__A universal quantum gate set for transmon qubits with strong ZZ interactions__

**Published: **March 23, 2021 (arXiv)

**Authors:**
*Junling Long,
Tongyu Zhao,
Mustafa Bal,
Ruichen Zhao,
Samantha V. Barron,
Hsiang-sheng Ku,
Joel A. Howard,
Xian Wu,
Corey Rae H. McRae,
Xiu-Hao Deng,
Guilhem J. Ribeill,
Meenakshi Singh,
Thomas A. Ohki,
Edwin Barnes,
Sophia E. Economou,
David P. Pappas,*

**Abstract:**

High-fidelity single- and two-qubit gates are essential building blocks for a fault-tolerant quantum computer. While there has been much progress in suppressing single-qubit gate errors in superconducting qubit systems, two-qubit gates still suffer from error rates that are orders of magnitude higher. One limiting factor is the residual ZZ-interaction, which originates from a coupling between computational states and higher-energy states. While this interaction is usually viewed as a nuisance, here we experimentally demonstrate that it can be exploited to produce a universal set of fast single- and two-qubit entangling gates in a coupled transmon qubit system. To implement arbitrary single-qubit rotations, we design a new protocol called the two-axis gate that is based on a three-part composite pulse. It rotates a single qubit independently of the state of the other qubit despite the strong ZZ-coupling. We achieve single-qubit gate fidelities as high as 99.1% from randomized benchmarking measurements. We then demonstrate both a CZ gate and a CNOT gate. Because the system has a strong ZZ-interaction, a CZ gate can be achieved by letting the system freely evolve for a gate time tg=53.8 ns. To design the CNOT gate, we utilize an analytical microwave pulse shape based on the SWIPHT protocol for realizing fast, low-leakage gates. We obtain fidelities of 94.6% and 97.8% for the CNOT and CZ gates respectively from quantum progress tomography.

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