Optimal implementation of quantum gates with two controls

Jens Palsberg; Nengkun Yu

doi:10.1016/j.laa.2024.03.039

Optimal implementation of quantum gates with two controls

Jens Palsberg
, Nengkun Yu

Computer Science

University of California at Los Angeles

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We give a detailed proof of a well-known theorem in quantum computing. The theorem characterizes the number of two-qubit gates that is necessary for implementing three-qubit quantum gates with two controls. For example, the theorem implies that five 2-qubit gates are necessary for implementing the Toffoli gate. No detailed proof was available earlier.

Original language	English
Pages (from-to)	206-261
Number of pages	56
Journal	Linear Algebra and Its Applications
Volume	694
DOIs	https://doi.org/10.1016/j.laa.2024.03.039
State	Published - Aug 1 2024

Keywords

Optimality
Quantum computing
Unitary matrices

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10.1016/j.laa.2024.03.039

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abstract = "We give a detailed proof of a well-known theorem in quantum computing. The theorem characterizes the number of two-qubit gates that is necessary for implementing three-qubit quantum gates with two controls. For example, the theorem implies that five 2-qubit gates are necessary for implementing the Toffoli gate. No detailed proof was available earlier.",

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AB - We give a detailed proof of a well-known theorem in quantum computing. The theorem characterizes the number of two-qubit gates that is necessary for implementing three-qubit quantum gates with two controls. For example, the theorem implies that five 2-qubit gates are necessary for implementing the Toffoli gate. No detailed proof was available earlier.

KW - Optimality

KW - Quantum computing

KW - Unitary matrices

UR - https://www.scopus.com/pages/publications/85190977506

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DO - 10.1016/j.laa.2024.03.039

M3 - Article

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VL - 694

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EP - 261

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

Optimal implementation of quantum gates with two controls

Abstract

Keywords

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