Transversal AND in Quantum Codes

• URL: http://arxiv.org/abs/2603.04548v1
• Date: Wed, 04 Mar 2026 19:31:49 GMT
• Title: Transversal AND in Quantum Codes
• Authors: Christine Li, Lia Yeh,
• Abstract summary: AND gate is not computation$x2014$on qubits, but it is a building for efficient simulation using qutrits.<n>A code with "T-inaries" implementation of the original unitary can be further to attaind a $mathopen[![![![2,4!]!]!
• Score: 0.5047352161741804
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The AND gate is not reversible$\unicode{x2014}$on qubits. However, it is reversible on qutrits, making it a building block for efficient simulation of qubit computation using qutrits. We first observe that there are multiple two-qutrit Clifford+T unitaries that realize the AND gate with T-count 3, and its generalizations to $n$ qubits with T-count $3n-3$. Our main result is the construction of a novel qutrit $\mathopen{[\![} 6,2,2 \mathclose{]\!]}$ quantum error-correcting code with a transversal implementation of the AND gate. The key insight in our approach is that a symmetric T-depth one circuit decomposition$\unicode{x2014}$composed of a CX circuit, T and T dagger gates, followed by the CX circuit in reverse$\unicode{x2014}$of a given unitary can be interpreted as a CSS code. We can increase the code distance by augmenting the code circuit with additional stabilizers while preserving the logical gate. This results in a code with a "built-in" transversal implementation of the original unitary, which can be further concatenated to attain a $\mathopen{[\![} 48,2,4 \mathclose{]\!]}$ code with the same transversal logical gate. Furthermore, we present several protocols for mixed qubit-qutrit codes which we call Qubit Subspace Codes, and for magic state distillation and injection.

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