Hardware-Native Gates

Learn how high-level gates are compiled to hardware-native operations.

Hardware-Native Gates

Why Native Gates Matter

Every quantum computer has a native gate set: the operations that can be directly applied to physical qubits without further decomposition. High-level gates like Hadamard (H), Toffoli (CCX), or arbitrary U3 rotations must be compiled into native gates before running on hardware.

Understanding native gates matters because:

1.Non-native gates introduce extra circuit depth after compilation
2.Some decompositions add noise-heavy two-qubit gates
3.Hardware-aware programming can eliminate compilation overhead

IBM Superconducting Native Gates

IBM's current quantum processors use the following native gate set:

Single-qubit gates:

•Rz( $θ$ ): Virtual Z rotation (zero noise: just a software phase update)
•SX ( $X$ ): Half-turn X rotation = Rx( $π /2$ )
•X: Full X rotation (equivalent to SX composed twice)

All single-qubit gates are physically implemented as a combination of Rz and SX. Since Rz is virtual, only SX and X require actual microwave pulses.

Two-qubit gate:

•CNOT (CX): The native two-qubit gate, implemented via cross-resonance driving

All other gates (H, Ry, Rz, CNOT, SWAP, Toffoli) compile into this set.

Hadamard Decomposition

The Hadamard gate is NOT native. Its decomposition:

H = Rz (π /2) SX Rz (π /2)

or equivalently (up to global phase):

H = Rz (π) SX Rz (π /2)

One H = 2 physical pulses (two SX gates equivalent) plus virtual Rz rotations. For a circuit with 100 Hadamard gates, the native gate count is 200 microwave pulses.

Google/Rigetti Native Gates

Google's Sycamore processor uses:

•SY ( $Y$ ): Half-turn Y rotation
•Rz( $θ$ ): Virtual Z rotation
•Fsim( $θ, ϕ$ ): Two-qubit fermionic simulation gate

The Fsim gate is more general than CNOT and can implement SWAP and iSWAP natively. This makes Google hardware particularly efficient for certain chemistry simulations.

Rigetti uses:

•Rx( $θ$ ) and Rz( $θ$ ): Arbitrary single-qubit rotations
•CZ: Controlled-Z (different from CNOT, but equally universal)

CNOT and CZ are interconvertible: CX(a,b) = H(b) CZ(a,b) H(b).

This is the opening of the lesson. The full walkthrough, the interactive circuit, and the graded challenge continue inside myqubit.

How this lesson works

A guided reading lesson with interactive knowledge checks. Concepts are explained step by step with circuit diagrams and runnable examples, and you confirm understanding before moving on.

Part of: Quantum Hardware & NISQ

Explore the physics of real quantum computers, understand noise, and learn near-term algorithms designed for today's noisy hardware.

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