Detecting quasi-degenerate ground states in 1D topological models via VQE

• URL: http://arxiv.org/abs/2408.15179v2
• Date: Thu, 29 Aug 2024 12:28:37 GMT
• Title: Detecting quasi-degenerate ground states in 1D topological models via VQE
• Authors: Carola Ciaramelletti, Martin Beseda, Mirko Consiglio, Luca Lepori, Tony J. G. Apollaro, Simone Paganelli,
• Abstract summary: We study the exact ground states of the Su--Schrieffer--Heeger open chain and of the Kitaev open chain. These models host symmetry-protected topological phases, characterized by edge modes with vanishing single-particle energy in the thermodynamic limit.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the exact ground states of the Su--Schrieffer--Heeger open chain and of the Kitaev open chain, using the Variational Quantum Eigensolver (VQE) algorithm. These models host symmetry-protected topological phases, characterized by edge modes with vanishing single-particle energy in the thermodynamic limit. The same fact prevents the standard VQE algorithm from converging to the correct ground state for finite chains, since it is quasi-degenerate in energy with other many-body states. Notably, this quasi-degeneracy cannot be removed by small perturbations, as in typical spin systems. We address this issue by imposing appropriate constraints on the VQE evolution and constructing appropriate variational circuits, to restrict the probed portion of the Hilbert space along the same evolution. These constraints stem from both general properties of the topological phases and of the studied Hamiltonians. In this way, the improved VQE algorithm achieves an accurate convergence to the exact ground states in each phase. The present approach promises large applicability, also to realistic systems and possibly with different topology, thanks to the very high fidelity achieved also on systems with a relatively high number of qubits.

Related papers

• Theory of the correlated quantum Zeno effect in a monitored qubit dimer [41.94295877935867]
  We show how the competition between two measurement processes give rise to two distinct Quantum Zeno (QZ) regimes. We develop a theory based on a Gutzwiller ansatz for the wavefunction that is able to capture the structure of the Hilbert phase diagram. We show how the two QZ regimes are intimately connected to the topology of the flow of the underlying non-Hermitian Hamiltonian governing the no-click evolution.
  arXiv  Detail & Related papers  (2025-03-28T19:44:48Z)
• State Permutation Control in Non-Hermitian Multiqubit Systems with Suppressed Non-Adiabatic Transitions [0.0]
  We introduce a model of interacting qubits governed by an effective non-Hermitian Hamiltonian that hosts EPs and possesses a completely real energy spectrum. Our findings indicate that, contrary to previous beliefs, non-Hermiticity can be utilized to achieve controlled state permutations in time-modulated multiqubit systems.
  arXiv  Detail & Related papers  (2025-01-27T15:57:21Z)
• Gapless Floquet topology [40.2428948628001]
  We study the existence of topological edge zero- and pi-modes despite the lack of bulk gaps in the quasienergy spectrum. We numerically study the effect of interactions, which give a finite lifetime to the edge modes in the thermodynamic limit with the decay rate consistent with Fermi's Golden Rule.
  arXiv  Detail & Related papers  (2024-11-04T19:05:28Z)
• Compact fermionic quantum state preparation with a natural-orbitalizing variational quantum eigensolving scheme [0.0]
  Near-term quantum state preparation is typically realized by means of the variational quantum eigensolver (VQE) algorithm. We present a refined VQE scheme that consists in topping VQE with state-informed updates of the elementary fermionic modes. For a fixed circuit structure, the method is shown to enhance the capabilities of the circuit to reach a state close to the target state without incurring too much overhead from shot noise.
  arXiv  Detail & Related papers  (2024-06-20T10:23:28Z)
• Ground or Excited State: a State-Specific Variational Quantum Eigensolver for Them All [0.0]
  Variational Quantum Eigensolver (VQE) provides a lucrative platform to determine molecular energetics in quantum devices. We propose a unified VQE framework that treats the ground and excited states in the same footings. We introduce the notion of totally symmetric, spin-scalar unitary which maintains the purity of the reference at each step of the optimization.
  arXiv  Detail & Related papers  (2023-08-21T13:39:58Z)
• Quantum Gate Generation in Two-Level Open Quantum Systems by Coherent and Incoherent Photons Found with Gradient Search [77.34726150561087]
  We consider an environment formed by incoherent photons as a resource for controlling open quantum systems via an incoherent control. We exploit a coherent control in the Hamiltonian and an incoherent control in the dissipator which induces the time-dependent decoherence rates.
  arXiv  Detail & Related papers  (2023-02-28T07:36:02Z)
• Non-Hermitian topological quantum states in a reservoir-engineered transmon chain [0.0]
  We show that a non-Hermitian quantum phase can be realized in a reservoir-engineered transmon chain. We show that genuine quantum effects are observable in this system via robust and slowly decaying long-range quantum entanglement of the topological end modes.
  arXiv  Detail & Related papers  (2022-10-06T15:21:21Z)
• Fermionic approach to variational quantum simulation of Kitaev spin models [50.92854230325576]
  Kitaev spin models are well known for being exactly solvable in a certain parameter regime via a mapping to free fermions. We use classical simulations to explore a novel variational ansatz that takes advantage of this fermionic representation. We also comment on the implications of our results for simulating non-Abelian anyons on quantum computers.
  arXiv  Detail & Related papers  (2022-04-11T18:00:01Z)
• A Quantum Optimal Control Problem with State Constrained Preserving Coherence [68.8204255655161]
  We consider a three-level $Lambda$-type atom subjected to Markovian decoherence characterized by non-unital decoherence channels. We formulate the quantum optimal control problem with state constraints where the decoherence level remains within a pre-defined bound.
  arXiv  Detail & Related papers  (2022-03-24T21:31:34Z)
• Fast Thermalization from the Eigenstate Thermalization Hypothesis [69.68937033275746]
  Eigenstate Thermalization Hypothesis (ETH) has played a major role in understanding thermodynamic phenomena in closed quantum systems. This paper establishes a rigorous link between ETH and fast thermalization to the global Gibbs state. Our results explain finite-time thermalization in chaotic open quantum systems.
  arXiv  Detail & Related papers  (2021-12-14T18:48:31Z)
• Probing ground state properties of the kagome antiferromagnetic Heisenberg model using the Variational Quantum Eigensolver [0.05076419064097732]
  We propose using the Variational Quantum Eigensolver (VQE) to find the ground state of the kagome lattice on a quantum computer. We find efficient ansatz circuits and show how physically interesting observables can be measured efficiently.
  arXiv  Detail & Related papers  (2021-08-18T10:58:27Z)
• Quasi-Locality Bounds for Quantum Lattice Systems. Part II. Perturbations of Frustration-Free Spin Models with Gapped Ground States [0.0]
  We study the stability with respect to a broad class of perturbations of gapped ground state phases of quantum spin systems. Under a condition of Local Topological Quantum Order, the bulk gap is stable under perturbations that decay at long distances faster than a stretched exponential.
  arXiv  Detail & Related papers  (2020-10-29T03:24:19Z)
• Simulating periodic systems on quantum computer [7.332046127518237]
  We present two schemes to improve the accuracy of quantum simulations for extended systems. One is a modified VQE algorithm, which introduces a unitary transformation of Hartree-Fock orbitals to avoid the complex Hamiltonian. The second is a Post-VQE approach combining VQE with the quantum subspace expansion approach (VQE/QSE)
  arXiv  Detail & Related papers  (2020-08-07T01:56:32Z)
• 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)
• Einselection from incompatible decoherence channels [62.997667081978825]
  We analyze an open quantum dynamics inspired by CQED experiments with two non-commuting Lindblad operators. We show that Fock states remain the most robust states to decoherence up to a critical coupling.
  arXiv  Detail & Related papers  (2020-01-29T14:15:19Z)

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.