Precision tomography of a three-qubit donor quantum processor in silicon (2106.03082v3)

Abstract: Nuclear spins were among the first physical platforms to be considered for quantum information processing, because of their exceptional quantum coherence and atomic-scale footprint. However, their full potential for quantum computing has not yet been realized, due to the lack of methods to link nuclear qubits within a scalable device combined with multi-qubit operations with sufficient fidelity to sustain fault-tolerant quantum computation. Here we demonstrate universal quantum logic operations using a pair of ion-implanted 31P donor nuclei in a silicon nanoelectronic device. A nuclear two-qubit controlled-Z gate is obtained by imparting a geometric phase to a shared electron spin, and used to prepare entangled Bell states with fidelities up to 94.2(2.7)%. The quantum operations are precisely characterised using gate set tomography (GST), yielding one-qubit average gate fidelities up to 99.95(2)%, two-qubit average gate fidelity of 99.37(11)% and two-qubit preparation/measurement fidelities of 98.95(4)%. These three metrics indicate that nuclear spins in silicon are approaching the performance demanded in fault-tolerant quantum processors. We then demonstrate entanglement between the two nuclei and the shared electron by producing a Greenberger-Horne-Zeilinger three-qubit state with 92.5(1.0)% fidelity. Since electron spin qubits in semiconductors can be further coupled to other electrons or physically shuttled across different locations, these results establish a viable route for scalable quantum information processing using donor nuclear and electron spins.

An Examination of Precision Tomography on a Silicon-Based Three-Qubit Quantum Processor

The paper presents significant advances in quantum computing by demonstrating precision tomography in a silicon-based quantum system. This research applies donor nuclear and electron spins to engineer a three-qubit quantum processor, showcasing promising fidelity metrics crucial for fault-tolerant quantum computing.

Research Overview

The study explores the use of phosphorus ($^{31}$P) donor nuclei coupled with electron spins in silicon, a system attractive for quantum processors due to silicon's mature fabrication technology and these qubits' excellent coherence properties. A key achievement is the implementation of a two-qubit controlled-Z (CZ) gate via a geometric phase on a shared electron spin, resulting in Bell state entanglements with fidelities up to 94.2%. The research further demonstrates quantum operations characterized using Gate Set Tomography (GST), yielding average gate fidelities of 99.95% for one-qubit operations and 99.37% for two-qubit operations, underscoring the technique for precise error diagnostics in quantum gates.

Key Results and Implications

Measurement results, notably the impressive gate fidelities, are approaching the thresholds required for fault-tolerant computation. This reinforces the feasibility of nuclear spins in silicon as a scalable and reliable platform for quantum information processing. Furthermore, the creation of a three-qubit Greenberger-Horne-Zeilinger (GHZ) state with a fidelity of 92.5% illustrates the potential of integrating additional electron qubits for scalable architectures. The unique use of electron-nuclear coupling and their manipulation via geometric phases provides a pathway for diverse quantum operations necessary for practical quantum technologies.

Analytical Techniques and Error Characterization

The use of GST stands out for its ability to isolate stochastic from coherent errors and further, separate those affecting target qubits from crosstalk impacting spectator qubits. This nuanced characterization enabled the detection of coherent entangling errors during single-qubit operations, attributed to unintended accumulations of geometric phases by the electron spin. Such insights were facilitated by GST, thus establishing it as a powerful tool for diagnostic error analysis which is essential for the realization of fault-tolerant systems.

Future Prospects

The findings suggest a route towards a scalable quantum processor architecture. Expanding the framework includes exploring group-V elements with higher nuclear spins for enhanced operations and error correction capabilities. Additionally, coupling with electron qubits through interactions such as exchange or coherent transport presents a viable approach to scaling the number of qubits.

Conclusions

This paper provides a rigorous examination of silicon-based quantum processors using donor nuclear and electron spins, revealing promising results in terms of gate fidelities and error diagnostics. It lays a foundation for future developments in building robust quantum technologies by advocating scalable designs that leverage the coherence and fidelity strengths of nuclear spins in silicon, integrated with the flexibility of electron spin controls. The research indicates an encouraging horizon for quantum computing architectures capable of meeting fault-tolerant standards, paving the way for practical quantum computation.