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The Smallest Code with Transversal T
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The Smallest Code with Transversal T
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We prove that the smallest distance 3 Quantum Error Correcting Code with a transversal gate outside the Clifford group is the well-known 15-qubit Reed-Muller code, also known as a tri-orthogonal code. Our result relies on fewer assumptions than previous works. We further extend this result by finding the minimal code that also possesses any other non Clifford transversal single-qubit gate.
Forward citations
Cited by 5 Pith papers
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Exploring the landscape of compact magic-state distillation factories
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High-rate CSS codes compile nonlocal Clifford and non-Clifford logical circuits into onsite phases and classical permutations, so MPS bond dimension stays fixed by the encoder while logical entanglement, magic, and no...
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Exploring the landscape of compact magic-state distillation factories
Classical repetition-code framing plus SAT search yields no-go theorems (no d>3 T-to-T on <8 qubits) and the smallest known unitary factories for d=4,5 T-states (10–11 qubits) and d=3,4 CCZ-states (9–10 qubits).
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A learning-based framework constructs logical operations for arbitrary quantum codes and co-designs non-additive encodings with noise models and desired gate sets via VarEFTQC.
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Local distillation from Reed Muller codes unfolding
Local 2D and 3D Reed-Muller distillation factories achieve output infidelities down to 8.256e-9 for CCZ states and 1.1811e-17 for T states from 10^{-3} input infidelity.
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