Catalytic z-rotations in constant T-depth

2025/06/18 by Isaac H. Kim, Kim, Isaac H. · 2 citations
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Geometric and Algebraic Topology #Mathematics and Applications #Quantum Physics (quant-ph) #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2506.15147

openalex publication_date 2025/06/18 · openalex created_date 2025/10/19 · openalex updated_date 2026/07/28

Abstract

We show that the T-depth of any single-qubit z-rotation can be reduced to 3 if a certain catalyst state is available. To achieve an ε-approximation, it suffices to have a catalyst state of size polynomial in log(1/ε). This implies that QNC⁰_f/qpoly admits a finite universal gate set consisting of Clifford+T. In particular, there are catalytic constant T-depth circuits that approximate multi-qubit Toffoli, adder, and quantum Fourier transform arbitrarily well. We also show that the catalyst state can be prepared in time polynomial in log (1/ε).

Citations

• Breaking even with magic: demonstration of a high-fidelity logical non-Clifford gate
• Experimental Demonstration of High-Fidelity Logical Magic States from Code Switching
• Quantum circuit lower bounds in the magic hierarchy
• Magic state cultivation: growing T states as cheap as CNOT gates
• Efficient Magic State Distillation by Zero-Level Distillation
• Assessing requirements to scale to practical quantum advantage
• Tutorial on the Quantikz Package
• Fast parallel circuits for the quantum Fourier transform
• Parallel Quantum Computation and Quantum Codes
• Parallel Quantum Computation and Quantum Codes
• Approximate formulas for some functions of prime numbers

Cited by

• Matchgate synthesis via Clifford matchgates and T gates
• Infinite temperature at zero energy

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