Clifford Dressed Time-Dependent Variational Principle

• URL: http://arxiv.org/abs/2407.01692v1
• Date: Mon, 1 Jul 2024 18:04:25 GMT
• Title: Clifford Dressed Time-Dependent Variational Principle
• Authors: Antonio Francesco Mello, Alessandro Santini, Guglielmo Lami, Jacopo De Nardis, Mario Collura,
• Abstract summary: 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.
• Score: 39.58317527488534
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose an enhanced Time-Dependent Variational Principle (TDVP) algorithm for Matrix Product States (MPS) that integrates Clifford disentangling techniques to efficiently manage entanglement growth. By leveraging the Clifford group, which maps Pauli strings to other Pauli strings while maintaining low computational complexity, we introduce a Clifford dressed single-site 1-TDVP scheme. During the TDVP integration, we apply a global Clifford transformation as needed to reduce entanglement by iteratively sweeping over two-qubit Clifford unitaries that connect neighboring sites in a checkerboard pattern. We validate the new algorithm numerically using various quantum many-body models, including both integrable and non-integrable systems. Our results demonstrate that the Clifford dressed TDVP significantly improves entanglement management and computational efficiency, achieving higher accuracy, extended simulation times, and enhanced precision in computed observables compared to standard TDVP approaches. Additionally, we propose incorporating Clifford gates directly within the two-site 2-TDVP scheme.

Related papers

• Augmenting Finite Temperature Tensor Network with Clifford Circuits [0.49157446832511503]
  Recent studies have highlighted the combination of network methods and the stabilizer formalism as a very effective framework for simulating quantum many-body systems. In this work, we adapt this paradigm for finite temperature simulations in the framework of Time-Dependent Variational Principle. Our numerical results demonstrate that Clifford circuits can significantly improve the efficiency and accuracy of finite temperature simulations.
  arXiv  Detail & Related papers  (2024-10-21T07:30:59Z)
• 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)
• Augmenting Density Matrix Renormalization Group with Clifford Circuits [0.49157446832511503]
  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.
  arXiv  Detail & Related papers  (2024-05-15T09:53:08Z)
• Minimal Clifford Shadow Estimation by Mutually Unbiased Bases [5.002981581926959]
  We introduce the minimal Clifford measurement (MCM) to reduce the number of possible random circuits to the minimum. Compared to the original Clifford measurements, our MCM significantly reduces the circuit complexity and the compilation costs.
  arXiv  Detail & Related papers  (2023-10-28T16:22:04Z)
• Semi-Federated Learning: Convergence Analysis and Optimization of A Hybrid Learning Framework [70.83511997272457]
  We propose a semi-federated learning (SemiFL) paradigm to leverage both the base station (BS) and devices for a hybrid implementation of centralized learning (CL) and FL. We propose a two-stage algorithm to solve this intractable problem, in which we provide the closed-form solutions to the beamformers.
  arXiv  Detail & Related papers  (2023-10-04T03:32:39Z)
• Simulation of IBM's kicked Ising experiment with Projected Entangled Pair Operator [71.10376783074766]
  We perform classical simulations of the 127-qubit kicked Ising model, which was recently emulated using a quantum circuit with error mitigation. Our approach is based on the projected entangled pair operator (PEPO) in the Heisenberg picture. We develop a Clifford expansion theory to compute exact expectation values and use them to evaluate algorithms.
  arXiv  Detail & Related papers  (2023-08-06T10:24:23Z)
• Clifford Circuit Optimization with Templates and Symbolic Pauli Gates [11.978356827088595]
  The Clifford group is a finite subgroup of the unitary group generated by the Hadamard, the CNOT, and the Phase gates. Here we consider the problem of finding a short quantum circuit implementing a given Clifford group element. Our methods aim to minimize the entangling gate count assuming all-to-all qubit connectivity.
  arXiv  Detail & Related papers  (2021-05-05T19:18:35Z)
• Doubly Robust Off-Policy Actor-Critic: Convergence and Optimality [131.45028999325797]
  We develop a doubly robust off-policy AC (DR-Off-PAC) for discounted MDP. DR-Off-PAC adopts a single timescale structure, in which both actor and critics are updated simultaneously with constant stepsize. We study the finite-time convergence rate and characterize the sample complexity for DR-Off-PAC to attain an $epsilon$-accurate optimal policy.
  arXiv  Detail & Related papers  (2021-02-23T18:56:13Z)
• A Generic Compilation Strategy for the Unitary Coupled Cluster Ansatz [68.8204255655161]
  We describe a compilation strategy for Variational Quantum Eigensolver (VQE) algorithms. We use the Unitary Coupled Cluster (UCC) ansatz to reduce circuit depth and gate count.
  arXiv  Detail & Related papers  (2020-07-20T22:26:16Z)
• Combining Deep Learning and Optimization for Security-Constrained Optimal Power Flow [94.24763814458686]
  Security-constrained optimal power flow (SCOPF) is fundamental in power systems. Modeling of APR within the SCOPF problem results in complex large-scale mixed-integer programs. This paper proposes a novel approach that combines deep learning and robust optimization techniques.
  arXiv  Detail & Related papers  (2020-07-14T12:38:21Z)

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.