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High-precision and low-depth quantum algorithm design for eigenstate problems.

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This study introduces a novel quantum algorithm for precisely estimating quantum system properties. The algorithm demonstrates efficient scaling and robustness, even on current quantum hardware.

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Area of Science:

  • Quantum Computing
  • Quantum Algorithms
  • Computational Physics

Background:

  • Estimating quantum system eigenstate properties is a significant challenge for both classical and quantum computation.
  • Existing universal quantum algorithms often rely on idealized models that are suboptimal for practical quantum circuit implementation.

Purpose of the Study:

  • To present a full-stack quantum algorithm design for accurate eigenenergy and eigenstate property estimation.
  • To achieve high precision and favorable scaling with system size in quantum simulations.

Main Methods:

  • Developed a quantum algorithm with a gate complexity of O(ε⁻¹ log(1/ε)) for generic Hamiltonians.
  • Designed circuits with near-optimal system-size scaling for lattice Hamiltonians, accommodating local qubit connectivity.
  • Implemented the algorithm on IBM quantum devices, utilizing up to 2000 two-qubit and 20,000 single-qubit gates.

Main Results:

  • Achieved high-precision eigenenergy estimation for Heisenberg-type Hamiltonians on real quantum hardware.
  • Demonstrated logarithmic dependence on inverse precision (ε) for gate complexity in generic Hamiltonian simulations.
  • Showcased noise robustness and low overhead in circuit compilation for lattice and molecular problems.

Conclusions:

  • The presented full-stack quantum algorithm offers a practical and efficient approach to estimating quantum system properties.
  • The algorithm's performance on IBM quantum devices validates its potential for tackling complex quantum problems with improved accuracy and scalability.
  • This work advances the practical application of quantum algorithms for scientific discovery.