Exact Synthesis of Multiqubit Clifford-Cyclotomic Circuits

2023/11/13 by Matthew Amy, Andrew N. Glaudell, Amy, Matthew +9 · 2 citations
Chemistry · #Asymmetric Hydrogenation and Catalysis #Catalytic Cross-Coupling Reactions #FOS: Physical sciences #Nanomaterials for catalytic reactions #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.2311.07741

openalex publication_date 2023/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let n≥ 8 be divisible by 4. The Clifford-cyclotomic gate set G_n is the universal gate set obtained by extending the Clifford gates with the z-rotation T_n = diag(1,ζ_n), where ζ_n is a primitive n-th root of unity. In this note, we show that, when n is a power of 2, a multiqubit unitary matrix U can be exactly represented by a circuit over G_n if and only if the entries of U belong to the ring ℤ[1/2,ζ_n]. We moreover show that log(n)-2 ancillas are always sufficient to construct a circuit for U. Our results generalize prior work to an infinite family of gate sets and show that the limitations that apply to single-qubit unitaries, for which the correspondence between Clifford-cyclotomic operators and matrices over ℤ[1/2,ζ_n] fails for all but finitely many values of n, can be overcome through the use of ancillas.

Cited by

• Universality of a standard two-qubit gate by catalytic embedding
• Contributions to the Theory of Clifford-Cyclotomic Circuits

Related

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