Quantum Map Processor
A computing language for exact quantum-amplitude systems.
In 2000, the Birmingham mathematician Richard Kaye proved that Minesweeper is not just a game but a computing language. Deciding whether a board is consistent is NP-complete, and his proof is constructive: he showed how to build wires and logic gates out of mine configurations, so a board can encode any Boolean circuit — on an unbounded grid, all the way to Turing-completeness. The Quantum Map Processor takes that language literally. Every clue — “exactly k mines among these n cells” — becomes a local tensor; a board becomes a tensor network; and a question about the board becomes a contraction.
The decisive ingredient is the weight placed on each satisfying branch. With every weight set to one, the contracted network counts and samples — a classical machine, verified by compiling a 4-bit ripple-carry adder out of Kaye gates and reproducing all 512 inputs through contraction alone. Allow complex weights and read probabilities by the Born rule, and the identical network becomes a quantum-amplitude machine: it reproduces Deutsch–Jozsa and Bernstein–Vazirani exactly, every amplitude matching analytic quantum mechanics to one part in 1016. The quantum behaviour is native, not grafted on. An unrevealed cell already carries the uniform amplitude vector — the |+⟩ state — and the clue tiles are themselves entanglers: clue(n,1) is the n-qubit W state and clue(n,k) the Dicke state, exactly. A single phase tile on the output wire of any classical circuit turns it into the phase oracle (−1)f(x). Because the state lives as a classical description, the engine can undo a measurement, branch into counterfactual histories and read out the entire Schmidt spectrum of any cut exactly. The price is honest and fixed: cost grows as 2w in width w, so the instrument serves the regime where correlations stay bounded.
The instrument has already found something. The corner-sharing clue(4,2) lattice realises a critical ice phase; decorating one of its branches with a phase θ generates a one-parameter family in which every local measurement statistic remains invariant while the entanglement reorganises, its area-law coefficient climbing 46% and peaking at θ = π/2, a state called i-ice. At widths up to seventeen, the phase deformation destroys the Rényi locking transition that ordinary ice possesses: the locking scale never arrives, but drifts upward as the logarithm of the width. It is a deformation invisible to every local probe that nonetheless collapses a transition at the boundary.
Its most immediate use is in front of real hardware. Neutral-atom and Rydberg simulators natively prepare these constraint-satisfying superpositions, but Monte Carlo references carry sampling noise, truncated tensor methods carry truncation error, and idealised references omit the always-on van der Waals interactions the device actually evolves under. The Quantum Map Processor supplies the missing standard: exact satisfying counts, occupation marginals, cut Rényi entropies at n = ½, 1, 2, 3 and ∞, and leading Schmidt levels for both ideal families and the stray-exact state. No Monte Carlo, no truncation: counts are exact integers, marginals exact rationals and spectra cross-checked along two independent numerical paths. Every quantity is an executable assertion, every important number is computed twice by routes that must agree, and the engine reproduces Lieb’s 1967 residual-entropy constant for square ice blind to within a quarter of a percent.