[Paper Review] Experimental implementation of universal holonomic quantum computation on solid-state spins with optimal control

Dong Yang, Shao-Chun Zhang+8 more|arXiv (Cornell University)|Feb 18, 2021

Diamond and Carbon-based Materials Research61 references29 citations

TL;DR

This paper demonstrates a high-fidelity, universal set of holonomic quantum gates in a solid-state spin system using nitrogen-vacancy (NV) centers in diamond at room temperature. By implementing an optimized nonadiabatic holonomic quantum computation (NHQC+) scheme with tailored microwave pulse shaping, the authors achieve robust single- and two-qubit gates that are resilient to control errors and decoherence, marking a critical advance toward fault-tolerant geometric quantum computation.

ABSTRACT

Experimental realization of a universal set of quantum logic gates with high-fidelity is critical to quantum information processing, which is always challenging by inevitable interaction between the quantum system and environment. Geometric quantum computation is noise immune, and thus offers a robust way to enhance the control fidelity. Here, we experimentally implement the recently proposed extensible nonadiabatic holonomic quantum computation with solid spins in diamond at room-temperature, which maintains both flexibility and resilience against decoherence and system control errors. Compared with previous geometric method, the fidelities of a universal set of holonomic single-qubit and two-qubit quantum logic gates are improved in experiment. Therefore, this work makes an important step towards fault-tolerant scalable geometric quantum computation in realistic systems.

Motivation & Objective

• To achieve high-fidelity universal quantum logic gates in a solid-state spin system under realistic conditions.
• To overcome the limitations of adiabatic holonomic quantum computation, such as long gate times and susceptibility to decoherence.
• To implement and experimentally validate the recently proposed nonadiabatic holonomic quantum computation with optimal control (NHQC+) scheme for both single- and two-qubit gates.
• To demonstrate robustness against control parameter fluctuations and system decoherence in a scalable, room-temperature platform.

Proposed method

• The NHQC+ scheme is implemented using electron and nuclear spins in a diamond NV center, with the electron spin (S=1) serving as the qubit and the nitrogen nuclear spin (I=1) as a control ancilla.
• Microwave pulses with time-dependent amplitudes and phases are used to drive transitions between the ancillary state |a⟩ and the qubit states |0⟩ and |1⟩, forming a bright state |b⟩.
• The geometric phase is induced via a single-loop evolution path that encloses a solid angle on the Bloch sphere, with the phase evolution governed by the von Neumann equation and coupled differential equations for β and ϕ.
• Optimal control is applied by shaping the pulse envelope using f = η(2β − sin(2β)) and ϕ(t = 0) = 0, ϕ(τ/2) = γG, with η = 0.4 chosen to minimize error sensitivity.
• Dynamical decoupling is employed to suppress decoherence during two-qubit gate operations, particularly protecting the longer-lived nuclear spin.
• Quantum process tomography (QPT) with maximum likelihood estimation is used to reconstruct and verify the process fidelity of the implemented gates.

Experimental results

Research questions

• RQ1 Can a universal set of holonomic quantum gates be experimentally realized in a solid-state spin system at room temperature with high fidelity and robustness to control errors?
• RQ2 How does the NHQC+ scheme improve gate fidelity compared to conventional nonadiabatic holonomic schemes under realistic control imperfections?
• RQ3 What is the optimal pulse shape and control parameter (e.g., η) that balances gate speed, error resilience, and decoherence suppression in a nonadiabatic holonomic gate?
• RQ4 Can two-qubit holonomic gates be implemented in a solid-state system with high fidelity despite complex energy level structures and control challenges?
• RQ5 To what extent does optimal control enhance the robustness of geometric gates against amplitude fluctuations in experimental settings?

Key findings

• The experiment achieves a process fidelity of 97.2% for the holonomic X gate and 96.8% for the X/2 gate, significantly improving over conventional NHQC methods.
• The NHQC+ scheme demonstrates robustness against control amplitude errors, with fidelity remaining above 95% even under 10% amplitude variation.
• The optimal control parameter η = 0.4 was found to minimize systematic error sensitivity while maintaining short gate duration (τ ≈ 200 ns), balancing speed and fidelity.
• Two-qubit holonomic gates were successfully implemented using dynamical decoupling, achieving high fidelity despite the electron spin's shorter coherence time.
• Quantum process tomography confirmed that the reconstructed process matrices were positive-definite after maximum likelihood estimation, validating the gate operations.
• The results demonstrate that geometric quantum computation via NHQC+ is a viable path toward fault-tolerant, scalable quantum information processing in realistic, room-temperature solid-state systems.