Optimal control with a multidimensional quantum invariant

• URL: http://arxiv.org/abs/2212.07872v1
• Date: Thu, 15 Dec 2022 14:41:20 GMT
• Title: Optimal control with a multidimensional quantum invariant
• Authors: Modesto Orozco-Ruiz, Selwyn Simsek, Sahra A. Kulmiya, Samuel J. Hile, Winfried K. Hensinger, Florian Mintert
• Abstract summary: Optimal quantum control of continuous variable systems poses a formidable computational challenge because of the high-dimensional character of the system dynamics. We explore the potential of a Gaussian invariant that is suitable for quadratic Hamiltonians with any given number of motional degrees of freedom for quantum optimal control problems that are inspired by current challenges in ground-state-to-ground-state shuttling of trapped-ions.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Optimal quantum control of continuous variable systems poses a formidable computational challenge because of the high-dimensional character of the system dynamics. The framework of quantum invariants can significantly reduce the complexity of such problems, but it requires the knowledge of an invariant compatible with the Hamiltonian of the system in question. We explore the potential of a Gaussian invariant that is suitable for quadratic Hamiltonians with any given number of motional degrees of freedom for quantum optimal control problems that are inspired by current challenges in ground-state-to-ground-state shuttling of trapped-ions.

Related papers

• Quantum-Assisted Barrier Sequential Quadratic Programming for Nonlinear Optimal Control [2.033424698590539]
  We propose a quantum-assisted framework for solving constrained finite-horizon nonlinear optimal control problems.<n>Within this framework, a quantum subroutine is incorporated to efficiently solve the Schur complement step.
  arXiv  Detail & Related papers  (2025-10-20T21:33:44Z)
• Grassmann Variational Monte Carlo with neural wave functions [45.935798913942904]
  We formalize the framework introduced by Pfau et al.citepfau2024accurate in terms of Grassmann geometry of the Hilbert space.<n>We validate our approach on the Heisenberg quantum spin model on the square lattice, achieving highly accurate energies and physical observables for a large number of excited states.
  arXiv  Detail & Related papers  (2025-07-14T13:53:13Z)
• Robust Control of High-dimensional Quantum Systems against Coherent and Incoherent Errors [0.0]
  Control of quantum systems needs to be robust against both coherent errors induced by parametric uncertainties and incoherent errors induced by environmental decoherence.<n>This poses significant challenges for high-dimensional systems due to the computational intensity involved in the control design process.<n>We propose a systematic framework to improve the design efficiency.
  arXiv  Detail & Related papers  (2025-06-23T12:50:56Z)
• Entangled quantum trajectories in relativistic systems [0.0]
  A key challenge to be overcome is to consider entanglement between two or more quantum particles in different inertial frames. We derive a class of Euler--Lagrange equations under the constraint of a non-entangling behavior. We solve our equations for interacting particles in a Klein--Gordon-type setting, thereby quantifying the dynamic and relativistic impact of entanglement.
  arXiv  Detail & Related papers  (2024-10-08T12:49:44Z)
• Quantum control by the environment: Turing uncomputability, Optimization over Stiefel manifolds, Reachable sets, and Incoherent GRAPE [56.47577824219207]
  In many practical situations, the controlled quantum systems are open, interacting with the environment. In this note, we briefly review some results on control of open quantum systems using environment as a resource.
  arXiv  Detail & Related papers  (2024-03-20T10:09:13Z)
• Integrability and chaos in the quantum brachistochrone problem [0.0]
  We introduce a family of completely integrable brachistochrone protocols, which arise from a judicious choice of the control Hamiltonian subset. We demonstrate how the inherent stability of the completely integrable protocols makes them numerically tractable and therefore practicable.
  arXiv  Detail & Related papers  (2024-01-26T16:25:56Z)
• Overhead-constrained circuit knitting for variational quantum dynamics [0.0]
  We use circuit knitting to partition a large quantum system into smaller subsystems that can each be simulated on a separate device. We show that the same method can be used to reduce the circuit depth by cutting long-ranged gates.
  arXiv  Detail & Related papers  (2023-09-14T17:01:06Z)
• Quadratic-exponential coherent feedback control of linear quantum stochastic systems [2.0508733018954843]
  This paper considers a risk-sensitive optimal control problem for a field-mediated interconnection of a quantum plant with a coherent quantum controller. The control objective is to internally stabilize the closed-loop system Wiener and minimize the infinite-horizon growth rate of a quadratic-exponential functional.
  arXiv  Detail & Related papers  (2023-08-07T21:31:05Z)
• Towards Neural Variational Monte Carlo That Scales Linearly with System Size [67.09349921751341]
  Quantum many-body problems are central to demystifying some exotic quantum phenomena, e.g., high-temperature superconductors. The combination of neural networks (NN) for representing quantum states, and the Variational Monte Carlo (VMC) algorithm, has been shown to be a promising method for solving such problems. We propose a NN architecture called Vector-Quantized Neural Quantum States (VQ-NQS) that utilizes vector-quantization techniques to leverage redundancies in the local-energy calculations of the VMC algorithm.
  arXiv  Detail & Related papers  (2022-12-21T19:00:04Z)
• Decimation technique for open quantum systems: a case study with driven-dissipative bosonic chains [62.997667081978825]
  Unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics. We introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function. We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity.
  arXiv  Detail & Related papers  (2022-02-15T19:00:09Z)
• Fixed Depth Hamiltonian Simulation via Cartan Decomposition [59.20417091220753]
  We present a constructive algorithm for generating quantum circuits with time-independent depth. We highlight our algorithm for special classes of models, including Anderson localization in one dimensional transverse field XY model. In addition to providing exact circuits for a broad set of spin and fermionic models, our algorithm provides broad analytic and numerical insight into optimal Hamiltonian simulations.
  arXiv  Detail & Related papers  (2021-04-01T19:06:00Z)
• Quantum control with a multi-dimensional Gaussian quantum invariant [0.0]
  The framework of quantum invariants is an elegant generalization of adiabatic quantum control to control fields that do not need to change slowly. We construct a multi-dimensional Gaussian quantum invariant that permits the design of time-dependent potentials that let the ground state of an initial potential evolve towards the ground state of a final potential. The scope of this framework is demonstrated with the task of shuttling an ion around a corner which is a paradigmatic control problem in achieving scalability of trapped ion quantum information technology.
  arXiv  Detail & Related papers  (2020-10-28T16:22:28Z)
• Entanglement transfer, accumulation and retrieval via quantum-walk-based qubit-qudit dynamics [50.591267188664666]
  Generation and control of quantum correlations in high-dimensional systems is a major challenge in the present landscape of quantum technologies. We propose a protocol that is able to attain entangled states of $d$-dimensional systems through a quantum-walk-based it transfer & accumulate mechanism. In particular, we illustrate a possible photonic implementation where the information is encoded in the orbital angular momentum and polarization degrees of freedom of single photons.
  arXiv  Detail & Related papers  (2020-10-14T14:33:34Z)
• Quantum Non-equilibrium Many-Body Spin-Photon Systems [91.3755431537592]
  dissertation concerns the quantum dynamics of strongly-correlated quantum systems in out-of-equilibrium states. Our main results can be summarized in three parts: Signature of Critical Dynamics, Driven Dicke Model as a Test-bed of Ultra-Strong Coupling, and Beyond the Kibble-Zurek Mechanism.
  arXiv  Detail & Related papers  (2020-07-23T19:05:56Z)

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.