https://doi.org/10.1140/epjqt/s40507-025-00398-3
Research
Robust-fidelity high-dimensional controlled-controlled-SUM gate with qudits
1
State key Laboratory of Extreme Environment Optoelectronic Dynamic Testing Technology and Instrument, North University of China, 030051, Taiyuan, Shanxi, China
2
Key Laboratory of Micr/onano Devices and Systems Ministry of Education, North University of China, 030051, Taiyuan, Shanxi, China
3
Beijing National Research Center for Information Science and Technology, Department of Electronic Engineering, Tsinghua University, 100084, Beijing, China
a
Duff@nuc.edu.cn
b
20240039@nuc.edu.cn
Received:
27
May
2025
Accepted:
28
July
2025
Published online:
6
August
2025
High-dimensional (HD) quantum systems are capable of processing more complex information and performing a wider array of quantum operations, in contrast to low-dimensional (LD) quantum systems, thereby improving the speed and fault tolerance of quantum computing. In the study, we propose a deterministic qudit-encoded 
-dimensional (64D) controlled-controlled-SUM (CCSUM) gate based on weak Kerr effect. The 64D CCSUM gate leverages the polarization and spatial degrees of freedom (DoFs) of three photons to encode 4D control and target qudits, thereby optimizing quantum resources and reducing costs. Moreover, the HD CCSUM gate functionality is implemented in a deterministic way by employing the X-Homodyne detector to measure coherent states, combined with related classical feed-forward operations. Through detailed analyses, the proposed HD CCSUM gate, under current technological conditions, exhibits robust fidelity and feasibility, offering a promising path toward the realization of HD quantum computing.
Key words: High dimension / Quantum gate / Quantum computing / Weak Kerr effect
© The Author(s) 2025
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