Computing with spin qubits at the surface code error threshold (2107.00628v1)

Abstract: High-fidelity control of quantum bits is paramount for the reliable execution of quantum algorithms and for achieving fault-tolerance, the ability to correct errors faster than they occur. The central requirement for fault-tolerance is expressed in terms of an error threshold. Whereas the actual threshold depends on many details, a common target is the ~1% error threshold of the well-known surface code. Reaching two-qubit gate fidelities above 99% has been a long-standing major goal for semiconductor spin qubits. These qubits are well positioned for scaling as they can leverage advanced semiconductor technology. Here we report a spin-based quantum processor in silicon with single- and two-qubit gate fidelities all above 99.5%, extracted from gate set tomography. The average single-qubit gate fidelities remain above 99% when including crosstalk and idling errors on the neighboring qubit. Utilizing this high-fidelity gate set, we execute the demanding task of calculating molecular ground state energies using a variational quantum eigensolver algorithm. Now that the 99% barrier for the two-qubit gate fidelity has been surpassed, semiconductor qubits have gained credibility as a leading platform, not only for scaling but also for high-fidelity control.

• The paper demonstrates silicon-based spin qubits surpassing the 99% fidelity threshold required for effective surface code error correction.
• The research employs gate set tomography to meticulously characterize and optimize single- and two-qubit gates, achieving fidelities above 99.5%.
• The study utilizes a VQE algorithm to compute molecular hydrogen's ground state energy, underscoring the potential for scalable, fault-tolerant quantum computation.

Overview of "Computing with Spin Qubits at the Surface Code Error Threshold"

This paper presents a significant step in the development of quantum processors, demonstrating a silicon-based spin qubit system achieving gate fidelities surpassing the 99% threshold set by the surface code for fault-tolerant quantum computation. The research highlights the successful implementation of high-fidelity single- and two-qubit gates through advanced methods including gate set tomography (GST) for characterization and optimization.

The authors report that both single-qubit and two-qubit gate fidelities exceed 99.5%, with an average single-qubit fidelity above 99% even when accounting for crosstalk and idling errors. This accomplishment is crucial because maintaining fidelities above the surface code threshold can enhance the practical applicability of quantum algorithms on near-term quantum processors.

Numerical Results and Methodology

The reported gate fidelities are obtained through GST, which provides detailed insights into the error processes affecting the quantum gates, separating coherent Hamiltonian errors from stochastic errors. The use of GST allows the researchers to calibrate their quantum gates effectively, achieving an impressive overall fidelity for the quantum operations involved. This fine-tuned control is supplemented by meticulous engineering of the two-qubit interaction Hamiltonian and noise reduction techniques, such as isotopic enrichment to eliminate nuclear spins and sophisticated Hamiltonian engineering.

The paper employs a variational quantum eigensolver (VQE) algorithm to compute the ground state energy of molecular hydrogen, achieving an accuracy within 20 milliHartree. This result demonstrates the practical applicability of the spin qubit system in performing quantum chemistry calculations, a key domain where quantum computers have potential significant advantages over classical counterparts.

Implications and Future Outlook

The findings establish semiconductor spin qubits as a strong candidate for scalable quantum computing, not only for their high gate fidelities but also for their compatibility with existing semiconductor manufacturing processes. The demonstrated results suggest that with further improvements in qubit readout fidelity and error reduction techniques, especially in addressing the crosstalk, semiconductor spin qubits could evolve towards fault-tolerant quantum computing systems.

From a theoretical perspective, the implications of achieving such high fidelities open up possibilities for exploring more complex quantum algorithms and systems in the NISQ (Noisy Intermediate-Scale Quantum) era. Practically, integrating these advances with existing technologies paves the way for developing more robust quantum processors capable of addressing real-world problems beyond simple quantum chemistry simulations.

Future research could focus on enhancing the integration of these high-fidelity gates within larger qubit architectures, possibly incorporating more sophisticated quantum error correction schemes. Additionally, exploring the interplay between different quantum platforms and harnessing the advantages of each could yield synergistic benefits as the field moves towards practical, large-scale quantum computing deployments.