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THE OSCILLATOR
A circuit that rings
LC circuit
Energy swaps between the capacitor and the inductor.
f = 1/(2π√(LC))
Nanohenries and femtofarads give gigahertz.
Equal steps
Its quantum energy levels are evenly spaced.
An LC circuit is a quantum oscillator, but not yet a qubit.
ANHARMONICITY
Make the steps uneven
The problem
With equal steps, a pulse climbs the whole ladder.
The junction
Swap the coil for a junction and the upper steps shrink.
Transmon
An anharmonicity of about −200 to −300 MHz.
Uneven steps let us use just the bottom two levels.
CHARGE NOISE
From Cooper-pair box to transmon
Cooper-pair box
1999: the first superconducting qubit, very charge sensitive.
Big capacitor
Raises EJ/EC to about 50.
Transmon
2007: charge noise all but disappears.
One design change made superconducting qubits practical.
DESIGN
Design a 5 GHz transmon
EC
Set by the size of the capacitor pads.
EJ
Set by the junction.
The formula
f01 ≈ √(8EJEC) − EC.
Fabrication's job is to build exactly these two numbers.
VARIATIONS
The transmon family
Pads and crosses
Different shapes, same physics.
Tunable
A SQUID lets the frequency move.
3D
A transmon in a metal box lives longer, but scales poorly.
Most of today's superconducting processors use transmons.
UNIT 18 STUDY COMPLETE
🔁
Ready for the Fab Challenge?
You've rung an LC circuit, made its energy steps uneven, tamed charge noise and designed your own transmon.