2026/03/17 by Christine Li, Lia Yeh
Physics and Astronomy · Computer Science · #quant-ph #cs.ET
paper · pdf · doi:10.1007/978-3-032-30839-9_1
published as Proceedings of the 18th International Conference on Reversible Computation 2026 Jul 9 (pp. 3-40). Turin, Italy · 40 pages
arxiv created 2026/03/17 · arxiv updated 2026/07/31
The AND gate is not reversible\unicodex2014on 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\unicodex2014composed of a CX circuit, T and T dagger gates, followed by the CX circuit in reverse\unicodex2014of 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.