Paper Qubits

A quantum computer, drawn in pencil and simulated exactly. Add gates, watch the arrows and clocks, then measure and compare what you get with the prediction.

Control the chip

Microwave pulse length

Wait before readout

Readout noise

From the chip to the notation

On the chip	In the notation
Left alone in the fridge, the circuit settles into its lowest energy level	\|0⟩
The next energy level up, 5.00 GHz higher	\|1⟩
A microwave pulse at exactly 5.00 GHz, length t	rotation R_y(θ), θ ∝ t
π/2 pulse: half of a full flip	\|0⟩ → (\|0⟩+\|1⟩)/√2 = \|+⟩ the H of lesson 1
π pulse: a full flip	X: \|0⟩ → \|1⟩
One readout: the dot lands left or right of the line	measurement → 0 or 1
Share of dots on the right, over many shots	P(1) = \|amplitude of \|1⟩\|²
Waiting: energy leaks out (T1 = 60 µs), phase blurs (T2 = 45 µs)	the arrow shrinks: noise

Control the chip

Coupler flux pulse amplitude

Readout noise

Leave the coupler off

From the chip to the notation

On the chip	In the notation
Two aluminium crosses: Q0 at 5.00 GHz, Q1 at 5.30 GHz	q0, q1; joint \|q1 q0⟩
A 26 ns pulse on each drive line, D0 and D1	R_y(π/2) on each ≈ H
A 60 ns flux pulse on the coupler between the crosses	CZ: \|11⟩ gets phase φ (ideal φ = 180°, a − sign)
A −π/2 pulse on D1 after the coupler	all together: CNOT q0→q1 (lesson 3)
Both arrows shrink while the coupler pulse plays	entangled: no state of its own
Two resonators on one feedline, read at the same time	measure both → 00…11
Both dots land on the same side far more often than chance	correlation: P(00) + P(11)
Coupler pulse too weak, too strong, or off	φ ≠ 180°: partly or not entangled

Pick a gate

run

What the compiler makes of it

RZ is free: the control software shifts the phase of the later pulses instead of playing anything. SX, X and CZ are real pulses. The native set here matches IBM-style chips; durations are typical, not one chip's specs.

Circuit

on control

In electronics

On the chip

Pulse schedule: the gate as the chip receives it

A flip-flop and a qubit, side by side

	Logic gate / flip-flop	Quantum gate / qubit
A bit is	a voltage on a node (0 V or ~0.8 V), held by feedback	which energy level a circuit is in, or any arrow in between
A gate is	transistors the data flows through, onto a new wire	a timed pulse sent to a qubit that stays put
A circuit is	wiring, fixed in silicon	a program, compiled to a pulse schedule and played in time
Speed	picoseconds per gate, GHz clocks	~36 ns per pulse, ~70 ns per coupler gate, ~1 µs to read
Memory lasts	as long as the power is on	~100 µs, then the qubit drifts back to \|0⟩ (lesson 0's wait slider)
Reading	free, repeatable, changes nothing	once; the result is 0 or 1 and the superposition is gone
Copying	fan a wire out to many inputs	impossible (no-cloning); you can only entangle
Reversible	no: AND and NAND throw information away	yes, every gate can be undone (measurement can't)
Errors	so rare they're ignored	about 1 in 1,000 per two-qubit gate on good chips

The chip, sketched

Reset
π/2 pulses
Coupler
−π/2 pulse
Readout
Collapse
Repeat

Fire a shot to watch both qubits, the coupler and the readout take their turns.

siliconaluminiumdrive lines D0, D1coupler + flux linereadoutjunctions

A real multi-qubit chip

Colour-coded micrograph of a 7 mm chip with four qubits Q1 to Q4 in the corners and four meandering resonators R1 to R4 between them, with an inset zooming in on one 700 micrometre qubit

Four qubits, 7 mm across Q1–Q4 are the qubits (orange), each with its own drive and flux line coming in from the edge, like D0, D1 and the flux line in the sketch. The inset zooms in on one qubit: 700 µm wide. One difference from the sketch: here neighbouring qubits talk through the meandering resonators R1–R4 instead of a small tunable coupler. Both are ways to let two qubits exchange energy on command. Salathé et al., Wallraff group, ETH Zurich, Phys. Rev. X 5, 021027 (2015). CC BY-SA 3.0

Pulse schedule: what the control electronics play, in nanoseconds

Each qubit on its own, and its readout dots

Q0 readout

Q1 readout

Both qubits together

How often the dots agree, against coupler amplitude. Click to set it.

The chip, sketched

Reset
Drive
Wait
Readout
Collapse
Repeat

Fire a shot to watch each part of the chip do its job.

siliconaluminium, superconductingdrive line + pulsereadout lineJosephson junction

The real thing, zooming in (click a photo to magnify, click again to reset)

A gold, multi-tiered dilution refrigerator hanging open, with coaxial cables running down through its plates — **The whole machine** A dilution refrigerator with its shields off. Each gold plate is colder than the one above; the chip sits at the bottom, at about 10 mK. The silver cables carry the pulses down and the readout tones back up: the blue and teal lines in the sketch. IQM quantum computer, Espoo. Photo: Ragsxl, CC BY-SA 4.0

A small square chip with four rainbow-tinted blocks, each holding six cross-shaped qubits joined by zig-zag lines to a central line — **A chip of 24 qubits** Each small “+” is one transmon, the same cross as the sketch. The zig-zags are readout resonators, all hanging off a straight feedline down the middle of each block. The rainbow is only light reflecting off the metal film. Transmons patterned by laser lithography. Photo: OJB Quantum, CC BY 4.0

Microscope image of a superconducting qubit: white metal lines on black, a red arrow pointing at the Josephson junction, and a grid of square holes in the surrounding metal — **One qubit, under a microscope** White is metal, black is where it was etched away. The red arrow marks the Josephson junction, the coral square in the sketch. The grid of square holes in the ground metal stops stray magnetic flux from getting trapped. NIST superconducting qubit (an earlier design than the transmon). Raymond Simmonds / NIST, public domain

The qubit's state

Readout: one dot per shot

Rabi oscillation: P(1) against pulse length

predictedmeasured on the chipfitted curveclick the chart to set the pulse length

Walk through a real lab (videos open on YouTube)

Step inside the Google Quantum AI labGoogle Quantum AI · 2024The Santa Barbara lab: fridges, wiring and the chips inside. Take a tour of Google's Quantum AI LabGoogle Quantum AI · 2023Research scientist Dripto Debroy walks through the campus for World Quantum Day. Lab Tour: How IBM tests quantum processorsIBM ResearchJerry Chow and Daniela Bogorin in the lab that checks qubit frequency, coherence and coupler tuning before a chip ships. Tour a Quantum Lab with Dr. Olivia LanesQiskit (IBM)Where the qubits sit inside a 15 mK cryostat, and the room-temperature electronics that drive them.

Each qubit on its own (Bloch sphere, drag to turn)

The whole state: one clock per outcome

Disc size is the amplitude (its area is the probability). The blue hand is the phase: right is +, left is −. Outcomes are written |q0…q0⟩.

Measure

predicted probabilitymeasured share of shots

Control the chip

From the chip to the notation

Control the chip

From the chip to the notation

Pick a gate

What the compiler makes of it

Circuit

In electronics

On the chip

Pulse schedule: the gate as the chip receives it

A flip-flop and a qubit, side by side

The chip, sketched

A real multi-qubit chip

Pulse schedule: what the control electronics play, in nanoseconds

Each qubit on its own, and its readout dots

Both qubits together

The chip, sketched

The real thing, zooming in (click a photo to magnify, click again to reset)

The qubit's state

Readout: one dot per shot

Rabi oscillation: P(1) against pulse length

Walk through a real lab (videos open on YouTube)

Each qubit on its own (Bloch sphere, drag to turn)

Search: rounds of oracle + diffuser

The whole state: one clock per outcome

Measure