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T-count and T-depth of any multi-qubit unitary

التفاصيل البيبلوغرافية
العنوان: T-count and T-depth of any multi-qubit unitary
المؤلفون: Vlad Gheorghiu, Michele Mosca, Priyanka Mukhopadhyay
المصدر: npj Quantum Information, Vol 8, Iss 1, Pp 1-10 (2022)
بيانات النشر: Nature Portfolio, 2022.
سنة النشر: 2022
المجموعة: LCC:Physics
LCC:Electronic computers. Computer science
مصطلحات موضوعية: Physics, QC1-999, Electronic computers. Computer science, QA75.5-76.95
الوصف: Abstract We design an algorithm to determine the (minimum) T-count of any n-qubit (n ≥ 1) unitary W of size 2 n × 2 n , over the Clifford+T gate set. The space and time complexity of our algorithm are $$O\left({2}^{2n}\right)$$ O 2 2 n and $$O\left({2}^{2n{{{{\mathcal{T}}}}}_{\epsilon }(W)+4n}\right)$$ O 2 2 n T ϵ ( W ) + 4 n , respectively. $${{{{\mathcal{T}}}}}_{\epsilon }(W)$$ T ϵ ( W ) (ϵ-T-count) is the (minimum) T-count of an exactly implementable unitary U ( $${{{\mathcal{T}}}}(U)$$ T ( U ) ), such that d(U,W) ≤ ϵ and $${{{\mathcal{T}}}}(U)\le {{{\mathcal{T}}}}({U}^{{\prime} })$$ T ( U ) ≤ T ( U ′ ) where $${U}^{{\prime} }$$ U ′ is any exactly implementable unitary with $$d({U}^{{\prime} },W)\le \epsilon$$ d ( U ′ , W ) ≤ ϵ . d(. , .) is the global phase invariant distance. Our algorithm can also be used to determine the (minimum) T-depth as well as the minimum non-Clifford-gate count or depth required to implement any multi-qubit unitary with a finite universal gate set like Clifford+CS, Clifford+V, etc. For small enough ϵ, we can synthesize the optimal circuits.
نوع الوثيقة: article
وصف الملف: electronic resource
اللغة: English
تدمد: 2056-6387
Relation: https://doaj.org/toc/2056-6387
DOI: 10.1038/s41534-022-00651-y
URL الوصول: https://doaj.org/article/35cc068b9e4346fda736adf7711755a4
رقم الأكسشن: edsdoj.35cc068b9e4346fda736adf7711755a4
قاعدة البيانات: Directory of Open Access Journals
الوصف
تدمد:20566387
DOI:10.1038/s41534-022-00651-y