Superconducting Qubits
How IBM, Google, and most industry players build physical qubits
By the end of this topic you'll be able to
A superconducting LC circuit — an inductor and a capacitor wired together — behaves quantum mechanically at sufficiently low temperatures, but its energy levels come out evenly spaced, exactly like a quantum harmonic oscillator.
That even spacing is a real obstacle to building a qubit from it: a microwave pulse tuned to drive the transition between the lowest two levels drives the transition from the second to the third level equally well, since both transitions have the identical energy gap.
What's needed is anharmonicity — unevenly spaced energy levels — so that a control pulse tuned to the 0-to-1 transition doesn't also excite unwanted transitions to higher levels.
The Josephson junction, a thin insulating barrier separating two superconductors, supplies exactly this: it behaves as a nonlinear inductor, and swapping it in for the ordinary inductor breaks the even spacing, isolating a usable two-level qubit subspace from the higher, unwanted levels above it.
Short dephasing times were, in Koch et al.'s own framing, one of the main obstacles to a working superconducting qubit; their 2007 paper introduced the transmon specifically to address it, by operating the circuit in a regime of significantly increased ratio of Josephson energy to charging energy, Ej/Ec.
Because the transmon's charge dispersion falls off exponentially with Ej/Ec while its anharmonicity only degrades by a weak power law, the design trades a modest amount of anharmonicity for a dramatic reduction in sensitivity to stray charge noise — an engineering tradeoff that has proven decisive, and the transmon (or a close variant of it) now underlies the large majority of industrial superconducting quantum processors.
Control and readout both operate through microwave engineering: gates are implemented with carefully shaped microwave pulses at the qubit's transition frequency, and readout is performed dispersively, by coupling the qubit to a microwave resonator whose frequency shifts slightly depending on the qubit's state.
Because Josephson junctions lose their special superconducting behavior above roughly 1 Kelvin, superconducting quantum processors have to run inside dilution refrigerators that cool the chip to a few millikelvin — reliably colder than deep space.
Try It Yourself
A transmon qubit has T1 = 100 μs. A two-qubit gate takes 200 ns to execute. Using the small-time approximation P(decay error) ≈ t/T1, estimate the probability that a T1-decay error occurs during a single gate.
- 1Convert to consistent units: T1 = 100 μs, gate time t = 200 ns = 0.2 μs.
- 2Compute the ratio: t/T1 = 0.2/100 = 0.002.
- 3This approximation comes from the exact decay probability 1 − e^{-t/T1}, which for t ≪ T1 is well approximated by its first-order Taylor term, t/T1 (the same small-angle-style approximation used throughout physics for small exponents).
- 4So P(decay error) ≈ 0.002, or about 0.2% per gate.
About a 0.2% chance of a T1-decay error per two-qubit gate — illustrating concretely why T1 needs to be orders of magnitude longer than gate time for a device to run many gates reliably in sequence.
Reference
| Josephson junction | Provides the anharmonicity needed to isolate a 2-level qubit | |
| Transmon qubit | Charge-noise-insensitive design, dominant in industry | |
| Dispersive readout | Measures qubit state via a coupled microwave resonator | |
| Operating temperature | Requires a dilution refrigerator |
Quick Check
Why can't you make a usable qubit from a plain superconducting LC circuit alone?
What does the transmon design specifically improve compared to earlier superconducting qubit designs?