SCIENCE CHINA Information Sciences, Volume 62, Issue 7: 072502(2019) https://doi.org/10.1007/s11432-018-9703-y

## Distinguishing unitary gates on the IBM quantum processor

• ReceivedJul 10, 2018
• AcceptedNov 21, 2018
• PublishedApr 18, 2019
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### Abstract

An unknown unitary gate, which is secretly chosen from several known ones, can always be distinguished perfectly. In this paper, we implement such a task on IBM's quantum processor. More precisely, we experimentally demonstrate the discrimination of two qubit unitary gates, the identity gate and the $\frac{2}{3}\pi$-phase shift gate, using two discrimination schemes — the parallel scheme and the sequential scheme. We program these two schemes on the ibmqx4, a $5$-qubit superconducting quantum processor via IBM cloud, with the help of the QSI modules. We report that both discrimination schemes achieve success probabilities at least 85%.

### Acknowledgment

This work was supported by National Natural Science Foundation of China (Grant Nos. 61672007, 11647140) and ERC Consolidator (Grant No. 615307-QPROGRESS). The authors were grateful to the use of the IBM Q experience, and acknowledge IBM Q community for their helpful discussions. The views expressed are those of the authors and do not reflect the official policy or position of IBM or the IBM Q experience team.

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• Figure 1

Parallel and sequential discrimination schemes. (a) The parallel scheme to distinguish the unknown operation $\mathcal{O}\in\{R_{\frac{2}{3}\pi},I\}$, where $U_p$ and $U_m$ indicate the state preparation and measurement circuits; (b) the sequential scheme to distinguish the unknown operation $\mathcal{O}\in\{R_{\frac{2}{3}\pi},I\}$, where $U_p$ and $U_m$ indicate the state preparation and measurement circuits.

• Figure 4

Statistical results in the parallel discrimination experiments. (a) Perform the circuit in Figure 1(a) by replacing $\mathcal{O}$ by $R_{\frac{2}{3}\pi}$ for 1024 times. After sorting the outputs, $834$ round outputs are either $01$ or $10$ (indicating $\mathcal{O}$ is $R_{\frac{2}{3}\pi}$), and $190$ round outputs are either $00$ or $11$ or other results (indicating $\mathcal{O}$ is not $R_{\frac{2}{3}\pi}$); (b) Perform the circuit in Figure 1(a) by replacing $\mathcal{O}$ by $I$ for 1024 times. After sorting the outputs, $875$ round outputs are either $00$ or $11$ (indicating $\mathcal{O}$ is $I$), and $149$ round outputs are either $01$ or $10$ or other results (indicating $\mathcal{O}$ is not $I$).

• Figure 5

Statistical results in the sequential discrimination experiments. (a) Perform the circuit in Figure 1(b) by replacing $\mathcal{O}$ by $R_{\frac{2}{3}\pi}$ for $1024$ times. After sorting the outputs, $857$ round outputs are $0$ (indicating $\mathcal{O}$ is $R_{\frac{2}{3}\pi}$), and $167$ round outputs are either $1$ or other results (indicating $\mathcal{O}$ is not $R_{\frac{2}{3}\pi}$); (b) Perform the circuit in Figure 1(b) by replacing $\mathcal{O}$ by $I$ for $1024$ times. After sorting the outputs, $1007$ round outputs are $1$ (indicating $\mathcal{O}$ is $I$), and $17$ round outputs are either $1$ or other results (indicating $\mathcal{O}$ is not $I$).

• Figure 6

(Color online) The discrimination success probability distributions for both sequential and parallel discrimination. For each round in each scheme, $R_{\frac{2}{3}\pi}$ or $I$ is chosen depending on a random coin-flip result. For each scheme, we execute the experiment for $10$ randomly chosen $\mathcal{O}$. In each box, the central mark indicates the median ($97%$ and $89%$ respectively), and the top and the bottom indicate the $75%$ and $25%$, respectively.

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