Play Quantum Minesweeper | Quantum Logic Puzzle Game

Game Setup

How to play

Goal: leave no mines on the board. From Level 1 up that means bringing every cell to zero chance of holding a mine — not working out where the mines are, but removing the possibility that there are any. (Level 0 is ordinary Minesweeper: there you win by opening every safe cell.)

What makes it quantum: a cell is not a fixed mine or a fixed blank. It can hold both possibilities at once, and it settles on one only when you measure it. Until then it has a probability of being a mine, and that probability is something you can change.

Your moves

Measure opens a cell. If it is safe, it shows how many mines to expect around it. If it is a mine, you lose. A cell that is half likely to be a mine adds 0.5 to its neighbours' numbers, so clues are often fractions.
Gates change a cell without opening it. This is how you lower a cell's chance of being a mine instead of gambling on it. Gates work only on cells you have not opened yet: an opened cell has already settled, and nothing moves it.
Pin marks a cell you suspect. It is a note to yourself and changes nothing about the board.

Open the ❓ panel and hover over anything on the game screen — a counter, a gate button, the probe — to read what it does.

Levels

Level 0 — Classical

Ordinary Minesweeper. Mines are fixed, and you win by opening every safe cell. Start here to warm up.
Level 1 — Superposition

A cell can now be in superposition: an even chance of mine or no mine. You can still measure it, but that is now a coin flip, so measuring is a gamble rather than a way to make progress. Gates are the safe way forward: apply one to an unopened cell and watch the clue numbers around it move.
Levels 2 to 4 — Entanglement

Cells can now be entangled: their outcomes are linked, so learning about one tells you something about another. A single mine may be spread across two cells, in a superposition of sitting in either one. Measuring one cell can then change the other, which makes the board harder to clear.

These levels give you two-qubit gates, which act on two cells at once. Use them to break the links before dealing with the mines. Levels 3 and 4 entangle three and four cells at a time.
Sandbox

No winning, no losing. Try gates and watch what they do. Use Reveal to see mine probabilities and the entanglement network without measuring or changing the board.

Start at Level 0 or 1, then use Sandbox to test one gate at a time. Watching a single gate move a single clue is the quickest way to learn what it does.

Game Setup - Advanced

Setup options

Simple Setup fills all of these in for you. Change them here to build a board the levels do not offer.

1. Board size

Rows $R$ and columns $C$. The board is $N = R \times C$ cells, one qubit each.

2. Mines and entanglement level

Mines $B$ is how many mines are placed. Entanglement level controls how they are prepared:

Level 0 — ordinary fixed mines: every cell is definitely $|0\rangle$ or $|1\rangle$.
Level 1 — each mine is an independent single cell in superposition, such as $|+\rangle$ or $|i\rangle$.
Level $k$ — mines are prepared in random entangled states over groups of $k$ cells. Level 2 gives Bell-pair-like states, Level 3 GHZ-type states, and so on.

While you play, the number of mines on the board is an average rather than a count: $$ \langle \text{Mines} \rangle = \sum_i p_i, \qquad p_i = \tfrac{1}{2}\left(1 - \langle Z_i \rangle\right), $$ where $p_i$ is the probability that cell $i$ holds a mine.

3. Win condition

Identify — win by opening every currently safe cell without ever measuring a mine.
Clear — win by driving every cell to mine probability zero. The mines are not hidden somewhere to be found: the goal is to make a mine outcome impossible.
Sandbox — free exploration, with no win and no loss. The read-only Reveal lens displays mine probabilities and entangled cells without measuring the board.

4. Move set

Which operations you may use:

Classic — measure (M) and pin (P) only.
One-qubit (core set) — adds $X$, $Y$, $Z$, $H$, $S$, which is enough to defuse single-cell mines.
One-qubit (full set) — adds $S^\dagger$, $\sqrt{X}$, $\sqrt{X}^\dagger$, $\sqrt{Y}$, $\sqrt{Y}^\dagger$, completing the single-qubit Clifford group.
Two-qubit — adds $CX$ and $SWAP$ to the core set.
Two-qubit (extended) — adds $CX$, $CY$, $CZ$ and $SWAP$ to the full set.

Either two-qubit set lets you create and undo entanglement yourself.

5. Entanglement probe regions

How many regions the probe offers this game: 0 for none, 1 to weigh one region against the rest of the board, or 2 to also compare two regions. Simple Setup picks a count to suit the level; choosing here overrides it.

The probe only reads the state. It never measures a cell, applies a gate or moves a pin, and it does not use up a move.

Region $A$ is reported as its entanglement entropy against the rest of the board, $$ S(A) = -\mathrm{Tr}\left(\rho_A \log_2 \rho_A\right), $$ in bits. For independent Bell pairs this counts the pairs straddling the region's boundary: selecting one member gives 1 bit, selecting both gives 0. A product state such as $|+\rangle$ gives 0 even though its mine outcome is still uncertain, and a reading of 0 does not rule out entanglement inside the region.

With two regions, disjoint regions $A$ and $B$ also report their mutual information $$ I(A:B) = S(A) + S(B) - S(A \cup B), $$ with $S(A)$, $S(B)$ and $S(A \cup B)$ shown alongside. This measures total correlation, classical as well as quantum. A Bell pair split between the two regions gives 2 bits, while cells from different pairs give 0. Take care beyond two cells: in a three-cell GHZ state, two cells share 1 bit this way even though their own two-cell state is not entangled. Do not read $I(A:B)$ as a count of pairwise links.

Regions stay selected while you switch back to gates and measurement, so you can compare a reading before and after a move. Opened cells may be selected, but still cannot be targeted by gates. Every reading describes the board as it stands, given the measurement outcomes so far.

This is not the linked-rings counter above the board, which adds up each cell's own entanglement separately. The region count survives a reset, a new game with the same settings, and a saved browser game; the cells you selected do not.