Improve Variational Quantum Eigensolver by Many-Body Localization

• URL: http://arxiv.org/abs/2407.11589v2
• Date: Thu, 5 Sep 2024 12:15:25 GMT
• Title: Improve Variational Quantum Eigensolver by Many-Body Localization
• Authors: Li Xin, Zhang-qi Yin,
• Abstract summary: Many-body localized floquet system has phase avoiding thermalization. We studied the variance of gradient for parameter updates under this circuit. We designed a new type of variational ansatz, called the'many-body localization ansatz'
• Score: 0.18416014644193066
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Variational quantum algorithms have been widely demonstrated in both experimental and theoretical contexts to have extensive applications in quantum simulation, optimization, and machine learning. However, the exponential growth in the dimension of the Hilbert space results in the phenomenon of vanishing parameter gradients in the circuit as the number of qubits and circuit depth increase, known as the barren plateau phenomena. In recent years, research in non-equilibrium statistical physics has led to the discovery of the realization of many-body localization. As a type of floquet system, many-body localized floquet system has phase avoiding thermalization with an extensive parameter space coverage and have been experimentally demonstrated can produce time crystals. We applied this circuit to the variational quantum algorithms for the calculation of many-body ground states and studied the variance of gradient for parameter updates under this circuit. We found that this circuit structure can effectively avoid barren plateaus. We also analyzed the entropy growth, information scrambling, and optimizer dynamics of this circuit. Leveraging this characteristic, we designed a new type of variational ansatz, called the 'many-body localization ansatz'. We applied it to solve quantum many-body ground states and examined its circuit properties. Our numerical results show that our ansatz significantly improved the variational quantum algorithm.

Related papers

• Efficient estimation of trainability for variational quantum circuits [43.028111013960206]
  We find an efficient method to compute the cost function and its variance for a wide class of variational quantum circuits. This method can be used to certify trainability for variational quantum circuits and explore design strategies that can overcome the barren plateau problem.
  arXiv  Detail & Related papers  (2023-02-09T14:05:18Z)
• Universality of critical dynamics with finite entanglement [68.8204255655161]
  We study how low-energy dynamics of quantum systems near criticality are modified by finite entanglement. Our result establishes the precise role played by entanglement in time-dependent critical phenomena.
  arXiv  Detail & Related papers  (2023-01-23T19:23:54Z)
• Trapped-Ion Quantum Simulation of Collective Neutrino Oscillations [55.41644538483948]
  We study strategies to simulate the coherent collective oscillations of a system of N neutrinos in the two-flavor approximation using quantum computation. We find that the gate complexity using second order Trotter- Suzuki formulae scales better with system size than with other decomposition methods such as Quantum Signal Processing.
  arXiv  Detail & Related papers  (2022-07-07T09:39:40Z)
• Gaussian initializations help deep variational quantum circuits escape from the barren plateau [87.04438831673063]
  Variational quantum circuits have been widely employed in quantum simulation and quantum machine learning in recent years. However, quantum circuits with random structures have poor trainability due to the exponentially vanishing gradient with respect to the circuit depth and the qubit number. This result leads to a general belief that deep quantum circuits will not be feasible for practical tasks.
  arXiv  Detail & Related papers  (2022-03-17T15:06:40Z)
• Surviving The Barren Plateau in Variational Quantum Circuits with Bayesian Learning Initialization [0.0]
  Variational quantum-classical hybrid algorithms are seen as a promising strategy for solving practical problems on quantum computers in the near term. Here, we introduce the fast-and-slow algorithm, which uses gradients to identify a promising region in Bayesian space. Our results move variational quantum algorithms closer to their envisioned applications in quantum chemistry, optimization, and quantum simulation problems.
  arXiv  Detail & Related papers  (2022-03-04T17:48:57Z)
• Numerical Simulations of Noisy Quantum Circuits for Computational Chemistry [51.827942608832025]
  Near-term quantum computers can calculate the ground-state properties of small molecules. We show how the structure of the computational ansatz as well as the errors induced by device noise affect the calculation.
  arXiv  Detail & Related papers  (2021-12-31T16:33:10Z)
• Quantum algorithms for quantum dynamics: A performance study on the spin-boson model [68.8204255655161]
  Quantum algorithms for quantum dynamics simulations are traditionally based on implementing a Trotter-approximation of the time-evolution operator. variational quantum algorithms have become an indispensable alternative, enabling small-scale simulations on present-day hardware. We show that, despite providing a clear reduction of quantum gate cost, the variational method in its current implementation is unlikely to lead to a quantum advantage.
  arXiv  Detail & Related papers  (2021-08-09T18:00:05Z)
• Continuous-time dynamics and error scaling of noisy highly-entangling quantum circuits [58.720142291102135]
  We simulate a noisy quantum Fourier transform processor with up to 21 qubits. We take into account microscopic dissipative processes rather than relying on digital error models. We show that depending on the dissipative mechanisms at play, the choice of input state has a strong impact on the performance of the quantum algorithm.
  arXiv  Detail & Related papers  (2021-02-08T14:55:44Z)
• Capacity and quantum geometry of parametrized quantum circuits [0.0]
  Parametrized quantum circuits can be effectively implemented on current devices. We evaluate the capacity and trainability of these circuits using the geometric structure of the parameter space. Our results enhance the understanding of parametrized quantum circuits for improving variational quantum algorithms.
  arXiv  Detail & Related papers  (2021-02-02T18:16:57Z)
• Exploring entanglement and optimization within the Hamiltonian Variational Ansatz [0.4881924950569191]
  We study a family of quantum circuits called the Hamiltonian Variational Ansatz (HVA) HVA exhibits favorable structural properties such as mild or entirely absent barren plateaus and a restricted state space. HVA can find accurate approximations to the ground states of a modified Haldane-Shastry Hamiltonian on a ring.
  arXiv  Detail & Related papers  (2020-08-07T01:28:26Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.