What is the difference between transmon and Xmon qubits?

Question

Transmon and Xmon qubits are two types of superconducting charge qubits that seem to be often used in superconducting quantum devices. However, I wasn't able to easily find direct comparisons between them. The Xmon architecture seems (1304.2322) to have been introduced by Martinis' group, as an alternative to the transmon qubit, so I would expect the former architecture to be better in at least some respects. On the other hand, it also seems (cond-mat/0703002 and 0712.3581 seem to be the relevant references) that the devices from IBM use transmon qubits.

What are the main differences between the two, from a practical point of view (in other words, when and why does one prefer one over the other)?

Answer 1

The transmon is a Josephson junction and capacitor in parallel. Originally, transmons were differential circuits, i.e. two transmons on the same chip were not galvanically connected in any way. In other words, transmons didn't share a ground reference. Furthermore, in the early days, transmons were almost always embedded into the middle of a harmonic resonator. The resonator, often referred to as a "bus resonator", was used to couple multiple qubits together, i.e. qubits embedded in the same resonator could couple to each other.

The important differences with the xmon were that

1. The xmon was grounded. Each xmon on a chip connects to a common ground plane with a nominally fixed voltage.

2. The xmon was not embedded into a resonator. Instead of coupling through a resonator, each xmon couples through a direct capacitance to each of its neighbors.

Nowadays, several research groups build qubits without the bus resonator and call them "transmons".

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Much more could be written. If someone leaves a comment asking for more details on any particular aspect of the difference between transmon and xmon, I will write more.

History of the name

Rob Schoelkopf told me the story of where the name "transmon" came from while we were at the Les Houches summer school on "Quantum Machines". The charge qubit suffered from low frequency noisey charge fluctuations that lead to dephasing. To get around the problem, Professor Schoelkopf thought to shunt the junction with a bit of transmission line. The line would be a short circuit at dc, allowing low frequency charge to equalize, but it would be a high impedance at the qubit's resonance frequency allowing the resonance to remain. The combination of a transmission line with the junction plasmon mode lead to the name "transmon".

In the end, it turned out that a capacitor was simpler than a transmission line and served a purpose equivalent to the transmission line, so the qubit wound up being a capacitor in parallel with the junction. However, the name "transmon" had already stuck (or maybe "capmon" just didn't sound as good).

Answer 2

In one sense, the Xmon qubit is a transmon qubit, in that they both operate in the $E_J>>E_c$ regime of the CPB Hamiltonian and take advantage of the exponentially suppressed charge noise vs. polynomial decrease in anharmonicity effect discussed in (Koch, 2007). You could work out the dynamics of a superconducting qubit-resonator system without ever knowing whether the equations were describing an Xmon or a transmon, so functionally its hard to differentiate the Xmon.

On the other hand, there are a lot of important design differences introduced in the Xmon: The qubit is grounded (mentioned above), the qubit is no longer embedded in the resonator, its conveniently tunable, the lifetime is enhanced (although the ibmqx3 chip that IBM uses for its quantum experience has qubits with $T_1\approx40 \space \mu s$ which matches the original Xmon lifetime). Also, the Xmon's shape is a great match for a surface code architecture that requires a tight-packed grid of qubits.

Practically, there are a lot of other transmon designs that offer some of the same benefits of the Xmon. So "transmon vs. Xmon" isn't the general question to ask; just go with the design that's got the best lifetimes and maybe tunability.