Augmenting Density Matrix Renormalization Group with Clifford Circuits

• URL: http://arxiv.org/abs/2405.09217v1
• Date: Wed, 15 May 2024 09:53:08 GMT
• Title: Augmenting Density Matrix Renormalization Group with Clifford Circuits
• Authors: Xiangjian Qian, Jiale Huang, Mingpu Qin,
• Abstract summary: We present the seamless integration of Clifford circuits within the Density Matrix Renormalization Group algorithm. This framework is useful not only for its current application but also for its potential to be easily adapted to various other numerical approaches.
• Score: 0.49157446832511503
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Density Matrix Renormalization Group (DMRG) or Matrix Product States (MPS) are widely acknowledged as highly effective and accurate methods for solving one-dimensional quantum many-body systems. However, the direct application of DMRG to the study two-dimensional systems encounters challenges due to the limited entanglement encoded in the wave-function ansatz. Conversely, Clifford circuits offer a promising avenue for simulating states with substantial entanglement, albeit confined to stabilizer states. In this work, we present the seamless integration of Clifford circuits within the DMRG algorithm, leveraging the advantages of both Clifford circuits and DMRG. This integration leads to a significant enhancement in simulation accuracy with small additional computational cost. Moreover, this framework is useful not only for its current application but also for its potential to be easily adapted to various other numerical approaches

Related papers

• Clifford Circuits Augmented Time-Dependent Variational Principle [0.49157446832511503]
  Recently proposed Clifford Circuits Augmented Matrix Product States (CA-MPS) seamlessly augments Density Matrix Renormalization Group with Clifford circuits. We generalize CA-MPS to the framework of Time-Dependent Variational Principle (TDVP) for time evolution simulations. We show that the Clifford circuits augmented TDVP method can reduce the entanglement entropy in the time evolution process.
  arXiv  Detail & Related papers  (2024-07-03T15:34:15Z)
• Clifford Dressed Time-Dependent Variational Principle [39.58317527488534]
  We propose an enhanced Time-Dependent Variational Principle (TDVP) algorithm for Matrix Product States (MPS) By leveraging the Clifford group, we introduce a Clifford dressed single-site 1-TDVP scheme. We validate the new algorithm numerically using various quantum many-body models, including both integrable and non-integrable systems.
  arXiv  Detail & Related papers  (2024-07-01T18:04:25Z)
• Two-Stage ML-Guided Decision Rules for Sequential Decision Making under Uncertainty [55.06411438416805]
  Sequential Decision Making under Uncertainty (SDMU) is ubiquitous in many domains such as energy, finance, and supply chains. Some SDMU are naturally modeled as Multistage Problems (MSPs) but the resulting optimizations are notoriously challenging from a computational standpoint. This paper introduces a novel approach Two-Stage General Decision Rules (TS-GDR) to generalize the policy space beyond linear functions. The effectiveness of TS-GDR is demonstrated through an instantiation using Deep Recurrent Neural Networks named Two-Stage Deep Decision Rules (TS-LDR)
  arXiv  Detail & Related papers  (2024-05-23T18:19:47Z)
• Quantum Krylov-Subspace Method Based Linear Solver [1.689689700250852]
  Quantum Krylov-subspace method (QKSM) is a hybrid classical-quantum algorithm. We introduce the quantum Krylov-subspace method based linear solver that not only reduces computational redundancy but also enhances efficiency and accuracy.
  arXiv  Detail & Related papers  (2024-05-10T09:50:06Z)
• Neutron-nucleus dynamics simulations for quantum computers [49.369935809497214]
  We develop a novel quantum algorithm for neutron-nucleus simulations with general potentials. It provides acceptable bound-state energies even in the presence of noise, through the noise-resilient training method. We introduce a new commutativity scheme called distance-grouped commutativity (DGC) and compare its performance with the well-known qubit-commutativity scheme.
  arXiv  Detail & Related papers  (2024-02-22T16:33:48Z)
• Deep Learning Assisted Multiuser MIMO Load Modulated Systems for Enhanced Downlink mmWave Communications [68.96633803796003]
  This paper is focused on multiuser load modulation arrays (MU-LMAs) which are attractive due to their low system complexity and reduced cost for millimeter wave (mmWave) multi-input multi-output (MIMO) systems. The existing precoding algorithm for downlink MU-LMA relies on a sub-array structured (SAS) transmitter which may suffer from decreased degrees of freedom and complex system configuration. In this paper, we conceive an MU-LMA system employing a full-array structured (FAS) transmitter and propose two algorithms accordingly.
  arXiv  Detail & Related papers  (2023-11-08T08:54:56Z)
• Matrix Product Renormalization Group: Potential Universal Quantum Many-Body Solver [0.0]
  We propose an improved formulation of continuous tensor network algorithms, which we name a matrix product renormalization group (MPRG) MPRG is a universal quantum many-body solver, which potentially works at both zero and finite temperatures, in two and higher dimensions, and is even applicable to open quantum systems.
  arXiv  Detail & Related papers  (2022-12-26T19:00:01Z)
• Collaborative Intelligent Reflecting Surface Networks with Multi-Agent Reinforcement Learning [63.83425382922157]
  Intelligent reflecting surface (IRS) is envisioned to be widely applied in future wireless networks. In this paper, we investigate a multi-user communication system assisted by cooperative IRS devices with the capability of energy harvesting.
  arXiv  Detail & Related papers  (2022-03-26T20:37:14Z)
• Error mitigation and quantum-assisted simulation in the error corrected regime [77.34726150561087]
  A standard approach to quantum computing is based on the idea of promoting a classically simulable and fault-tolerant set of operations. We show how the addition of noisy magic resources allows one to boost classical quasiprobability simulations of a quantum circuit.
  arXiv  Detail & Related papers  (2021-03-12T20:58:41Z)
• Transcorrelated Density Matrix Renormalization Group [0.0]
  We introduce the transcorrelated Density Matrix Renormalization Group (tcDMRG) theory for the efficient approximation of the energy for strongly correlated systems. tcDMRG encodes the wave function as a product of a fixed Jastrow or Gutzwiller correlator and a matrix product state. We demonstrate fast energy convergence of tcDMRG, which indicates that tcDMRG could increase the efficiency of standard DMRG beyond quasi-monodimensional systems.
  arXiv  Detail & Related papers  (2020-09-05T23:20:14Z)
• A Dynamical Systems Approach for Convergence of the Bayesian EM Algorithm [59.99439951055238]
  We show how (discrete-time) Lyapunov stability theory can serve as a powerful tool to aid, or even lead, in the analysis (and potential design) of optimization algorithms that are not necessarily gradient-based. The particular ML problem that this paper focuses on is that of parameter estimation in an incomplete-data Bayesian framework via the popular optimization algorithm known as maximum a posteriori expectation-maximization (MAP-EM) We show that fast convergence (linear or quadratic) is achieved, which could have been difficult to unveil without our adopted S&C approach.
  arXiv  Detail & Related papers  (2020-06-23T01:34:18Z)

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.