Three bits against three qubits
Every card is an arrow. A Bit card may only point up (0) or down (1). A QBit card may also point sideways — and that is where the advantage, and the trouble, comes from. Here the app plays Nature: it keeps the hidden state and applies the physics, exactly.
Quantum Penny — D. A. Meyer, 1999
The coin starts heads (↑). You are Q. Make a move, then the classical player secretly flips the coin or doesn't, then you move again. Nature measures: you win on heads.
What's going on
Six secrets; you play QBit on odd secrets and Bit on even ones. A right guess scores your pot, which starts at n + 1 and drops by one for each shot or question after the first.
Qubit Lab
Three Bit cards make 2³ = 8 states and you can see all of it. Three QBit cards can be set 4³ = 64 ways — but a measurement still hands you back only 3 bits, one of 8 outcomes. The 64 are what you can prepare, not what you can read.
Bits — click a card to flip it (NOT)
QBits — gates under each card
Nature's view — the 8 amplitudes
Bar height is the amplitude (blue positive, red negative); the percentage under it is the chance of reading that outcome. Try H on a card, then Z, then H again: the negative sign is invisible to a measurement until the second H makes it interfere.
The balcony
Step off the dance floor and watch simulated tables learn and play your design before real people do.
The physics is exact; the players are a model whose every assumption is listed in engine/agents.js and
calibrated against in-person play.
Learning curve
Share of players who know H–oracle–H after each secret, by who sits at the table.
Experience arc
QBit minus Bit score on each secret. Above zero, quantum is winning.
Crossover
QBit minus Bit score by noise level, this design, from the full simulated DOE.
What matters most
Main-effect range of each factor across the whole simulated DOE (biggest level mean minus smallest).
Watch a match
From simulated DOE to in-person DOE
Rules, short
Full rules and the design rationale live in DESIGN.md; the printable kit is
print/cards.html (print to PDF, 9 cards a page).
The cards
A QBit card shows its state by which way it points. Read the arrow against the table: ↑ |0⟩, → |+⟩, ↓ |1⟩, ← |−⟩. Written as basis|value that is Z|0, X|0, Z|1, X|1 — two classical bits to set a card, one bit when you read it.
| Gate | What Nature does to the card |
|---|---|
| X NOT | ↑↔↓; sideways cards stay |
| Z Phase | →↔←; upright cards stay |
| H Hadamard | ↑↔→ and ↓↔← |
| M Measure (Z) | ↑ reads 0, ↓ reads 1; a sideways card is a fair coin and is turned to match |
Hidden Key in one minute
- Nature draws a secret n-bit string and shuffles the noise deck for the level.
- Bit player: set your Bit cards to a question x. Nature answers one bit — the parity of the secret AND x.
- QBit player: lay a circuit — a gate slot before and after the Oracle on each wire. Nature runs it: after every column it draws a noise card (a wire and an X or Z flip), the Oracle applies Z to every wire where the secret has a 1, and finally every card is measured.
- After each shot or question you may guess. Right: score your pot (n + 1, minus one per extra shot or question). Wrong: lose the stake.
- Rotate roles each secret. With three players at a table, the third is Nature.
Why it is not just an analogy
With the gates X, Z, H, Pauli noise and measurement, a row of four-way cards is the exact quantum
state. test/verify.js checks every card rule against a state-vector simulator — 777 checks. Entangling gates
(CNOT) produce states no row of cards can show, so they stay in the app until a later module.