Grover's algorithm in a four-qubit silicon processor above the fault-tolerant threshold.

Area of Science:

• Quantum Computing
• Solid-State Physics

Background:

• Silicon spin qubits are promising for quantum computation.
• Scaling up qubit count while maintaining high fidelity is a significant challenge.
• Previous work has been limited to two-qubit algorithms.

Purpose of the Study:

• To demonstrate a three-qubit Grover's search algorithm on a silicon quantum processor.
• To achieve high-fidelity quantum operations with an increased number of qubits.
• To explore the potential for scalable quantum computing using silicon spin qubits.

Main Methods:

• Utilized a four-qubit silicon processor with precision-patterned phosphorus atoms.
• Achieved single-qubit fidelities above 99.9% due to long coherence times.
• Implemented efficient single-pulse multi-qubit operations using electron-nuclear hyperfine interaction for controlled-Z gates.

Main Results:

• Successfully executed a three-qubit Grover's search algorithm with ~95% success probability.
• Demonstrated controlled-Z gates between all pairs of nuclear spins with fidelities above 99%.
• Created a three-qubit Greenberger-Horne-Zeilinger state with 96.2% fidelity.
• All control fidelities were above the fault-tolerant threshold.

Conclusions:

• High-fidelity quantum operations are achievable with an increased number of silicon spin qubits.
• The demonstrated processor architecture and control methods are suitable for executing multi-qubit algorithms.
• Coupling of nuclear spin registers via electron-electron exchange offers a path towards larger, fault-tolerant quantum processors.