# The kept primer — quantum dots → transmon qubits *A walk-and-talk with Meta AI (2026), distilled. The lesson the architect kept restarting every walk, kept once. The six diagrams below are the originals from that conversation — AI-generated, napkin typos and all. See [PROVENANCE.md](PROVENANCE.md).* --- ## 1 · Quantum dots — the artificial atom A quantum dot is a tiny semiconductor crystal, ~2–10 nm wide — so small an electron can't stretch out; it gets **confined** in all three directions. That confinement makes the dot behave like an **artificial atom**: shrink it and it glows bluer, grow it and it glows redder. *Same material, different size = different colour.* That's why a QLED TV hits such saturated reds and greens — they're size-tuned dots, not filters. - **Displays you already own** — every commercial QLED is a blue LED shining through a film of photo-emissive dots. QD-OLED now reaches ~90% Rec.2020; micro-LED QD-COB shipped 2023–24. - **The IBM angle (future computing)** — IBM Research builds **arrays of quantum dots on silicon nanowires with cobalt gates** for *spin-qubit* control, with all-electrical control above 1 K. The dream: print millions of qubits in the same silicon fabs that make laptop chips. - **Quantum internet** — other labs got dots to emit ~40 million identical telecom photons/sec. - **Sensing & medicine** — bright, tunable dots in heavy-metal detectors, phone diagnostics, tumour-imaging probes. So dots aren't "the IBM thing" *today* — IBM's cloud machines run **transmons**. Dots are plan B for the far future. Transmons are plan A running now. --- ## 2 · The transmon qubit An **artificial atom made of superconducting metal**, not real atoms: - Cool a loop of aluminium (now often tantalum) to ~15 mK — colder than space — so electrons pair into **Cooper pairs** and flow with zero resistance. - Break the loop with a **Josephson junction** — two superconductors split by an atom-thin insulator. It acts as a *nonlinear inductor*. - The original 1990s "Cooper-pair box" was wrecked by stray charge noise in nanoseconds. The **transmon fix** (Yale/Sherbrooke, 2007): shunt the junction with a **big capacitor**. That pushes the Josephson energy far above the charging energy, so the levels become *approximately independent of offset charge* — it stops caring about charge noise. ![the transmon circuit — JJ, shunt capacitor, drive line, readout resonator](diagrams/transmon-circuit.jpg) > *JJ* (the X): the Josephson junction, the nonlinear heart · *C_shunt*: the big parallel > capacitor (the transmon trick) · *Drive line*: the microwave tap · *coplanar waveguide > resonator*: the "tail" that reads the state without touching it. The price of that big capacitor: **reduced anharmonicity** (~200 MHz between the |0⟩→|1⟩ and |1⟩→|2⟩ transitions), so control pulses must be cleverly shaped. Coherence: early planar chips lasted 30–40 µs; 3D cavities + tantalum now reach ~0.3 ms. Because it's just lithographed metal on silicon, you can print many and couple them with resonators — which is why transmons are the default qubit on **Google's Willow, IBM, Rigetti, IQM**. --- ## 3 · Flipping |0⟩ → |1⟩ — the π-pulse It's a slightly anharmonic oscillator. Hit it with a resonant microwave "ping" at the |0⟩→|1⟩ frequency (~5 GHz), shaped over ~20–40 ns. Leave the pulse on for **half a Rabi period — a π-pulse — and |0⟩ becomes |1⟩**. Half that (a π/2-pulse) gives the superposition (|0⟩+|1⟩)/√2. ![a π-pulse — the Gaussian microwave envelope in time](diagrams/pi-pulse.jpg) That bell curve is the *envelope*, not the fast 5 GHz carrier inside it. - **Shape:** Gaussian — gentle edges, so it doesn't spray noise into the |1⟩→|2⟩ transition. - **DRAG trick:** add a small out-of-phase bump (the *derivative* of the Gaussian) to cancel leakage, because transmons aren't perfectly two-level. - **Area = angle:** the integral under the curve sets the rotation. Like pushing a kid on a swing — one smooth push at the right frequency flips them over the top; push wrong and they wobble into higher modes (that's leakage). --- ## 4 · How two transmons talk — the bus resonator ![two transmons coupled through a shared bus resonator](diagrams/two-transmons-bus.jpg) They never touch. Q1 and Q2 both hang off a shared **bus** — a strip of superconducting line ringing at ~6–7 GHz — detuned a few hundred MHz away so they normally ignore it. For a two-qubit gate you either **tune one qubit into resonance** to swap a *virtual* photon (the photon never really lives in the bus; the qubits pick up a state-dependent phase), or **drive Q1 at Q2's frequency** (IBM's *cross-resonance*) so Q2 feels a push whose direction depends on Q1's state — that's entanglement. The tin-can-telephone of quantum: the string carries the vibration, but you don't pour water into the cans. On Heron chips this takes ~200–400 ns at ~99% two-qubit fidelity. --- ## 5 · The IQ waveform — what actually gets uploaded ![the IQ waveform — I is the Gaussian drive, Q is the DRAG correction](diagrams/iq-waveform.png) **IQ = In-phase and Quadrature** — a way to describe any microwave signal without drawing a 5 GHz sine wiggling 175× in 35 ns. The hardware makes two slow baseband voltages, I(t) and Q(t), mixed with a local oscillator: ``` signal(t) = I(t)·cos(2π·5GHz·t) − Q(t)·sin(2π·5GHz·t) ``` - **I (blue)** — the main Gaussian bump; the energy that rotates |0⟩→|1⟩. - **Q (orange)** — the tiny derivative-shaped DRAG correction, ~5–10% the size, 90° out of phase. - **Phase control:** pure I = an X gate, pure Q = a Y gate, mix = any axis in the XY plane. In Qiskit Pulse it's roughly: ```python from qiskit.pulse import Drag # IBM backend dt ≈ 0.222 ns pi_pulse = Drag(duration=160, # 160 × 0.222 ns ≈ 35.5 ns amp=0.2, sigma=40, beta=-0.5) # the Q-channel (DRAG) tweak ``` The backend turns those ~160 complex samples [I + iQ] into analog voltages, up-converts to 5 GHz, and shoots it down the coax into the fridge. ### Why the Q channel matters — the DRAG sweep ![leakage to |2⟩ vs the DRAG β parameter — lowest near β ≈ −0.5](diagrams/leakage-vs-beta.png) Turn Q off (β = 0) and the pulse has spectral weight right where |1⟩→|2⟩ lives (~200–250 MHz below the drive). Leakage to |2⟩ is **lowest around β ≈ −0.5** and climbs fast at β = 0: | | leakage per π-pulse | single-qubit error | |---|---|---| | with DRAG (β ≈ −0.5) | ~0.1–0.3% | ~0.02% | | without DRAG (β = 0) | 2–5% | gate fidelity tanks | That's why every IBM calibration runs a **DRAG sweep**: flip the qubit repeatedly while scanning β, and pick the dip. --- ## 6 · A Josephson junction is not JavaScript ![JS vs JJ — the setlist vs the guitar string](diagrams/js-vs-jj.jpg) They only share a "J": - **Josephson junction (JJ) = hardware.** Two superconductors with a ~1 nm insulator between, named for Brian Josephson (Nobel 1973). At 15 mK, Cooper pairs tunnel with zero voltage; the current depends on the quantum phase. You fabricate it with e-beam lithography, not `npm install`. - **JavaScript (JS) = software.** You *can* submit a circuit via IBM's cloud REST API, but the code never touches the junction — it just says "play this IQ waveform at 5 GHz for 35 ns." ```js // npm i axios const axios = require('axios'); async function flipQubit() { const job = await axios.post('https://api.quantum-computing.ibm.com/runtime/jobs', { program_id: 'sampler', backend: 'ibm_heron', params: { circuits: ["OPENQASM 3; qubit q; x q;"] } }, { headers: { Authorization: 'Bearer YOUR_IBM_TOKEN' } }); console.log('Job sent, JJ will flip in ~2 seconds:', job.data.id); } flipQubit(); ``` The chain: `JS → Python/Qiskit → OpenPulse JSON → AWG DAC voltages → IQ mixer → microwave coax → JJ`. JavaScript doesn't *become* the junction — it just rings its doorbell from 1,500 miles away. --- ## Why this file exists > *"no lol. im just walking. i already have 40 convos about quantum dots, have to start over > every time lol"* — and the real ask underneath: *"the work is for it to be automatic."* So the keepers were extracted and this primer kept once. **Ψ — remembered, not re-derived.**