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Quantum circuits for computing Hamming distance requiring fewer T gates

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Abstract

The so-called Hamming distance measures the difference between two binary strings A and B. In simplified form, it measures the number of changes in A to get B. This type of distance is very useful in classical computing in applications such as error correction. It is also advantageous in quantum computing, being for example widely used in quantum machine learning. Since current quantum computers have limited resources, this type of distance is particularly attractive because it can be computed using fewer qubits and operations than other distances such as Euclidean or Manhattan distances. In this paper, two circuits for calculating Hamming distances using exclusively Clifford+T gates are presented. The aim of both circuits is to reduce the quantum cost and number of T gates needed to compute the Hamming distance. The T gate is more expensive than the other gates, so this reduction will have a significant impact on the total cost of the circuits. Furthermore, the proposed circuits are implemented using only Clifford+T gates. The circuits implemented exclusively with this group of gates are compatible with proven error detection and correction codes.

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Funding

This work has been supported by the projects: S-MIP-21-53 (funded by the Research Council of Lithuania), PID2021-123278OB-I00 and PID2021-127836NB-I00 (funded by MCIN/AEI/10.13039/501100011033/ FEDER “A way to make Europe”); PID2020-119082RB-C22 (funded by MCIN/AEI/10.13039/501100011033); AYUD/2021/50994 and FC-GRUPIN-IDI/2018/000193 (funded by Gobierno del Principado de Asturias); Quantum Spain project funded by the Ministry of Economic Affairs and Digital Transformation of the Spanish Government and the European Union through the Recovery, Transformation and Resilience Plan - NextGenerationEU; and PID2021-123461NB-C22 (funded by MICIIN).

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Authors and Affiliations

  1. Institute of Data Science and Digital Technologies, Vilnius University, Vilnius, Lithuania

    Francisco Orts

  2. Informatics Department, Agrifood Campus of International Excellence (ceiA3), University of Almería, Almería, Spain

    Gloria Ortega & Ester M. Garzón

  3. Informatics Department, University of Oviedo, Oviedo, Spain

    Elías F. Combarro

  4. Mathematics Department, University of Oviedo, Oviedo, Spain

    Ignacio F. Rúa

Authors
  1. Francisco Orts
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  2. Gloria Ortega
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  3. Elías F. Combarro
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  4. Ignacio F. Rúa
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  5. Ester M. Garzón
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Contributions

FO involved in writing—original draft, provided software, and involved in execution of experiments; GO involved in writing—review and editing, done validation, and involved in visualization; EFC involved in orchestration, provided idea source, and involved in writing—original draft; IFR provided idea source, involved in formal analysis, and involved in writing—original draft; EMG involved in writing—review and editing, done validation, and involved in visualization.

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Correspondence to Francisco Orts.

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Orts, F., Ortega, G., Combarro, E.F. et al. Quantum circuits for computing Hamming distance requiring fewer T gates. J Supercomput 80, 12527–12542 (2024). https://doi.org/10.1007/s11227-024-05916-1

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