quantum gate directory
Sycamore
Symbol
$\mathrm{SYC}$
Qubits: $2$
Description:
Google's native two-qubit gate, the fSim gate at $\theta = \pi/2$, $\phi = \pi/6$.
Alternate notations:
- $\mathrm{SYC}$
- $\mathrm{fSim}(\pi/2, \pi/6)$
SDK Support
| 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 | — |
Groups
This gate is contained in the following groups:
Reference
Quantum supremacy using a programmable superconducting processor (2019)
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.
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