Variational quantum simulation of critical Ising model with symmetry averaging

• URL: http://arxiv.org/abs/2210.15053v2
• Date: Sat, 29 Apr 2023 00:48:11 GMT
• Title: Variational quantum simulation of critical Ising model with symmetry averaging
• Authors: Troy J. Sewell, Ning Bao, Stephen P. Jordan
• Abstract summary: We investigate the use of deep multi-scale entanglement renormalization circuits as a variational ansatz for ground states of gapless systems. We find that DMERA strongly outperforms a standard QAOA-style ansatz, and that a major source of systematic error in correlation functions approximated using DMERA is the breaking of the translational and Kramers-Wannier symmetries of the transverse-field Ising model.
• Score: 0.2578242050187029
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Here, we investigate the use of deep multi-scale entanglement renormalization (DMERA) circuits as a variational ansatz for ground states of gapless systems. We use the exactly-solvable one-dimensional critical transverse-field Ising model as a testbed. Numerically exact simulation of the ansatz can in this case be carried out to hundreds of qubits by exploiting efficient classical algorithms for simulating matchgate circuits. We find that, for this system, DMERA strongly outperforms a standard QAOA-style ansatz, and that a major source of systematic error in correlation functions approximated using DMERA is the breaking of the translational and Kramers-Wannier symmetries of the transverse-field Ising model. We are able to reduce this error by up to four orders of magnitude by symmetry averaging, without incurring additional cost in qubits or circuit depth. We propose that this technique for mitigating systematic error could be applied to NISQ simulations of physical systems with other symmetries.

Related papers

• Adaptive variational quantum dynamics simulations with compressed circuits and fewer measurements [4.2643127089535104]
  We show an improved version of the adaptive variational quantum dynamics simulation (AVQDS) method, which we call AVQDS(T) The algorithm adaptively adds layers of disjoint unitary gates to the ansatz circuit so as to keep the McLachlan distance, a measure of the accuracy of the variational dynamics, below a fixed threshold. We also show a method based on eigenvalue truncation to solve the linear equations of motion for the variational parameters with enhanced noise resilience.
  arXiv  Detail & Related papers  (2024-08-13T02:56:43Z)
• Matrix product state ansatz for the variational quantum solution of the Heisenberg model on Kagome geometries [0.0]
  We develop a quantum circuit ansatz inspired by the Density Matrix Renormalization Group (DMRG) algorithm. We find that, with realistic error rates, our DMRG-VQE hybrid algorithm delivers good results for strongly correlated systems.
  arXiv  Detail & Related papers  (2024-01-04T16:53:47Z)
• An Optimization-based Deep Equilibrium Model for Hyperspectral Image Deconvolution with Convergence Guarantees [71.57324258813675]
  We propose a novel methodology for addressing the hyperspectral image deconvolution problem. A new optimization problem is formulated, leveraging a learnable regularizer in the form of a neural network. The derived iterative solver is then expressed as a fixed-point calculation problem within the Deep Equilibrium framework.
  arXiv  Detail & Related papers  (2023-06-10T08:25:16Z)
• Tutorial: Calibration refinement in quantum annealing [0.3425341633647624]
  Quantum annealers are susceptible to nonidealities including crosstalk, device variation, and environmental noise. "shimming" can significantly improve performance, but often relies on ad-hoc methods that exploit symmetries in both the problem being solved and the quantum annealer itself. We introduce methods for finding exploitable symmetries in Ising models, and discuss how to use these symmetries to suppress unwanted bias.
  arXiv  Detail & Related papers  (2023-04-20T14:48:37Z)
• Formal Controller Synthesis for Markov Jump Linear Systems with Uncertain Dynamics [64.72260320446158]
  We propose a method for synthesising controllers for Markov jump linear systems. Our method is based on a finite-state abstraction that captures both the discrete (mode-jumping) and continuous (stochastic linear) behaviour of the MJLS. We apply our method to multiple realistic benchmark problems, in particular, a temperature control and an aerial vehicle delivery problem.
  arXiv  Detail & Related papers  (2022-12-01T17:36:30Z)
• Inverting brain grey matter models with likelihood-free inference: a tool for trustable cytoarchitecture measurements [62.997667081978825]
  characterisation of the brain grey matter cytoarchitecture with quantitative sensitivity to soma density and volume remains an unsolved challenge in dMRI. We propose a new forward model, specifically a new system of equations, requiring a few relatively sparse b-shells. We then apply modern tools from Bayesian analysis known as likelihood-free inference (LFI) to invert our proposed model.
  arXiv  Detail & Related papers  (2021-11-15T09:08:27Z)
• Performance of teleportation-based error correction circuits for bosonic codes with noisy measurements [58.720142291102135]
  We analyze the error-correction capabilities of rotation-symmetric codes using a teleportation-based error-correction circuit. We find that with the currently achievable measurement efficiencies in microwave optics, bosonic rotation codes undergo a substantial decrease in their break-even potential.
  arXiv  Detail & Related papers  (2021-08-02T16:12:13Z)
• Extracting Governing Laws from Sample Path Data of Non-Gaussian Stochastic Dynamical Systems [4.527698247742305]
  We infer equations with non-Gaussian L'evy noise from available data to reasonably predict dynamical behaviors. We establish a theoretical framework and design a numerical algorithm to compute the asymmetric L'evy jump measure, drift and diffusion. This method will become an effective tool in discovering the governing laws from available data sets and in understanding the mechanisms underlying complex random phenomena.
  arXiv  Detail & Related papers  (2021-07-21T14:50:36Z)
• Sampling asymmetric open quantum systems for artificial neural networks [77.34726150561087]
  We present a hybrid sampling strategy which takes asymmetric properties explicitly into account, achieving fast convergence times and high scalability for asymmetric open systems. We highlight the universal applicability of artificial neural networks, underlining the universal applicability of neural networks.
  arXiv  Detail & Related papers  (2020-12-20T18:25:29Z)
• Unbiased Gradient Estimation for Variational Auto-Encoders using Coupled Markov Chains [34.77971292478243]
  The variational auto-encoder (VAE) is a deep latent variable model that has two neural networks in an autoencoder-like architecture. We develop a training scheme for VAEs by introducing unbiased estimators of the log-likelihood gradient. We show experimentally that VAEs fitted with unbiased estimators exhibit better predictive performance.
  arXiv  Detail & Related papers  (2020-10-05T08:11:55Z)
• Quantum-optimal-control-inspired ansatz for variational quantum algorithms [105.54048699217668]
  A central component of variational quantum algorithms (VQA) is the state-preparation circuit, also known as ansatz or variational form. Here, we show that this approach is not always advantageous by introducing ans"atze that incorporate symmetry-breaking unitaries. This work constitutes a first step towards the development of a more general class of symmetry-breaking ans"atze with applications to physics and chemistry problems.
  arXiv  Detail & Related papers  (2020-08-03T18:00:05Z)

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.