Native Gate Set

A native gate set is the collection of quantum gates that a specific quantum processor can directly execute in hardware. Every quantum circuit written using arbitrary gates must be decomposed (transpiled) into this set before it can run on the device. The choice of native gate set is determined by the physics of the qubit platform and the control electronics.

Common native gate sets

Different hardware vendors use different native gates based on the interactions naturally available in their systems:

Platform	Native gates	Notes
IBM (superconducting)	$\sqrt{X}$, $R_z$, CX	CX via cross-resonance interaction
Google (superconducting)	$\sqrt{X}$, $R_z$, $\sqrt{\text{iSWAP}}$, CZ	Tunable couplers enable multiple two-qubit gates
IonQ (trapped ion)	$R_x$, $R_y$, $R_z$, XX (Molmer-Sorensen)	All-to-all connectivity
Quantinuum (trapped ion)	$R_z$, $R_y$, ZZ	High-fidelity gates with full connectivity
Rigetti (superconducting)	$R_x$, $R_z$, CZ	CZ via parametric coupling

The single-qubit gates are typically rotations (members of the rotation gates family), because any single-qubit unitary can be decomposed into at most three rotation gates via the Euler decomposition:

$U = R_z(\alpha) R_y(\beta) R_z(\gamma)$

or equivalently using $R_z$ and $\sqrt{X}$ combinations.

Universality

A gate set is universal if any unitary operation can be approximated to arbitrary precision using a finite sequence of gates from the set. For universality, a gate set needs:

1. A set of single-qubit gates that can reach any point on the Bloch sphere
2. At least one entangling two-qubit gate

All the native gate sets listed above are universal. The Solovay-Kitaev theorem guarantees that any single-qubit gate can be approximated to precision $\epsilon$ using $O(\log^c(1/\epsilon))$ gates from a finite universal set, where $c \approx 3.97$ (improvable with better decomposition algorithms).

Gate decomposition costs

The choice of native gate set affects how many physical operations are needed to implement a given logical gate. For example:

• A Toffoli gate decomposes into 6 CX gates and 9 single-qubit gates in the IBM native set
• A SWAP gate requires 3 CX gates
• A Hadamard gate requires 2 $R_z$ gates and 1 $\sqrt{X}$ gate in the IBM native set

Since two-qubit gates have much higher error rates than single-qubit gates (typically 10x worse), the two-qubit gate count after decomposition is the primary cost metric.

Why it matters for learners

Understanding native gate sets explains why the same abstract circuit performs differently on different hardware backends. It also clarifies why transpilation is necessary and why some algorithms are better suited to certain platforms. When comparing hardware specifications, the native gate set and its associated fidelities are among the most important characteristics.

See also

• Transpilation
• Quantum Gate
• Rotation Gates
• CNOT Gate
• iSWAP Gate