Spectral stabilizability

• URL: http://arxiv.org/abs/2212.12245v2
• Date: Sun, 2 Apr 2023 14:26:54 GMT
• Title: Spectral stabilizability
• Authors: Tomasz Linowski, {\L}ukasz Rudnicki, Clemens Gneiting
• Abstract summary: We develop conditions for stabilizability based on the target state's eigendecomposition. We use the spectral approach to derive upper bounds on stabilizability for a number of exemplary open system scenarios.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Decoherence represents a major obstacle towards realizing reliable quantum technologies. Identifying states that can be uphold against decoherence by purely coherent means, i.e., {\it stabilizable states}, for which the dissipation-induced decay can be completely compensated by suitable control Hamiltonians, can help to optimize the exploitation of fragile quantum resources and to understand the ultimate limits of coherent control for this purpose. In this work, we develop conditions for stabilizability based on the target state's eigendecomposition, both for general density operators and for the covariance matrix parameterization of Gaussian states. Unlike previous conditions for stabilizability, these spectral conditions are both necessary and sufficient and are typically easier to use, extending their scope of applicability. To demonstrate its viability, we use the spectral approach to derive upper bounds on stabilizability for a number of exemplary open system scenarios, including stabilization of generalized GHZ and W states in the presence of local dissipation and stabilization of squeezed thermal states under collective damping.

Related papers

• Extremality of stabilizer states [0.0]
  We investigate the extremality of stabilizer states to reveal their exceptional role in the space of all $n$-qubit/qudit states. Our results highlight the remarkable information-theoretic properties of stabilizer states.
  arXiv  Detail & Related papers  (2024-03-20T14:30:59Z)
• Frequency-resolved Purcell effect for the dissipative generation of steady-state entanglement [49.1574468325115]
  We report a driven-dissipative mechanism to generate stationary entangled $W$ states among strongly-interacting quantum emitters placed within a cavity. The non-harmonic energy structure of the interacting ensemble allows this transition to be resonantly selected by the cavity. Evidence of this purely dissipative mechanism should be observable in state-of-the-art cavity QED systems in the solid-state.
  arXiv  Detail & Related papers  (2023-12-19T18:04:22Z)
• Sufficient condition for universal quantum computation using bosonic circuits [44.99833362998488]
  We focus on promoting circuits that are otherwise simulatable to computational universality. We first introduce a general framework for mapping a continuous-variable state into a qubit state. We then cast existing maps into this framework, including the modular and stabilizer subsystem decompositions.
  arXiv  Detail & Related papers  (2023-09-14T16:15:14Z)
• Critical behaviors of non-stabilizerness in quantum spin chains [0.0]
  Non-stabilizerness measures the extent to which a quantum state deviates from stabilizer states. In this work, we investigate the behavior of non-stabilizerness around criticality in quantum spin chains.
  arXiv  Detail & Related papers  (2023-09-01T18:00:04Z)
• Defining stable phases of open quantum systems [0.0]
  We show that uniformity is satisfied in a canonical classical cellular automaton. We conjecture some sufficient conditions for a channel to exhibit uniformity and therefore stability.
  arXiv  Detail & Related papers  (2023-08-28T17:55:31Z)
• 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)
• Unconventional mechanism of virtual-state population through dissipation [125.99533416395765]
  We report a phenomenon occurring in open quantum systems by which virtual states can acquire a sizable population in the long time limit. This means that the situation where the virtual state remains unpopulated can be metastable. We show how these results can be relevant for practical questions such as the generation of stable and metastable entangled states in dissipative systems of interacting qubits.
  arXiv  Detail & Related papers  (2022-02-24T17:09:43Z)
• Stabilizing Preparation of Quantum Gaussian States via Continuous Measurement [2.6663319869017523]
  The evolution of the open quantum system is described in terms of the quantum master equation. We present necessary and sufficient conditions for the system to have a unique stabilizing steady Gaussian state.
  arXiv  Detail & Related papers  (2021-09-27T01:18:04Z)
• Pointwise Feasibility of Gaussian Process-based Safety-Critical Control under Model Uncertainty [77.18483084440182]
  Control Barrier Functions (CBFs) and Control Lyapunov Functions (CLFs) are popular tools for enforcing safety and stability of a controlled system, respectively. We present a Gaussian Process (GP)-based approach to tackle the problem of model uncertainty in safety-critical controllers that use CBFs and CLFs.
  arXiv  Detail & Related papers  (2021-06-13T23:08:49Z)
• Stabilizing entanglement in two-mode Gaussian states [0.0]
  We analyze the stabilizability of entangled two-mode Gaussian states in three benchmark dissipative models. All three models exhibit a tradeoff between state entanglement and purity in the entanglement maximizing limit.
  arXiv  Detail & Related papers  (2020-07-08T10:12:48Z)
• Fine-Grained Analysis of Stability and Generalization for Stochastic Gradient Descent [55.85456985750134]
  We introduce a new stability measure called on-average model stability, for which we develop novel bounds controlled by the risks of SGD iterates. This yields generalization bounds depending on the behavior of the best model, and leads to the first-ever-known fast bounds in the low-noise setting. To our best knowledge, this gives the firstever-known stability and generalization for SGD with even non-differentiable loss functions.
  arXiv  Detail & Related papers  (2020-06-15T06:30:19Z)

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.