Quantum signal processing (QSP) has emerged as a promising framework to manipulate and determine properties of quantum systems. QSP not only unifies most existing quantum algorithms but also provides tools to discover new ones. Quantum signal processing is applicable to single-qubit or multiqubit systems that can be “qubitized” so one can exploit the SU(2) structure of system evolution within special invariant two-dimensional subspaces. In the context of quantum algorithms, this SU(2) structure is artificially imposed on the system through highly nonlocal evolution operators that are difficult to implement on near-term quantum devices. In this work, we propose QSP protocols for the infinite-dimensional Onsager Lie algebra, which is relevant to the physical dynamics of quantum devices that can simulate the transverse-field Ising model. To this end, we consider QSP sequences in the Heisenberg picture, allowing us to exploit the emergent SU(2) structure in momentum space and “synthesize” QSP sequences for the Onsager algebra. Our results demonstrate a concrete connection between QSP techniques and noisy intermediate scale quantum protocols. We provide examples and applications of our approach in diverse fields ranging from space-time dual quantum circuits and quantum simulation to quantum control.
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Scattering in the Ising model with the quantum Lanczos algorithm *
Abstract Time evolution and scattering simulation in phenomenological models are of great interest for testing and validating the potential for near-term quantum computers to simulate quantum field theories. Here, we simulate one-particle propagation and two-particle scattering in the one-dimensional transverse Ising model for 3 and 4 spatial sites with periodic boundary conditions on a quantum computer. We use the quantum Lanczos algorithm to obtain all energy levels and corresponding eigenstates of the system. We simplify the quantum computation by taking advantage of the symmetries of the system. These results enable us to compute one- and two-particle transition amplitudes, particle numbers for spatial sites, and the transverse magnetization as functions of time. The quantum circuits were executed on various IBM Q superconducting hardware. The experimental results are in very good agreement with the values obtained using exact diagonalization.
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- Award ID(s):
- 1937008
- NSF-PAR ID:
- 10316461
- Date Published:
- Journal Name:
- New Journal of Physics
- Volume:
- 23
- Issue:
- 4
- ISSN:
- 1367-2630
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1088/1367-2630/abe63d
