Ground or Excited State: a State-Specific Variational Quantum Eigensolver for Them All

• URL: http://arxiv.org/abs/2308.10719v1
• Date: Mon, 21 Aug 2023 13:39:58 GMT
• Title: Ground or Excited State: a State-Specific Variational Quantum Eigensolver for Them All
• Authors: Dibyendu Mondal and Rahul Maitra
• Abstract summary: 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Variational Quantum Eigensolver (VQE) provides a lucrative platform to determine molecular energetics in near-term quantum devices. While the VQE is traditionally tailored to determine the ground state wavefunction with the underlying Rayleigh-Ritz principle, the access to specific symmetry-adapted excited states remains elusive. This often requires high depth circuit or additional ancilla qubits along with prior knowledge of the ground state wavefunction. We propose a unified VQE framework that treats the ground and excited states in the same footings. With the knowledge of the irreducible representations of the spinorbitals, we construct a multi-determinantal reference that is adapted to a given spatial symmetry where additionally, the determinants are entangled through appropriate Clebsch-Gordan coefficients to ensure the desired spin-multiplicity. We introduce the notion of totally symmetric, spin-scalar unitary which maintains the purity of the reference at each step of the optimization. The state-selectivity safeguards the method against any variational collapse while leading to any targeted low-lying eigenroot of arbitrary symmetry. The direct access to the excited states shields our approach from the cumulative error that plagues excited state calculations in a quantum computer and with few parameter count, it is expected to be realized in near-term quantum devices.

Related papers

• 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)
• Hermitian-preserving ansatz and variational open quantum eigensolver [0.0]
  We propose a new variational quantum algorithm named Variational Open Quantum Eigensolver (VOQE) In VOQE, density matrices of mixed states are represented by pure states in doubled Hilbert space. We show the workflow of VOQE on solving steady states of the LMEs of the driven XXZ model and implement VOQE to solve the spectrum of the non-Hermitian Hamiltonians of the Ising spin chain in an imaginary field.
  arXiv  Detail & Related papers  (2024-03-06T05:34:13Z)
• Many-Body Excited States with a Contracted Quantum Eigensolver [0.0]
  We develop an excited state approach based on the contracted quantum eigensolver (ES-CQE) We show the ES-CQE near-exact accuracy across the majority of states, covering regions of strong and weak electron correlation.
  arXiv  Detail & Related papers  (2023-05-16T17:53:07Z)
• Universality of critical dynamics with finite entanglement [68.8204255655161]
  We study how low-energy dynamics of quantum systems near criticality are modified by finite entanglement. Our result establishes the precise role played by entanglement in time-dependent critical phenomena.
  arXiv  Detail & Related papers  (2023-01-23T19:23:54Z)
• Canonically consistent quantum master equation [68.8204255655161]
  We put forth a new class of quantum master equations that correctly reproduce the state of an open quantum system beyond the infinitesimally weak system-bath coupling limit. Our method is based on incorporating the knowledge of the reduced steady state into its dynamics.
  arXiv  Detail & Related papers  (2022-05-25T15:22:52Z)
• 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)
• Bernstein-Greene-Kruskal approach for the quantum Vlasov equation [91.3755431537592]
  The one-dimensional stationary quantum Vlasov equation is analyzed using the energy as one of the dynamical variables. In the semiclassical case where quantum tunneling effects are small, an infinite series solution is developed.
  arXiv  Detail & Related papers  (2021-02-18T20:55:04Z)
• Stability of quantum eigenstates and kinetics of wave function collapse in a fluctuating environment [0.0]
  The work analyzes the stability of the quantum eigenstates when they are submitted to fluctuations. In the limit of sufficiently slow kinetics, the quantum eigenstates show to remain stationary configurations. The work shows that the final stationary eigenstate depends by the initial configuration of the superposition of states.
  arXiv  Detail & Related papers  (2020-11-25T10:41:53Z)
• Extremal quantum states [0.41998444721319206]
  We peruse quantumness from a variety of viewpoints, concentrating on phase-space formulations. The symmetry-transcending properties of the Husimi $Q$ function make it our basic tool. We use these quantities to formulate extremal principles and determine in this way which states are the most and least "quantum"
  arXiv  Detail & Related papers  (2020-10-09T18:00:02Z)
• 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.