hardware natives 2 qubits
Sycamore
Google's native two-qubit gate, the fSim gate at $\theta = \pi/2$, $\phi = \pi/6$.
The Sycamore gate is the native entangling gate of Google's Sycamore processor, used in the 2019 quantum-supremacy experiment. It is the FSim gate at the specific angles $\theta = \pi/2$, $\phi = \pi/6$.
$$ \mathrm{SYC} = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 0 & -i & 0 \\ 0 & -i & 0 & 0 \\ 0 & 0 & 0 & \mathrm{e}^{-i\pi/6} \end{bmatrix} $$
Properties
- Excitation-preserving: on the single-excitation subspace it acts as a full iSWAP-style exchange (with phase $-i$ rather than iSWAP's $+i$), and it adds a $-\pi/6$ phase on $|11\rangle$ from the dispersive interaction.
- The $|11\rangle$ phase makes it not Clifford, unlike iSWAP.
- A CZ — and hence a CNOT, up to Hadamards — compiles into two Sycamore gates plus single-qubit rotations; a SWAP takes three.
Usage
- Chosen for hardware reasons: both the exchange ($\theta$) and dispersive ($\phi$) couplings are turned on simultaneously, giving the fastest high-fidelity gate the hardware supports rather than the cleanest algebraic form.
The unitary, drawn
Every entry of the matrix as a disc. The area is the transition probability $|U_{jk}|^2$; the colour and the hand are the phase. Rows are outputs $\langle j|$, columns inputs $|k\rangle$, in the computational basis.
Phase
Disc area $= |U_{jk}|^2$. Hover an entry for its value, or take the JSON.
Weyl chamber
Where this gate sits among all two-qubit gates, up to single-qubit rotations before and after.
Coordinates:
not entangling entangling perfect entangler
$(a, b, c)$ means the gate equals $e^{i(a\,XX + b\,YY + c\,ZZ)}$ up to single-qubit gates, reduced to the chamber $\pi/4 \ge a \ge b \ge |c|$ (the convention of the canonical gate, Qiskit and Cirq). The $a = \pi/4$ face is a mirror: $(\pi/4, b, c)$ and $(\pi/4, b, -c)$ are the same gate. Drag the figure to rotate it, double-click to reset.
SDK support
How to call this gate in each framework. Hover a ⓘ for a note; the support matrix compares every gate at once.
| SDK | Name |
|---|---|
| Qiskit | — |
| PennyLane | — |
| Cirq | cirq_google.SYC |
| Q# | — |
| PyQuil | — ⓘ |
| Braket | — |
| BQSKit | bqskit.ir.gates.SycamoreGate |
| Qibo | qibo.gates.SYC ⓘ |
| pytket | pytket.circuit.OpType.Sycamore ⓘ |
| Stim | — |
| OpenQASM | — |