Xmon

Description

The Xmon is a planar transmon variant developed by the Martinis group (later Google Quantum AI) featuring a cross-shaped capacitor geometry. Introduced by Barends et al. (2013), the ”+” shape provides four natural coupling points — one for readout and up to three for nearest-neighbor qubit-qubit coupling — enabling a scalable 2D grid layout.

The Xmon shares the same physics as the transmon ($E_J/E_C\gg 1$, charge-insensitive regime) but its geometry is optimized for multi-qubit integration. Each arm of the cross can capacitively couple to a bus resonator or neighboring Xmon, and the design minimizes spurious cross-talk. The qubit frequency is typically tunable via a SQUID loop (split junction), enabling parametric two-qubit gates (e.g., $i$SWAP or CZ via flux pulses).

The Xmon was the qubit used in Google’s Sycamore processor (2019 quantum supremacy demonstration) and subsequent Willow processor.

Figure

Hamiltonian

Identical to the transmon:

$H=4E_C(\hat{n}-n_g{)}^2-E_J({\Phi }_{\text{ext}})\cos \hat{\phi }$

For the tunable variant (asymmetric SQUID):

$E_J({\Phi }_{\text{ext}})=E_{J,\Sigma }\sqrt{{\cos }^2\left(\pi \frac{{\Phi }_{\text{ext}}}{{\Phi }_0}\right)+d^2{\sin }^2\left(\pi \frac{{\Phi }_{\text{ext}}}{{\Phi }_0}\right)}$

where $E_{J,\Sigma }=E_{J1}+E_{J2}$ and $d=(E_{J1}-E_{J2})/E_{J,\Sigma }$ is the junction asymmetry.

Motivation

Earlier transmon designs used coaxial or lumped-element capacitors that did not naturally tile into 2D arrays. The cross geometry solves the layout problem: it provides controllable coupling to 4 neighbors in a square lattice while maintaining low crosstalk and individual readout.

Key Metrics

Metric	Value	Notes	Fidelity reference
$T_1$	20–100 μs	Planar geometry	Barends 2013
1Q gate fidelity	99.84–99.9%+	Sycamore RB: 99.84% avg; Willow improved	Barends et al. 2014, Arute et al. 2019
2Q gate fidelity	99.4–99.9%	CZ or $i$SWAP via flux pulse; Sycamore 99.4% CZ avg	Barends et al. 2014, Arute et al. 2019
Anharmonicity	−200 to −250 MHz	Same as transmon	—
Transition frequency	4–7 GHz	Tunable via flux	—
Coupling to neighbors	4 (cross arms)	Square lattice layout	—
Operating temperature	10–20 mK	Dilution refrigerator	—

Linked Papers

• barends-2013-xmon

Related Entries

• transmon
• gmon
• circuit-qed