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Three Zeeman levels of spin-1 electron or nucleus are called as qutrits in quantum computation. Then, ISK (I = 1, S = 1, K = 1) spin system can be represented as three-qutrit states. Quantum circuits and algorithms consist of quantum logic gates. By using SWAP logic gate, two quantum states are exchanged. Topological quantum computing can be applied in quantum error correction. In this study, first, Yang-Baxter equation is modified for ISK (I = 1, S = 1, K = 1) spin system. Then three-qutrit topological SWAP logic gate is obtained. This SWAP logic gate is applied for three-qutrit states of ISK (I = 1, S = 1, K = 1) spin system. Three-qutrit SWAP logic gate is also applied to the product operators of ISK (I = 1, S = 1, K = 1) spin system. For these two applications, expected exchange results are found.

journal of applied mathematics and physics

Three-Qutrit Topological SWAP Logic Gate for ISK (&amp;lt;i&amp;gt;I&amp;lt;/i&amp;gt; = 1, &amp;lt;i&amp;gt;S&amp;lt;/i&amp;gt; = 1, &amp;lt;i&amp;gt;K&amp;lt;/i&amp;gt; = 1) Spin System