Spin Qubits at NQCP

from the perspective of a software engineer

Who's JC?

DTU/KTH graduate 2013

cryptography
systems security

Who's JC?

Renaissance nerd

OS
embedded
networking
web services
video streaming
reverse engineering

Who's JC?

History at NBI:

2016–2020	Centre for Ice and Climate (PICE)
2026–	NNF Quantum Computer Programme (NQCP)

CIC / PICE

NQCP

Who's JC not?

An expert in:

quantum physics
quantum computers

There will be simplifications.

Information theory

Computing before "computers"

1800s1930s1940s1950s1960s–70s Ideas

1843 Lovelace: a program for Babbage’s engine

1854 Boole: logic as algebra

1936 Turing, Church: what is computable?

1937 Shannon: switching circuits as Boolean algebra

1945 von Neumann: stored-program design, on paper

1948 Shannon: information theory, the “bit”

Machines

Babbage’s Analytical Engine: never built

“Computers” are still people

1941 Zuse Z3 (relays)

1945 ENIAC (vacuum tubes)

1948 Manchester Baby: first stored program

1958 Integrated circuit

1971 Microprocessor

Bits and logic

Quantum information theory

|+⟩

|+i⟩

|−i⟩

Q = 0.50·|0⟩ + 0.50·|1⟩

|ψ⟩ = cos(126°/2)·|0⟩ + e^i155°·sin(126°/2)·|1⟩

→ / ← to step · drag to look around

1. BIT (opens the slide): Before any quantum talk — a classical bit: 0 or 1, nothing in between. The red ball jumps straight from one to the other: classical state changes are discrete jumps.

2. LINE: What if we allowed a real-valued mix of the two? We'd get a point somewhere on a line between them — one number between 0 and 1. One degree of freedom. Still not enough to describe a qubit. The plate (top right) shows the live coefficients: Q = a·|0> + b·|1> (a + b = 1).

3. ROTATE: Relabel the ends honestly — 0 goes to the top, 1 to the bottom — and lift the view: the 0-end of the line swings up to |0> at the north pole, |1> at the south. The line was an axis all along, and two more axes live around it.

4. SPHERE: Let the coefficients be complex, normalize, and every state alpha|0> + beta|1> lives on the Bloch sphere. The view sits in the corner so no axis hides behind another: |0> up, |1> down; |+> comes out of the screen toward your lower left, |+i> toward your lower right. Their labels are tiny on purpose.

5. TRAVEL: The dot — now the tip of a state vector — is no longer stuck on the line: it leaves for the surface, sweeps a latitude circle (phase!), then spirals (mix again). Two knobs, not one. The live |psi> equation ticks along as it wanders.

6. ANGLES: Fixing the state takes two numbers — theta, the angle away from |0> at the north pole (the mix), and phi, the phase around. The plate (top right) plugs them straight in: theta inside cos(theta/2) and sin(theta/2) — note the half! — blue, and phi in the phase factor, green. (Normalized; global phase ignored.)

After this: qubit operations.

Operations on qubits

OPEN: The same sphere again — the state still drifting on its surface. Capital-letter gates are the qubit's verbs: X, Z, H. On the Bloch sphere every unary gate is one rotation, so each beat is the same trick: highlight an axis (orange), and the vector sweeps a half circle about it while the plate (top right) shows what that does to theta and phi.

7. GATE X: the classical bit-flip — a half-turn about the x-axis, the one pointing at you through the screen (orange). The mix swings to its complement — watch the plate: theta and the live coefficients trade places, and the phase mirrors by 180°.

8. GATE Z: same half-turn idea, about the vertical |0>–|1> pole axis. Watch theta hold dead still in the plate — the mix is untouched. Z only slaps the phase: phi jumps by exactly 180°. Different axis, different physical story: from here, phase is the angle.

9. GATE H: the celebrity — a half-turn about the diagonal between the |0> pole and |+> (the point facing you). It takes the classical |0> onto the equator: cos(45°), sin(45°) — a live (|0> + |1>)/√2 superposition. Every unary gate is one of these rotations.

Qubit interactions

10. CLASSICAL: binary logic REDUCES — XOR two bits and the answer is one bit, b3. State size shrinks; you can throw the inputs away. (Nuance if asked: real classical circuits keep the inputs around too; pure XOR alone can't be undone.)

10a. BRACES (second press): left side is two bits, right side is one bit — binary logic COMPRESSES. The answer is smaller than the question.

11a. BRACES AGAIN (fourth press): same braces, quantum side: two qubits in, two qubits out. NO reduction — the state never shrinks; it only entangles.

11. QUANTUM: CNOT is the quantum XOR — on basis states it is literally bit-XOR into the target. But quantum gates must be reversible: nothing shrinks, two qubits come out. Careful with the causal story: the size doesn't stay unchanged BECAUSE they entangle — it can never change, gates are unitary. Entanglement is the other fact: on superpositions the pair comes out as one joint state that no longer factors into “qubit 1's arrow plus qubit 2's arrow” — each alone sinks to the center of its own Bloch ball. This is where the Bloch sphere honestly stops helping, by design of nature, not of the software.

Transition: “so how big is this joint state, really?” — next slide.

Simulation

qubits	state vector	memory
1	2 numbers	32 B
2	2² numbers	64 B
3	2³ numbers	128 B
20	~10⁶ numbers	~16 MB MP3 file
50	~10¹⁵ numbers	~18 PB state of the art
≈ 4 100 Shor, RSA-2048	~10¹²³³ numbers	~10¹²³⁴ B more numbers than atoms in the universe

So it may come as a surprise that we can actually simulate quantum circuits on classical computers precisely (if we for a second ignore floating point precision).

Each qubit's state can be represented by two complex numbers, about 8 bytes each. Qubit state 16 bytes.

Scales fine in the beginning. Phone can simulate 20 qubits without breaking a sweat

Every qubit we add doubles the memory complexity.

14. SHOR: factoring RSA-2048 takes on the order of 4 100 logical qubits (“clean” qubits with error correction — at today's fidelities that's roughly 20 million physical ones, Gidney-Ekerå 2019). Its state vector would hold ~10^1233 numbers — beyond the ~10^80 atoms in the observable universe.

PUNCHLINE (for the IT crowd): there is nothing mystical to simulate — a classical computer can compute any of this exactly; it just cannot STORE the intermediate state. The quantum computer isn't doing math we can't do; it's storing something we can't store.

NQCP

Pathfinder model
Moving up the ladder

NQCP

Algorithms & Applications
Education & Outreach
Intra- & Interconnects
Materials
Quantum Error Correction
Qubit control & readout
- Superconducting
- Semiconductor spin
- Photonics
- Neutral atoms
Theory and simulation / data

Semiconductor spin

Pros	Cons
Fabricated with familiar chip-making techniques	Needs temperatures below ~100 mK
Qubits are extremely small and dense	Control is fiddly and sensitive

Spin Qubit Pilot line

Chip design

Isometric chip cutaway showing gate electrodes and substrate layer stack

Chip design

→ / ← to step

The board, die, fan-out, and bond geometry are explanatory rather than a manufacturing drawing. The zoom beat makes the signal path explicit: gate, on-die route, edge pad, bond wire, package.

The top view keeps only P1–P10; the sensor dots are omitted to keep this short talk focused. P5/P6 and the simplified B1/B2/B3 geometry are pedagogical—the real barriers around P5 lie towards P1, P2, P8 and P9.

The side view is a schematic representative cut, not a literal cut through the complete device. Layer thicknesses are not to scale.

The carriers in the device are holes; for this audience the visible wording deliberately says charges.

The yellow effective potential uses arbitrary units. The charges remain in the Ge layer, but the schematic curve may extend slightly into the SiGe buffer so strong wells stay rounded and readable.

The gold arcs represent schematic control wiring and bond-wire fan-out, not a literal cross-section of the package wiring.

The five DAC values are illustrative, not calibrated device settings. In this hole-device convention, making a gate more negative generally accumulates holes and lowers the local hole-energy landscape, so a larger negative magnitude produces a deeper yellow well.

Pauli-spin-blockade readout is simplified to moved versus blocked to communicate spin-to-charge conversion, not the complete state model.

Spin Qubits at NQCP

Who's JC?

Who's JC?

Who's JC?

CIC / PICE

NQCP

NQCP

Who's JC not?

Information theory

Computing before "computers"

Bits and logic

Quantum information theory

Operations on qubits

Qubit interactions

Simulation

NQCP

NQCP

NQCP

Semiconductor spin

Spin Qubit Pilot line

Chip design

Chip design

Chip design

Chip design

Chip design

Chip design

Software in Quantum control

Thank you