Simultaneous estimation of multiple eigenvalues with short-depth quantum
circuit on early fault-tolerant quantum computers
- URL: http://arxiv.org/abs/2303.05714v4
- Date: Sun, 1 Oct 2023 01:37:23 GMT
- Title: Simultaneous estimation of multiple eigenvalues with short-depth quantum
circuit on early fault-tolerant quantum computers
- Authors: Zhiyan Ding and Lin Lin
- Abstract summary: 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.
- Score: 5.746732081406236
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: 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.
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