Gradient-based reconstruction of molecular Hamiltonians and density matrices from time-dependent quantum observables

• URL: http://arxiv.org/abs/2205.05251v1
• Date: Wed, 11 May 2022 03:44:17 GMT
• Title: Gradient-based reconstruction of molecular Hamiltonians and density matrices from time-dependent quantum observables
• Authors: Wucheng Zhang, Ilia Tutunnikov, Ilya Sh. Averbukh, Roman V. Krems
• Abstract summary: We consider a quantum system with a time-independent Hamiltonian parametrized by a set of unknown parameters $alpha$. We show that it is possible to obtain closed-form expressions for the gradients of the distance between $cal O(t)$ and a calculated observable. These gradients can be used in projected gradient descent to infer $alpha$, $P$ and the relevant density matrix from dynamical observables.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: We consider a quantum system with a time-independent Hamiltonian parametrized by a set of unknown parameters $\alpha$. The system is prepared in a general quantum state by an evolution operator that depends on a set of unknown parameters $P$. After the preparation, the system evolves in time, and it is characterized by a time-dependent observable ${\cal O}(t)$. We show that it is possible to obtain closed-form expressions for the gradients of the distance between ${\cal O}(t)$ and a calculated observable with respect to $\alpha$, $P$ and all elements of the system density matrix, whether for pure or mixed states. These gradients can be used in projected gradient descent to infer $\alpha$, $P$ and the relevant density matrix from dynamical observables. We combine this approach with random phase wave function approximation to obtain closed-form expressions for gradients that can be used to infer population distributions from averaged time-dependent observables in problems with a large number of quantum states participating in dynamics. The approach is illustrated by determining the temperature of molecular gas (initially, in thermal equilibrium at room temperature) from the laser-induced time-dependent molecular alignment.

Related papers

• Variational method for learning Quantum Channels via Stinespring Dilation on neutral atom systems [0.0]
  Quantum systems interact with their environment, resulting in non-reversible evolutions. For many quantum experiments, the time until which measurements can be done might be limited. We introduce a method to approximate a given target quantum channel by means of variationally approximating equivalent unitaries on an extended system.
  arXiv  Detail & Related papers  (2023-09-19T13:06:44Z)
• A hybrid method for quantum dynamics simulation [2.6340447642310383]
  We propose a hybrid approach to simulate quantum many body dynamics by combining Trotter based quantum algorithm with classical dynamic mode decomposition. Our method predicts observables of a quantum state in the long time by using data from a set of short time measurements from a quantum computer.
  arXiv  Detail & Related papers  (2023-07-27T23:43:13Z)
• Stochastic approach to evolution of a quantum system interacting with a wave packet in squeezed number state [0.0]
  We determine filtering and master equations for a quantum system interacting with wave packet of light in a continuous-mode squeezed number state. We formulate the problem of conditional evolution of a quantum system making use of model of repeated interactions and measurements.
  arXiv  Detail & Related papers  (2023-03-21T19:42:15Z)
• Observation of partial and infinite-temperature thermalization induced by repeated measurements on a quantum hardware [62.997667081978825]
  We observe partial and infinite-temperature thermalization on a quantum superconducting processor. We show that the convergence does not tend to a completely mixed (infinite-temperature) state, but to a block-diagonal state in the observable basis.
  arXiv  Detail & Related papers  (2022-11-14T15:18:11Z)
• Linear Response for pseudo-Hermitian Hamiltonian Systems: Application to PT-Symmetric Qubits [0.0]
  We develop the linear response theory formulation suitable for application to various pHH systems. We apply our results to two textitPT-symmetric non-Hermitian quantum systems.
  arXiv  Detail & Related papers  (2022-06-18T10:05:30Z)
• Probing finite-temperature observables in quantum simulators of spin systems with short-time dynamics [62.997667081978825]
  We show how finite-temperature observables can be obtained with an algorithm motivated from the Jarzynski equality. We show that a finite temperature phase transition in the long-range transverse field Ising model can be characterized in trapped ion quantum simulators.
  arXiv  Detail & Related papers  (2022-06-03T18:00:02Z)
• Prethermalization, thermalization, and Fermi's golden rule in quantum many-body systems [0.3921666708205728]
  We study the prethermalization and thermalization dynamics of local observables in weakly perturbed nonintegrable systems. We show that the slow thermalizing dynamics is characterized by a rate $propto g2$, which can be accurately determined using a Fermi golden rule (FGR) equation.
  arXiv  Detail & Related papers  (2021-09-03T18:48:55Z)
• Observation of Time-Crystalline Eigenstate Order on a Quantum Processor [80.17270167652622]
  Quantum-body systems display rich phase structure in their low-temperature equilibrium states. We experimentally observe an eigenstate-ordered DTC on superconducting qubits. Results establish a scalable approach to study non-equilibrium phases of matter on current quantum processors.
  arXiv  Detail & Related papers  (2021-07-28T18:00:03Z)
• Visualizing spinon Fermi surfaces with time-dependent spectroscopy [62.997667081978825]
  We propose applying time-dependent photo-emission spectroscopy, an established tool in solid state systems, in cold atom quantum simulators. We show in exact diagonalization simulations of the one-dimensional $t-J$ model that the spinons start to populate previously unoccupied states in an effective band structure. The dependence of the spectral function on the time after the pump pulse reveals collective interactions among spinons.
  arXiv  Detail & Related papers  (2021-05-27T18:00:02Z)
• 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)
• Evolution of a Non-Hermitian Quantum Single-Molecule Junction at Constant Temperature [62.997667081978825]
  We present a theory for describing non-Hermitian quantum systems embedded in constant-temperature environments. We find that the combined action of probability losses and thermal fluctuations assists quantum transport through the molecular junction.
  arXiv  Detail & Related papers  (2021-01-21T14:33:34Z)

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.