Xmon

Figure

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.

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. This geometry was the key enabler for scaling to the 53-qubit Sycamore and 72-qubit Willow processors.

Experimental Status

First demonstration — Barends et al. (2013):

• Introduced the cross-shaped capacitor geometry for planar transmon qubits
• Demonstrated $T_1$ of 20–40 μs in the initial devices
• Showed compatibility with scalable 2D grid layouts

Surface code threshold — Barends et al. (2014):

• Demonstrated single-qubit gate fidelity of 99.92% and two-qubit gate fidelity of 99.4% via randomized benchmarking
• First superconducting qubit system to reach the surface code fault-tolerance threshold
• Five-qubit device with simultaneous high-fidelity single- and two-qubit gates

Quantum supremacy — Arute et al. (2019):

• 53-qubit Sycamore processor using Xmon qubits
• Average single-qubit gate fidelity 99.84%, average CZ fidelity 99.4%
• Completed a random circuit sampling task in 200 seconds that would take classical supercomputers ~10,000 years

Key Metrics

Metric	Value	Notes	Fidelity reference
$T_1$	20–100 μs	Planar geometry	Barends et al. 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	—

References

Original proposal / first demonstration

• R. Barends et al., “Coherent Josephson Qubit Suitable for Scalable Quantum Integrated Circuits,” Phys. Rev. Lett. 111, 080502 (2013) — arXiv:1304.2322

Experimental demonstrations

• R. Barends et al., “Superconducting quantum circuits at the surface code threshold for fault tolerance,” Nature 508, 500 (2014) — arXiv:1402.4848
• F. Arute et al., “Quantum supremacy using a programmable superconducting processor,” Nature 574, 505 (2019) — arXiv:1910.11333

Linked Papers

• barends-2013-xmon

Related Entries

• transmon — parent qubit type
• gmon — related Google qubit variant with tunable coupling
• circuit-qed — underlying hardware platform