Direct Gradient Computation for Barren Plateaus in Parameterized Quantum Circuits

• URL: http://arxiv.org/abs/2503.05145v2
• Date: Wed, 16 Apr 2025 08:42:49 GMT
• Title: Direct Gradient Computation for Barren Plateaus in Parameterized Quantum Circuits
• Authors: Yuhan Yao, Yoshihiko Hasegawa,
• Abstract summary: barren plateau phenomenon is where parametrized quantum circuits become vanishingly small.<n>Previous studies attempted to explain the barren plateau phenomenon using the Weingarten formula.<n>Our approach provides a more accurate framework for analyzing quantum circuit optimization.
• Score: 1.6574413179773757
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The barren plateau phenomenon, where the gradients of parametrized quantum circuits become vanishingly small, poses a significant challenge in quantum machine learning. While previous studies attempted to explain the barren plateau phenomenon using the Weingarten formula, the reliance on the Weingarten formula leads to inaccurate conclusions. In this study, we consider a unitary operator \(U\) consisting of rotation gates and perform an exact calculation of the expectation required for the gradient computation. Our approach allows us to obtain the gradient expectation and variance directly. Our analysis reveals that gradient expectations are not zero, as opposed to the results derived using the Weingarten formula, but depend on the number of qubits in the system. Furthermore, we demonstrate how the number of effective parameters, circuit depth, and gradient variance are interconnected in deep parameterized quantum circuits. Numerical simulations further confirm the validity of our theoretical results. Our approach provides a more accurate framework for analyzing quantum circuit optimization.

Related papers

• Improve Variational Quantum Eigensolver by Many-Body Localization [0.18416014644193066]
  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'
  arXiv  Detail & Related papers  (2024-07-16T10:49:40Z)
• Here comes the SU(N): multivariate quantum gates and gradients [1.7809113449965783]
  Variational quantum algorithms use non-commuting optimization methods to find optimal parameters for a parametrized quantum circuit. Here, we propose a gate which fully parameterizes the special unitary group $mathrm(N) gate. We show that the proposed gate and its optimization satisfy the quantum limit of the unitary group.
  arXiv  Detail & Related papers  (2023-03-20T18:00:04Z)
• 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)
• Quantum gradient evaluation through quantum non-demolition measurements [0.0]
  We discuss a Quantum Non-Demolition Measurement protocol to estimate the derivatives of a cost function with a quantum computer. This is a key step for the implementation of variational quantum circuits.
  arXiv  Detail & Related papers  (2023-01-17T19:00:08Z)
• Escaping from the Barren Plateau via Gaussian Initializations in Deep Variational Quantum Circuits [63.83649593474856]
  Variational quantum circuits have been widely employed in quantum simulation and quantum machine learning in recent years.<n>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.<n>This result leads to a general standpoint that deep quantum circuits would not be feasible for practical tasks.
  arXiv  Detail & Related papers  (2022-03-17T15:06:40Z)
• 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)
• Toward Trainability of Deep Quantum Neural Networks [87.04438831673063]
  Quantum Neural Networks (QNNs) with random structures have poor trainability due to the exponentially vanishing gradient as the circuit depth and the qubit number increase. We provide the first viable solution to the vanishing gradient problem for deep QNNs with theoretical guarantees.
  arXiv  Detail & Related papers  (2021-12-30T10:27:08Z)
• Analytical and experimental study of center line miscalibrations in M\o lmer-S\o rensen gates [51.93099889384597]
  We study a systematic perturbative expansion in miscalibrated parameters of the Molmer-Sorensen entangling gate. We compute the gate evolution operator which allows us to obtain relevant key properties. We verify the predictions from our model by benchmarking them against measurements in a trapped-ion quantum processor.
  arXiv  Detail & Related papers  (2021-12-10T10:56:16Z)
• Mitigated barren plateaus in the time-nonlocal optimization of analog quantum-algorithm protocols [0.0]
  algorithmic classes such as variational quantum algorithms have been shown to suffer from barren plateaus. We present an approach to quantum algorithm optimization that is based on trainable Fourier coefficients of Hamiltonian system parameters.
  arXiv  Detail & Related papers  (2021-11-15T21:13:10Z)
• Bosonic field digitization for quantum computers [62.997667081978825]
  We address the representation of lattice bosonic fields in a discretized field amplitude basis. We develop methods to predict error scaling and present efficient qubit implementation strategies.
  arXiv  Detail & Related papers  (2021-08-24T15:30:04Z)
• Boundaries of quantum supremacy via random circuit sampling [69.16452769334367]
  Google's recent quantum supremacy experiment heralded a transition point where quantum computing performed a computational task, random circuit sampling. We examine the constraints of the observed quantum runtime advantage in a larger number of qubits and gates.
  arXiv  Detail & Related papers  (2020-05-05T20:11:53Z)

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.