Emergence of noise-induced barren plateaus in arbitrary layered noise models

• URL: http://arxiv.org/abs/2310.08405v3
• Date: Wed, 13 Nov 2024 10:11:34 GMT
• Title: Emergence of noise-induced barren plateaus in arbitrary layered noise models
• Authors: Marco Schumann, Frank K. Wilhelm, Alessandro Ciani,
• Abstract summary: In variational quantum algorithms the parameters of a parameterized quantum circuit are optimized in order to minimize a cost function that encodes the solution of the problem. We discuss how, and in which sense, the phenomenon of noise-induced barren plateaus emerges in parameterized quantum circuits with a layered noise model.
• Score: 44.99833362998488
• License:
• Abstract: In variational quantum algorithms the parameters of a parameterized quantum circuit are optimized in order to minimize a cost function that encodes the solution of the problem. The barren plateau phenomenon manifests as an exponentially vanishing dependence of the cost function with respect to the variational parameters, and thus hampers the optimization process. We discuss how, and in which sense, the phenomenon of noise-induced barren plateaus emerges in parameterized quantum circuits with a layered noise model. Previous results have shown the existence of noise-induced barren plateaus in the presence of local Pauli noise [arXiv:2007.14384]. We extend these results analytically to arbitrary completely-positive trace preserving maps in two cases: 1) when a parameter-shift rule holds, 2) when the parameterized quantum circuit at each layer forms a unitary $2$-design. The second example shows how highly expressive unitaries give rise not only to standard barren plateaus [arXiv:1803.11173], but also to noise-induced ones. In the second part of the paper, we study numerically the emergence of noise-induced barren plateaus in QAOA circuits focusing on the case of MaxCut problems on $d$-regular graphs and amplitude damping noise.

Related papers

• Controlled phase gate in exchange coupled quantum dots affected by quasistatic charge noise [0.0]
  We study the influence of quasistatic noise in quantum dot detuning on the controlled phase gate for spin qubits. We show that an exponential decay of the sequential fidelity is still valid for the weak noise.
  arXiv  Detail & Related papers  (2023-12-20T10:05:56Z)
• Doubly Stochastic Models: Learning with Unbiased Label Noises and Inference Stability [85.1044381834036]
  We investigate the implicit regularization effects of label noises under mini-batch sampling settings of gradient descent. We find such implicit regularizer would favor some convergence points that could stabilize model outputs against perturbation of parameters. Our work doesn't assume SGD as an Ornstein-Uhlenbeck like process and achieve a more general result with convergence of approximation proved.
  arXiv  Detail & Related papers  (2023-04-01T14:09:07Z)
• Latent Class-Conditional Noise Model [54.56899309997246]
  We introduce a Latent Class-Conditional Noise model (LCCN) to parameterize the noise transition under a Bayesian framework. We then deduce a dynamic label regression method for LCCN, whose Gibbs sampler allows us efficiently infer the latent true labels. Our approach safeguards the stable update of the noise transition, which avoids previous arbitrarily tuning from a mini-batch of samples.
  arXiv  Detail & Related papers  (2023-02-19T15:24:37Z)
• High-Order Qubit Dephasing at Sweet Spots by Non-Gaussian Fluctuators: Symmetry Breaking and Floquet Protection [55.41644538483948]
  We study the qubit dephasing caused by the non-Gaussian fluctuators. We predict a symmetry-breaking effect that is unique to the non-Gaussian noise.
  arXiv  Detail & Related papers  (2022-06-06T18:02:38Z)
• Learning Noise via Dynamical Decoupling of Entangled Qubits [49.38020717064383]
  Noise in entangled quantum systems is difficult to characterize due to many-body effects involving multiple degrees of freedom. We develop and apply multi-qubit dynamical decoupling sequences that characterize noise that occurs during two-qubit gates.
  arXiv  Detail & Related papers  (2022-01-26T20:22:38Z)
• Modeling and mitigation of cross-talk effects in readout noise with applications to the Quantum Approximate Optimization Algorithm [0.0]
  Noise mitigation can be performed up to some error for which we derive upper bounds. Experiments on 15 (23) qubits using IBM's devices to test both the noise model and the error-mitigation scheme. We show that similar effects are expected for Haar-random quantum states and states generated by shallow-depth random circuits.
  arXiv  Detail & Related papers  (2021-01-07T02:19:58Z)
• Evaluating the noise resilience of variational quantum algorithms [0.0]
  We simulate the effects of different types of noise in state preparation circuits of variational quantum algorithms. We find that the inclusion of redundant parameterised gates makes the quantum circuits more resilient to noise.
  arXiv  Detail & Related papers  (2020-11-02T16:56:58Z)
• Noise-Induced Barren Plateaus in Variational Quantum Algorithms [0.3562485774739681]
  Variational Quantum Algorithms (VQAs) may be a path to quantum advantage on Noisy Intermediate-Scale Quantum (NISQ) computers. We rigorously prove a serious limitation for noisy VQAs, in that the noise causes the training landscape to have a barren plateau.
  arXiv  Detail & Related papers  (2020-07-28T17:52:21Z)
• Shape Matters: Understanding the Implicit Bias of the Noise Covariance [76.54300276636982]
  Noise in gradient descent provides a crucial implicit regularization effect for training over parameterized models. We show that parameter-dependent noise -- induced by mini-batches or label perturbation -- is far more effective than Gaussian noise. Our analysis reveals that parameter-dependent noise introduces a bias towards local minima with smaller noise variance, whereas spherical Gaussian noise does not.
  arXiv  Detail & Related papers  (2020-06-15T18:31:02Z)

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.