Quantum Entanglement Key to 250-Year-Old Math Puzzle
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- Robin Simoens and Simeon Ball used a computer algorithm to search mathematical graphs representing the 6-by-6 grid, proving that no solution to the 36 officers problem exists without quantum entanglement.
- The problem was originally posed to Leonhard Euler by Russian Empress Catherine the Great in the 1700s, with Gaston Tarry rigorously proving a century later that no classical arrangement of 36 officers from six regiments exists.
- Karol Życzkowski at Jagiellonian University and colleagues showed in 2022 that a quantum solution exists, inventing a new absolutely maximally entangled (AME) state equivalent to entangling four six-sided dice so tightly that rolling two predicts the other two.
- Jamie Vicary at the University of Cambridge, who co-invented quantum Latin squares, said AMEs made with a quantum computer's qubits can act as error-correcting codes that protect qubits from computational errors.
- Simoens and Ball are now studying solutions to the 7-by-7 Latin square problem that are genuinely quantum rather than classical, according to the source.
- Życzkowski called the result significant because the solution is 'as simple as possible, since the effect of quantum entanglement is indispensable,' per the source.
Why it matters: For quantum computing engineers, the result pins down entanglement as a necessary structural ingredient for the best error-correcting codes (AMEs), not an incidental feature. This narrows the search for optimal qubit-protection schemes, directly relevant to making quantum computers practically useful.
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