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Direct Energy Gap Calculations in Heisenberg Spin Systems Using Superconducting Quantum Devices.

Boni Paul1,2, Sudhindu Bikash Mandal1, Kenji Sugisaki1,3,4,5

  • 1Centre for Quantum Engineering Research and Education, TCG Centres for Research and Education in Science and Technology, Kolkata, India.

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Summary

We developed a quantum algorithm for calculating spin-state energy gaps, crucial for spin chemistry. Our method is suitable for current quantum computers, achieving high accuracy on hardware demonstrations.

Keywords:
Heisenberg Hamiltonianmatch gatenoisy intermediate‐scale quantumquantum many body simulationsquantum noise suppressionquantum phase difference estimationquantum phase estimationspin‐state energy gap

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Area of Science:

  • Quantum Chemistry
  • Quantum Computing
  • Spin Physics

Background:

  • Accurate calculation of spin-state energy gaps is fundamental to understanding spin chemistry.
  • The Quantum Phase Difference Estimation (QPDE) algorithm offers a direct quantum computation method for these gaps.
  • Current QPDE implementations often require quantum circuits too deep for noisy intermediate-scale quantum (NISQ) devices.

Purpose of the Study:

  • To assess the feasibility of applying the QPDE algorithm to multi-spin systems relevant to molecular magnetism.
  • To investigate the suitability of QPDE for NISQ devices by analyzing circuit depth.
  • To demonstrate the practical application of QPDE on quantum hardware for calculating spin-state energy gaps.

Main Methods:

  • Applied the QPDE algorithm to two- and three-spin Heisenberg Hamiltonians.
  • Investigated various Hamiltonian geometries and coupling strengths, including symmetric, asymmetric, and spin-frustrated configurations.
  • Analyzed the quantum circuit depth for the time-evolution operator, noting its match gate-like structure.

Main Results:

  • The quantum circuit for the time-evolution operator demonstrated a constant depth, indicating NISQ suitability.
  • Proof-of-principle calculations were performed on an IBM quantum processor.
  • The hardware demonstrations achieved 85%-96% accuracy in determining spin-state energy gaps.

Conclusions:

  • The QPDE algorithm, with its constant-depth circuit structure, is well-suited for NISQ implementation in spin chemistry.
  • This work represents a significant step towards practical quantum computations for complex molecular spin systems.
  • The high accuracy achieved in hardware demonstrations validates the potential of QPDE for real-world applications.