hardware natives 2 qubits
Echoed Cross-Resonance
A native two-qubit Clifford gate for cross-resonance hardware, locally equivalent to CNOT.
The echoed cross-resonance (ECR) gate is an entangling operation used on superconducting processors based on the cross-resonance interaction.
$$ ECR = \frac{1}{\sqrt{2}} \begin{pmatrix} 0 & 1 & 0 & i \\ 1 & 0 & -i & 0 \\ 0 & i & 0 & 1 \\ -i & 0 & 1 & 0 \end{pmatrix} $$
Properties
- Clifford and entangling.
- Locally equivalent to CNOT via single-qubit Clifford gates.
- Implemented using echoed cross-resonance pulses.
Usage
- Native two-qubit gate on cross-resonance superconducting devices.
- Compiled to or from CNOT in Clifford circuits.
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 | qiskit.circuit.library.ECRGate |
| PennyLane | pennylane.ECR ⓘ |
| Cirq | — |
| Q# | — |
| PyQuil | — |
| Braket | braket.circuits.gates.ECR |
| BQSKit | bqskit.ir.gates.ECRGate |
| Qibo | qibo.gates.ECR ⓘ |
| pytket | pytket.circuit.OpType.ECR |
| Stim | — |
| OpenQASM | — |