Single Shot i-Toffoli Gate in Dispersively Coupled Superconducting Qubits*

Quantum algorithms often benefit from the ability to execute multi-qubit (>2) gates. To date such multi-qubit  gates are typically decomposed into single- and two-qubit gates, particularly in superconducting qubit architectures. The ability to perform multi-qubit operations in a single step could vastly improve the fidelity and execution time of many algorithms.

Here, we propose a single shot method for executing an i-Toffoli gate (a Toffoli gate combined with a contolled phase gate) using currently existing superconducting hardware. We show numerical evidence for an average gate fidelity over 97% (process fidelity over 98%) and a gate time of 500 ns for superconducting qubits interacting via tunable couplers. Whereas a Toffoli gate is a controlled-controlled-not gate on three qubits, our method can be extended to implement gates with more than two control qubits and to detect qubit cluster parity.