Grover’s algorithm in a four-qubit silicon processor above the fault-tolerant threshold
Ian Thorvaldson, D. Poulos, Christian M. Moehle, S. H. Misha, Hermann Edlbauer, J. Reiner, Hao Geng, B. Voisin, Michael T. Jones, M. B. Donnelly, Luis Fabián Peña, Charles D. Hill, Casey R. Myers, J. G. Keizer, Yousun Chung, S. K. Gorman, Ludwik Kranz, M. Y. Simmons
Abstract
Spin qubits in silicon are strong contenders for the realization of a practical quantum computer, having demonstrated single- and two-qubit gates with fidelities above the fault-tolerant threshold, and entanglement of three qubits. However, maintaining high-fidelity operations while increasing the qubit count remains challenging and therefore only two-qubit algorithms have been executed. Here we utilize a four-qubit silicon processor with all control fidelities above the fault-tolerant threshold and demonstrate a three-qubit Grover's search algorithm with a ~95% probability of finding the marked state. Our processor is made of three phosphorus atoms precision-patterned into isotopically pure silicon, which localise one electron. The long coherence times of the qubits enable single-qubit fidelities above 99.9% for all qubits. Moreover, the efficient single-pulse multi-qubit operations enabled by the electron-nuclear hyperfine interaction facilitate controlled-Z gates between all pairs of nuclear spins with fidelities above 99% when using the electron as an ancilla. These control fidelities, combined with high-fidelity non-demolition readout of all nuclear spins, allow the creation of a three-qubit Greenberger-Horne-Zeilinger state with 96.2% fidelity. Looking ahead, coupling neighbouring nuclear spin registers, as the one shown here, via electron-electron exchange may enable larger, fault-tolerant quantum processors.