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Interaction-free measurements and counterfactual computation in IBM quantum computers

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Abstract

The possibility of interaction-free measurements and counterfactual computations is a striking feature of quantum mechanics pointed out around 20 years ago. We have designed simple quantum circuits that realize both phenomena in real 5-qubit, 15-qubit and 20-qubit IBM quantum computers. In particular, counterfactual computation in its simplest form (Jozsa protocol) cannot be directly implemented in present quantum computers, requiring the design of a modified quantum circuit. The results are in general close to the theoretical expectations. For the larger circuits (with numerous gates and consequently larger errors), we implement a simple error mitigation procedure which improve appreciably the performance.

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Notes

  1. The Mitchison and Jozsa bound has been discussed in refs. [5,6,7].

  2. We have verified this in the ibmqx2 5-bit quantum computer [18]. Namely, about 14% of the outputs (instead of the theoretical 0%) correspond to a state that has no interpretation in that context.

  3. This is equivalent to reset the q1 qubit at \(|0\rangle \). However, that operation is not yet supported by the IBM quantum computer.

  4. Alternatively, one can use the readout errors for the different qubits provided by the IBM Quantum Experience platform everyday [18]. The result is similar albeit less accurate.

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Acknowledgements

We thank E. López and G. Sierra for inspiring conversations and advise. We also thank the IBM Quantum team for making multiple devices available via the IBM Quantum Experience. The access to the IBM Quantum Experience has been provided by the CSIC IBM Q Hub. We acknowledge the SEV-2016-0597 of the Centro de Excelencia Severo Ochoa Programme. B.Z. is further supported by the Programa Atracción de Talento de la Comunidad de Madrid under Grant no. 2017-T2/TIC-5455, from the Comunidad de Madrid/UAM “Proyecto de Jovenes Investigadores” Grant no. SI1/PJI/2019-00294, from Spanish “Proyectos de I+D de Generacion de Conocimiento” via grants PGC2018-096646-A-I00 and PGC2018-095161-B-I00.

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  1. Instituto de Física Teórica, IFT-UAM/CSIC, Universidad Autónoma de Madrid, Cantoblanco, Madrid, Spain

    J. Alberto Casas & Bryan Zaldivar

  2. Departamento de Física Teórica, Universidad Autónoma de Madrid, Cantoblanco, Madrid, Spain

    Bryan Zaldivar

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  1. J. Alberto Casas
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Casas, J.A., Zaldivar, B. Interaction-free measurements and counterfactual computation in IBM quantum computers. Quantum Inf Process 20, 114 (2021). https://doi.org/10.1007/s11128-021-03055-7

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