Euler’s “36 Officers” problem is a specific form of magic square known as an “orthogonal Latin square” solved using quantum entanglement.

Figure 1. Euler’s 36 officers puzzle in quantum computing.

Figure 1 shows that Leonhard Euler, a prominent mathematician, posed a question over 240 years ago: if six army regiments each contain six commanders of six different ranks, can they organize in a square so that no rank or regiment repeated in any row or column.

After failing to find a solution, Euler called the issue intractable — and the French mathematician Gaston Tarry proved him correct over a century later.

The mathematicians Parker, Bose, and Shrikhande demonstrated an even stronger result 60 years later, when the introduction of computers eliminated the necessity for laboriously testing every conceivable combination by hand.

A new work, which is now available as a preprint and has submitted to the journal Physical Review Letters, has supposedly discovered a solution. Only one condition applies: the cops must be in a state of quantum entanglement.

“I think their study is quite beautiful,” non-participating quantum physicist Gemma De las Cuevas told Quanta Magazine. [1]

Suhail Rather of the Indian Institute of Technology Madras (IITM), Adam Burchardt of Jagiellonian University in Poland, and their colleagues wondered if the problem could be solved if the objects were quantum mechanical instead of classical.

The researchers used a computer algorithm to search for such quantum solutions of Euler’s “36 officers” problem. They started from a classical configuration that had only a few repetitions in the rows and columns and tried to improve it by adding in superposition. They found that a full quantum solution to the 6×6 problem exists for a particular set of superposition states. [2]

The results could have real impacts on quantum data storage, according to Quanta Magazine. Entangled states can be used in quantum computing to ensure that data is safe even in the case of an error — a process called quantum error correction.

By entangling 36 quantum officers in a state of interdependent relationships, the researchers found what is called an absolutely maximally entangled state. Such states can be important for resilient data storage in quantum computing. [3]

References:

1. https://qsstudy.com/243-year-old-impossible-puzzle-solved-using-quantum-entanglement/
2. Source: https://physics.aps.org/articles/v15/29
3. https://www.livescience.com/math-puzzle-quantum-solution

Cite this article:

Sri Vasagi K (2022), Euler’s 36 Officers puzzle solved using Quantum Entanglement, AnaTechMaz, pp.28