Fig. 3: Results for implementation of Grover’s algorithm in a d = 5 qudit.

a Density matrices reconstructed from state tomography of the qudit after each step of the algorithm. The qudit is initialized in the \(\left|0\right\rangle\) state, followed by the preparation of the equal superposition state, the oracle operation that marks the \(\left|2\right\rangle\) state, and the reflection operation that amplifies the amplitude of the marked state. The size (color) of the square blocks represents the magnitude (phase) of the corresponding entry of the density matrix. b Result of performing Grover’s search, with oracles that mark each qudit state, after one round of oracle-reflection operation. The measurement results are represented by the number within each block. The theoretically achievable fidelity is 96.8% and the average fidelity of the experiment is 96.8(3)%, where the error represents one standard deviation. The average SSO is 99.9(1)% and the highest possible SSO is 100%. c The success probability of the algorithm versus the number of repetitions N of the oracle-reflection operations. The yellow and blue markers represent the highest possible fidelity and the experimental result, respectively. The blue solid line represents a linear fit to the data points and the success probability per iteration is determined to be 99.28(2)%. The light-blue shaded region represents the expected fidelity determined from a master-equation-based simulation and the measured coherence time (see Supplementary Information for coherence time measurements).