Fig. 4
Hidden Shift (HS) algorithm implementation on 10 qubits. a Shows a textbook implementation of the HS algorithm with hidden shift 1111101010. The circuit for each oracle was measured at least 50 times. We trace out the spectator ion and interpret the binary output state of the 10-qubit register as an integer. The full output distribution is shown in b. c Shows the probability of detecting the encoded shift s for each of the 1024 oracle implementations versus the number of single-qubit gates (m). The shaded area represents the expected fidelity \({{\mathcal{F}}}_{\,\text{2Q}\,}^{10}{{\mathcal{F}}}_{\,\text{1Q}}^{\text{m}\,}{{\mathcal{F}}}_{\,\text{SPAM}\,}^{10}\) (where \({{\mathcal{F}}}_{\text{2Q}}\) is the fidelity of two-qubit gates, \({{\mathcal{F}}}_{\text{1Q}}\) is the fidelity of single-qubit gates, and \({{\mathcal{F}}}_{\text{SPAM}}\) is the average SPAM fidelity) if all of our gates share the best measured fidelity or, alternatively, all share the worst fidelity. Additionally, the success probability is reduced by crosstalk onto adjacent ions from the individually addressing Raman beams. This error impacts the result of the HS oracles more than the BV oracles. The result of a shared average fidelity is plotted as a dashed line. The average probability of success is 35\(\%\), and 1017 of the 1024 oracle implementations correctly return the hidden shift as the maximal probability state.
