SciPost Phys. 12, 122 (2022) ·
published 8 April 2022
|
· pdf
Simulating the dynamics of many-body quantum systems is believed to be one of the first fields that quantum computers can show a quantum advantage over classical computers. Noisy intermediate-scale quantum (NISQ) algorithms aim at effectively using the currently available quantum hardware. For quantum simulation, various types of NISQ algorithms have been proposed with individual advantages as well as challenges.
In this work, we propose a new algorithm, truncated Taylor quantum simulator (TQS), that shares the advantages of existing algorithms and alleviates some of the shortcomings. Our algorithm does not have any classical-quantum feedback loop and bypasses the barren plateau problem by construction. The classical part in our hybrid quantum-classical algorithm corresponds to a quadratically constrained quadratic program (QCQP) with a single quadratic equality constraint, which admits a semidefinite relaxation. The QCQP based classical optimization was recently introduced as the classical step in quantum assisted eigensolver (QAE), a NISQ algorithm for the Hamiltonian ground state problem. Thus, our work provides a conceptual unification between the NISQ algorithms for the Hamiltonian ground state problem and the Hamiltonian simulation. We recover differential equation-based NISQ algorithms for Hamiltonian simulation such as quantum assisted simulator (QAS) and variational quantum simulator (VQS) as particular cases of our algorithm.
We test our algorithm on some toy examples on current cloud quantum computers. We also provide a systematic approach to improve the accuracy of our algorithm.
Wayne J. Chetcuti, Tobias Haug, Leong-Chuan Kwek, Luigi Amico
SciPost Phys. 12, 033 (2022) ·
published 21 January 2022
|
· pdf
We study the persistent current in a system of SU($N$) fermions with
repulsive interaction confined in a ring-shaped potential and pierced by an
effective magnetic flux. By applying a combination of Bethe ansatz and
numerical analysis, we demonstrate that, as a combined effect of spin
correlations, interactions and applied flux a specific phenomenon can occur in
the system: spinon creation in the ground state. As a consequence, peculiar
features in the persistent current arise. The elementary flux quantum, which
fixes the persistent current periodicity, is observed to evolve from a single
particle one to an extreme case of fractional flux quantum, in which one
quantum is shared by all the particles. We show that the persistent current
depends on the number of spin components $N$, number of particles and
interaction in a specific way that in certain physical regimes has universality
traits. At integer filling fractions, the persistent current is suppressed
above a threshold of the repulsive interaction by the Mott spectral gap.
Despite its mesoscopic nature, the current displays a clear finite size scaling
behavior. Specific parity effects in the persistent current landscape hold.
