Variational Quantum Eigensolver for Approximate Diagonalization of Downfolded Hamiltonians using Generalized Unitary Coupled Cluster Ansatz

• URL: http://arxiv.org/abs/2011.01985v1
• Date: Tue, 3 Nov 2020 20:03:51 GMT
• Title: Variational Quantum Eigensolver for Approximate Diagonalization of Downfolded Hamiltonians using Generalized Unitary Coupled Cluster Ansatz
• Authors: Nicholas P. Bauman and Jaroslav Chl\'adek and Libor Veis and Ji\v{r}\'i Pittner and Karol Kowalski
• Abstract summary: Generalized Unitary Coupled Cluster (GUCC) is a formalism for the diagonalization of downfolded/effective Hamiltonians in active spaces. We consider their form defined by freezing core orbitals, which enables us to deal with larger systems. We consider various solvers to identify solutions of the GUCC equations.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper we discuss the utilization of Variational Quantum Solver (VQE) and recently introduced Generalized Unitary Coupled Cluster (GUCC) formalism for the diagonalization of downfolded/effective Hamiltonians in active spaces. In addition to effective Hamiltonians defined by the downfolding of a subset of virtual orbitals we also consider their form defined by freezing core orbitals, which enables us to deal with larger systems. We also consider various solvers to identify solutions of the GUCC equations. We use N$_2$, H$_2$O, and C$_2$H$_4$, and benchmark systems to illustrate the performance of the combined framework.

Related papers

• Systematic many-fermion Hamiltonian input scheme and spectral calculations on quantum computers [0.0]
  We present a novel input scheme for general second-quantized Hamiltonians of relativistic or non-relativistic many-fermion systems. Based on our input scheme, we propose a hybrid quantum-classical framework for spectral calculations on future quantum hardwares.
  arXiv  Detail & Related papers  (2024-02-14T06:29:32Z)
• Generation of C-NOT, SWAP, and C-Z Gates for Two Qubits Using Coherent and Incoherent Controls and Stochastic Optimization [56.47577824219207]
  We consider a general form of the dynamics of open quantum systems determined by the Gorini-Kossakowsky-Sudarchhan-Lindblad type master equation. We analyze the control problems of generating two-qubit C-NOT, SWAP, and C-Z gates using piecewise constant controls and optimization.
  arXiv  Detail & Related papers  (2023-12-09T17:55:47Z)
• Hybrid quantum-classical algorithm for the transverse-field Ising model in the thermodynamic limit [0.0]
  We describe a hybrid quantum-classical approach to treat quantum many-body systems in the thermodynamic limit. This is done by combining numerical linked-cluster expansions (NLCE) with the variational quantum eigensolver (VQE)
  arXiv  Detail & Related papers  (2023-10-11T15:41:09Z)
• 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)
• Expanding the reach of quantum optimization with fermionic embeddings [2.378735224874938]
  In this work, we establish a natural embedding for this class of LNCG problems onto a fermionic Hamiltonian. We show that our quantum representation requires only a linear number of qubits. We provide evidence that this rounded quantum relaxation can produce high-quality approximations.
  arXiv  Detail & Related papers  (2023-01-04T19:00:01Z)
• Optimal control for state preparation in two-qubit open quantum systems driven by coherent and incoherent controls via GRAPE approach [77.34726150561087]
  We consider a model of two qubits driven by coherent and incoherent time-dependent controls. The dynamics of the system is governed by a Gorini-Kossakowski-Sudarshan-Lindblad master equation. We study evolution of the von Neumann entropy, purity, and one-qubit reduced density matrices under optimized controls.
  arXiv  Detail & Related papers  (2022-11-04T15:20:18Z)
• Calculating non-linear response functions for multi-dimensional electronic spectroscopy using dyadic non-Markovian quantum state diffusion [68.8204255655161]
  We present a methodology for simulating multi-dimensional electronic spectra of molecular aggregates with coupling electronic excitation to a structured environment. A crucial aspect of our approach is that we propagate the NMQSD equation in a doubled system Hilbert space but with the same noise.
  arXiv  Detail & Related papers  (2022-07-06T15:30:38Z)
• On optimization of coherent and incoherent controls for two-level quantum systems [77.34726150561087]
  This article considers some control problems for closed and open two-level quantum systems. The closed system's dynamics is governed by the Schr"odinger equation with coherent control. The open system's dynamics is governed by the Gorini-Kossakowski-Sudarshan-Lindblad master equation.
  arXiv  Detail & Related papers  (2022-05-05T09:08:03Z)
• Variational solutions to fermion-to-qubit mappings in two spatial dimensions [0.0]
  We present a variational Monte-Carlo framework to study fermionic systems through higher-dimensional (>1D) Jordan-Wigner transformations. We provide exact solutions to the parity and Gauss-law constraints that are encountered in bosonization procedures.
  arXiv  Detail & Related papers  (2022-05-02T08:38:00Z)
• General Solution and Canonical Quantization of the Conic Path Constrained Second-Class System [0.0]
  We consider the problem of constrained motion along a conic path under a given external potential function. We perform the canonical quantization in a consistent way in terms of the corresponding Dirac brackets. The complete Dirac brackets algebra in phase space as well as its physical realization in terms of differential operators is explicitly obtained.
  arXiv  Detail & Related papers  (2022-02-15T13:46:56Z)
• Unraveling the topology of dissipative quantum systems [58.720142291102135]
  We discuss topology in dissipative quantum systems from the perspective of quantum trajectories. We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians.
  arXiv  Detail & Related papers  (2020-07-12T11:26:02Z)

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.