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Controlled gates for multi-level quantum computation

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Abstract

Multi-level (ML) quantum logic can potentially reduce the number of inputs/outputs or quantum cells in a quantum circuit which is a limitation in current quantum technology. In this paper we propose theorems about ML-quantum and reversible logic circuits. New efficient implementations for some basic controlled ML-quantum logic gates, such as three-qudit controlled NOT, Cycle, and Self Shift gates are proposed. We also propose lemmas about r-level quantum arrays and the number of required gates for an arbitrary n-qudit ML gate. An equivalent definition of quantum cost (QC) of binary quantum gates for ML-quantum gates is introduced and QC of controlled quantum gates is calculated.

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Authors and Affiliations

  1. International Center for Science, High Technology and Environmental Sciences, Shahid Bahonar Kerman University, Kerman, Iran

    Majid Mohammadi

  2. Department of Computer Engineering, Shahid Bahonar Kerman University, Kerman, Iran

    Aliakbar Niknafs

  3. Department of Electrical and Computer Engineering, Shahid Beheshti University, Tehran, Iran

    Mohammad Eshghi

Authors
  1. Majid Mohammadi
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  2. Aliakbar Niknafs
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  3. Mohammad Eshghi
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Correspondence to Majid Mohammadi.

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Mohammadi, M., Niknafs, A. & Eshghi, M. Controlled gates for multi-level quantum computation. Quantum Inf Process 10, 241–256 (2011). https://doi.org/10.1007/s11128-010-0192-z

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  • DOI: https://doi.org/10.1007/s11128-010-0192-z

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