantum algorithms on a highly interconnected platform. The ongoing development of exchange-based electron gates between spin registers [3] will enable further extensions to the full HHL algorithm in the future.

[1] Thorvaldson et.al., arXiv:2404.08741 (2024)

[2] Harrow et al., PRL, 103 (2009) 150502

[3] He et al., Nature, 571 (2019) 371-375