https://doi.org/10.1140/epjqt/s40507-025-00347-0
Research
A probabilistic quantum algorithm for imaginary-time evolution based on Taylor expansion
1
Future Research Laboratory, China Mobile Research Institute, 100053, Beijing, China
2
School of Science, Beijing University of Posts and Telecommunications, 100876, Beijing, China
3
School of Transportation, Beijing Jiaotong University, 100044, Beijing, China
4
School of Electronic Engineering, Beijing University of Posts and Telecommunications, 100876, Beijing, China
5
Beijing Key Laboratory of Space-Ground Interconnection and Convergence, Beijing University of Posts and Telecommunications, 100876, Beijing, China
6
State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, 100876, Beijing, China
Received:
20
August
2024
Accepted:
27
March
2025
Published online:
3
April
2025
Imaginary-time evolution is a powerful tool for obtaining the ground state of a quantum system, but the complexity of classical algorithms designed for simulating imaginary-time evolution will increase significantly as the size of the quantum system becomes larger. Here, a probabilistic quantum algorithm based on Taylor expansion for implementing imaginary-time evolution is introduced. For Hamiltonians composed of Pauli product terms, the quantum circuit requires only a single ancillary qubit and is exclusively constructed using elementary single-qubit and two-qubit gates. Furthermore, similar principles are used to extend the algorithm to the case where the Hamiltonian takes a more general form. The algorithm only requires negligible precomputed numerical calculations, without the need for complex classical pre-mathematical calculations or optimization loops. We demonstrate the algorithm by solving the ground state energy of hydrogen molecules and Heisenberg Hamiltonians. Moreover, we conducted experiments on real quantum computers through the quantum cloud platform to find the ground state energy of Heisenberg Hamiltonians. Our work extends the methods for realizing imaginary-time evolution on quantum computers, and our algorithm exhibits potential for implementation on near-term quantum devices, particularly when the Hamiltonian consists of Pauli product terms.
Key words: Quantum algorithm / Linear combination of unitaries / Imaginary-time evolution / Ground state simulation
© The Author(s) 2025
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