Entanglement Proved Essential to Quantum Euler Problem
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- The 36 officers problem — originally posed by Catherine the Great to Leonhard Euler in the 1700s, asks whether 36 officers from six regiments can fill a 6x6 grid so each row and column contains one of every rank and regiment; Euler concluded no, and Gaston Tarry rigorously proved it impossible over a century later.
- Karol Życzkowski at Jagiellonian University — in 2022, showed the problem could be solved if it was made quantum, allowing each officer to exist in a superposition of rank and regiment.
- Robin Simoens at Ghent University, working with Simeon Ball at the Polytechnic University of Catalonia, built on Życzkowski's 2022 work and proved that entanglement is the indispensable ingredient, ruling out any simpler solution using superposition alone.
- Życzkowski's 2022 solution — required all 36 officers to be linked through quantum entanglement and effectively invented a new absolutely maximally entangled (AME) state, which Życzkowski likens to four dice so correlated that rolling two predicts the outcome of the other two.
- Jamie Vicary at the University of Cambridge — who co-invented quantum Latin squares, says AMEs can serve as error-correcting codes for qubits, making the entanglement finding directly relevant to building practical quantum computers.
- Simoens and Ball — are now studying genuinely quantum (rather than classical) solutions to the 7-by-7 Latin square problem; the work appears in Physical Review Letters.
Why it matters: For quantum computing to scale, qubits need error-correcting codes — exactly what AME states like the one at the heart of this solution can become, per Cambridge's Jamie Vicary. The proof that entanglement is indispensable, not optional, narrows the design space for those codes and confirms entanglement as the essential resource rather than excess machinery.
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