Heralded fidelity-robust high-dimensional quantum computing

Abstract In high-dimensional quantum systems, qudits offer a richer resource than traditional two-dimensional qubits, increasing the capacity of quantum channels and enhancing the efficiency of fault-tolerant quantum computation. These advantages can be utilized to solve complex problems across various fields. In the paper, we propose a 2-qudit controlled-NOT (CNOT) gate in a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mn>4</mml:mn> <mml:mo>×</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:math> -dimensional space and a 3-qudit controlled-controlled-NOT (Toffoli) gate in a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mn>4</mml:mn> <mml:mo>×</mml:mo> <mml:mn>4</mml:mn> <mml:mo>×</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:math> -dimensional space, both equipped with error-heralded units. Our designs do not require auxiliary photons or extra negatively charged nitrogen-vacancy (NV − ) center, resulting in saving resources. Moreover, since the imperfect NV − -cavity interaction processes are predicted in real-time by sensitive single-photon detectors, both high-dimensional CNOT and Toffoli gates boast robust fidelities using existing technology. Furthermore, our protocols simplify circuits with error-heralded units, significantly contributing to the effectiveness of quantum information technology and paving the way for advanced high-dimensional quantum computing.