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PreprintarXiv licencearXiv

Time reversal of complex evolution on a quantum computer

  • Mahdi Kourehpaz
  • Dima L. Shepelyansky
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Abstract

The Boltzmann-Loschmidt dispute in 1876-1877 discussed the problem of time reversal of ther- malization from time reversible classical equations of motion. Here, 150 years later, we highlight this problem in the frame of quantum computing. A quantum protocol is proposed that allows to perform a time reversal of complex evolution in the regime of many-body quantum chaos with many qubits. The system represents an evolution of qubits on a square lattice with inter-qubit next-nearest static couplings with a driven pulsed magnetic field. The system entropy grows rapidly to maximal values but returns to initial small values after time reversal. This time reversal is shown to be stable with respect to quantum gate imperfections. However, similar to the Lorenz butterfly effect, there is the butterfly effect of qubit when inversion of only one qubit breaks time reversibility of the whole system. It is argued that this protocol is accessible to nowadays quantum computers and annealers with hundreds of qubits.

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Cite

BibTeXRIS
BibTeX
@misc{kourehpaz2026time,
  title = {{Time reversal of complex evolution on a quantum computer}},
  author = {Mahdi Kourehpaz and Dima L. Shepelyansky},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.22489},
  eprint = {2608.22489},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.22489},
}
RIS
TY  - UNPB
TI  - Time reversal of complex evolution on a quantum computer
AU  - Mahdi Kourehpaz
AU  - Dima L. Shepelyansky
PY  - 2026
DA  - 2026/08/23
PB  - arXiv
DO  - 10.48550/arxiv.2608.22489
UR  - https://arxiv.org/abs/2608.22489
AB  - The Boltzmann-Loschmidt dispute in 1876-1877 discussed the problem of time reversal of ther- malization from time reversible classical equations of motion. Here, 150 years later, we highlight this problem in the frame of quantum computing. A quantum protocol is proposed that allows to perform a time reversal of complex evolution in the regime of many-body quantum chaos with many qubits. The system represents an evolution of qubits on a square lattice with inter-qubit next-nearest static couplings with a driven pulsed magnetic field. The system entropy grows rapidly to maximal values but returns to initial small values after time reversal. This time reversal is shown to be stable with respect to quantum gate imperfections. However, similar to the Lorenz butterfly effect, there is the butterfly effect of qubit when inversion of only one qubit breaks time reversibility of the whole system. It is argued that this protocol is accessible to nowadays quantum computers and annealers with hundreds of qubits.
ER  -