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Krylov diagonalization of large many-body Hamiltonians on a quantum processor.
Nobuyuki Yoshioka1,2, Mirko Amico3, William Kirby4
1Department of Applied Physics, University of Tokyo, Bunkyo-ku, Japan. ny.nobuyoshioka@gmail.com.
Nature Communications
|June 24, 2025
Summary
Researchers used a superconducting quantum processor and the Krylov quantum diagonalization algorithm to estimate low energies of many-body systems. This method shows exponential convergence, offering a scalable alternative to variational quantum algorithms for quantum computing.
Area of Science:
- Computational quantum sciences
- Quantum computing algorithms
- Many-body physics
Background:
- Estimating low energies of many-body systems is crucial for computational quantum sciences.
- Variational quantum algorithms face challenges in convergence and scalability on current quantum processors.
- There is a need for alternative approaches for large-scale quantum experiments on pre-fault-tolerant devices.
Purpose of the Study:
- To compute eigenenergies of quantum many-body systems on a superconducting quantum processor.
- To explore the efficacy of the Krylov quantum diagonalization algorithm for quantum many-body systems.
- To demonstrate a scalable method for ground state energy estimation.
Main Methods:
- Utilized a superconducting quantum processor to execute Trotterized unitary evolutions.
- Constructed subspaces of the many-body Hilbert space.
- Applied the Krylov quantum diagonalization algorithm, analogous to classical diagonalization.
- Classically diagonalized many-body interacting Hamiltonians within the constructed subspaces.
Main Results:
- Successfully computed eigenenergies for quantum many-body systems on two-dimensional lattices up to 56 sites.
- Demonstrated exponential convergence towards an estimate of the ground state energy.
- Validated the Krylov quantum diagonalization algorithm on a quantum processor.
Conclusions:
- Quantum diagonalization algorithms can complement classical methods for quantum system computations.
- The Krylov quantum diagonalization algorithm offers a promising approach for scalable quantum energy estimation.
- This work paves the way for more advanced quantum simulations on near-term quantum devices.
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