Generating families of three-qubit gates from simultaneous two-qubit gates, part 1: theory

Decoherence of qubits limits near-term quantum computers to only run low-depth quantum circuits with acceptable fidelity. This severely restricts what quantum algorithms can be compiled and implemented on such devices. One way to overcome these limitations is to expand the available gate set from single- and two-qubit gates to multi-qubit gates, which entangle three or more qubits in a single step. Here, we show that such multi-qubit gates can be realized by the simultaneous application of multiple two-qubit gates to a group of qubits where at least one qubit is involved in two or more of the two-qubit gates. Multi-qubit gates implemented in this way are as fast as, and often even faster than, the constituent two-qubit gate operations. Importantly, these multi-qubit gates are ready to be used in current quantum-computing platforms without any modification of the quantum processor. We demonstrate this idea for two specific cases: simultaneous controlled-Z gates and simultaneous iSWAP gates. We show how the resulting multi-qubit gates relate to other well-known multi-qubit gates and simulate gate fidelities well above 99%.