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  • Simultaneous estimation of multiple eigenvalues with short-depth quantum circuit on early fault-tolerant quantum computers
Title: Simultaneous estimation of multiple eigenvalues with short-depth quantum circuit on early fault-tolerant quantum computers
We introduce a multi-modal, multi-level quantum complex exponential least squares (MM-QCELS) method to simultaneously estimate multiple eigenvalues of a quantum Hamiltonian on early fault-tolerant quantum computers. Our theoretical analysis demonstrates that the algorithm exhibits Heisenberg-limited scaling in terms of circuit depth and total cost. Notably, the proposed quantum circuit utilizes just one ancilla qubit, and with appropriate initial state conditions, it achieves significantly shorter circuit depths compared to circuits based on quantum phase estimation (QPE). Numerical results suggest that compared to QPE, the circuit depth can be reduced by around two orders of magnitude under several settings for estimating ground-state and excited-state energies of certain quantum systems.  more » « less
Award ID(s):
2016245
PAR ID:
10506499
Author(s) / Creator(s):
;
Publisher / Repository:
Quantum Publishers
Date Published:
Journal Name:
Quantum
Volume:
7
ISSN:
2521-327X
Page Range / eLocation ID:
1136
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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