Counterdiabatic driving for random-gap Landau-Zener transitions

• URL: http://arxiv.org/abs/2601.10659v1
• Date: Thu, 15 Jan 2026 18:28:23 GMT
• Title: Counterdiabatic driving for random-gap Landau-Zener transitions
• Authors: Georgios Theologou, Mikkel F. Andersen, Sandro Wimberger,
• Abstract summary: Landau--Zener (LZ) model describes a two-level quantum system that undergoes an avoided crossing.<n>An auxiliary control field $H_textCD$ can be reverse-engineered so that the full Hamiltonian $H_textCD$ reproduces adiabaticity.<n>We find a trade-off between instantaneous adiabaticity and the final transition probability.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The Landau--Zener (LZ) model describes a two-level quantum system that undergoes an avoided crossing. In the adiabatic limit, the transition probability vanishes. An auxiliary control field $H_\text{CD}$ can be reverse-engineered so that the full Hamiltonian $H_0 + H_\text{CD}$ reproduces adiabaticity for all parameter values. Our aim is to construct a single control field $H_1$ that drives an ensemble of LZ-type Hamiltonians with a distribution of energy gaps. $H_1$ works best statistically, minimizing the average transition probability. We restrict our attention to a special class of $H_1$ controls, motivated by $H_\text{CD}$. We found a systematic trade-off between instantaneous adiabaticity and the final transition probability. Certain limiting cases with a linear sweep can be treated analytically; one of them being the LZ system with Dirac $δ(t)$ function. Comprehensive and systematic numerical simulations support and extend the analytic results.

Related papers

• Theta-term in Russian Doll Model: phase structure, quantum metric and BPS multifractality [45.88028371034407]
  We investigate the phase structure of the deterministic and disordered versions of the Russian Doll Model (RDM)<n>We find the pattern of phase transitions in the global charge $Q(theta,gamma)$, which arises from the BA equation.<n>We conjecture that the Hamiltonian of the RDM model describes the mixing in particular 2d-4d BPS sector of the Hilbert space.
  arXiv  Detail & Related papers  (2025-10-23T17:25:01Z)
• Spectral statistics and energy-gap scaling in $k-$local spin Hamiltonians [0.0]
  We investigate the spectral properties of all-to-all interacting spin Hamiltonians acting on exactly $k$ spins.<n>For $mu = 0$, we demonstrate that the random matrix ensemble is determined by the parity of system size $L$ and locality $k$.<n>Our work introduces a semi-solvable model that captures universal features of random-matrix statistics, and spectral gap formation.
  arXiv  Detail & Related papers  (2025-10-17T17:11:38Z)
• Near-Optimal Clustering in Mixture of Markov Chains [74.3828414695655]
  We study the problem of clustering $T$ trajectories of length $H$, each generated by one of $K$ unknown ergodic Markov chains over a finite state space of size $S$.<n>We derive an instance-dependent, high-probability lower bound on the clustering error rate, governed by the weighted KL divergence between the transition kernels of the chains.<n>We then present a novel two-stage clustering algorithm.
  arXiv  Detail & Related papers  (2025-06-02T05:10:40Z)
• KPZ scaling from the Krylov space [83.88591755871734]
  Recently, a superdiffusion exhibiting the Kardar-Parisi-Zhang scaling in late-time correlators and autocorrelators has been reported. Inspired by these results, we explore the KPZ scaling in correlation functions using their realization in the Krylov operator basis.
  arXiv  Detail & Related papers  (2024-06-04T20:57:59Z)
• Projected Langevin dynamics and a gradient flow for entropic optimal transport [0.8057006406834466]
  We introduce analogous diffusion dynamics that sample from an entropy-regularized optimal transport. By studying the induced Wasserstein geometry of the submanifold $Pi(mu,nu)$, we argue that the SDE can be viewed as a Wasserstein gradient flow on this space of couplings.
  arXiv  Detail & Related papers  (2023-09-15T17:55:56Z)
• Weak universality, quantum many-body scars and anomalous infinite-temperature autocorrelations in a one-dimensional spin model with duality [0.0]
  We study a one-dimensional spin-$1/2$ model with three-spin interactions and a transverse magnetic field $h$. We compute the critical exponents $z$, $beta$, $gamma$ and $nu$, and the central charge $c$. For a system with periodic boundary conditions, there are an exponentially large number of exact mid-spectrum zero-energy eigenstates.
  arXiv  Detail & Related papers  (2023-07-20T18:00:05Z)
• Unitary k-designs from random number-conserving quantum circuits [0.0]
  Local random circuits scramble efficiently and accordingly have a range of applications in quantum information and quantum dynamics. We show that finite moments cannot distinguish the ensemble that local random circuits generate from the Haar ensemble on the entire group of number-conserving unitaries.
  arXiv  Detail & Related papers  (2023-06-01T18:00:00Z)
• A hybrid quantum algorithm to detect conical intersections [39.58317527488534]
  We show that for real molecular Hamiltonians, the Berry phase can be obtained by tracing a local optimum of a variational ansatz along the chosen path. We demonstrate numerically the application of our algorithm on small toy models of the formaldimine molecule.
  arXiv  Detail & Related papers  (2023-04-12T18:00:01Z)
• Theory of free fermions under random projective measurements [43.04146484262759]
  We develop an analytical approach to the study of one-dimensional free fermions subject to random projective measurements of local site occupation numbers. We derive a non-linear sigma model (NLSM) as an effective field theory of the problem.
  arXiv  Detail & Related papers  (2023-04-06T15:19:33Z)
• The Franke-Gorini-Kossakowski-Lindblad-Sudarshan (FGKLS) Equation for Two-Dimensional Systems [62.997667081978825]
  Open quantum systems can obey the Franke-Gorini-Kossakowski-Lindblad-Sudarshan (FGKLS) equation. We exhaustively study the case of a Hilbert space dimension of $2$.
  arXiv  Detail & Related papers  (2022-04-16T07:03:54Z)
• Critical phase boundary and finite-size fluctuations in Su-Schrieffer-Heeger model with random inter-cell couplings [0.0]
  In this work, we investigate a special sort of a disorder when inter-cell hopping amplitudes are random. Using a definition for $mathbbZ$-topological invariant $nuin 0; 1$ in terms of a non-Hermitian part of the total Hamiltonian, we calculate $langlenurangle averaged by random realizations.
  arXiv  Detail & Related papers  (2021-11-30T15:35:58Z)
• Sample Complexity of Asynchronous Q-Learning: Sharper Analysis and Variance Reduction [63.41789556777387]
  Asynchronous Q-learning aims to learn the optimal action-value function (or Q-function) of a Markov decision process (MDP) We show that the number of samples needed to yield an entrywise $varepsilon$-accurate estimate of the Q-function is at most on the order of $frac1mu_min (1-gamma)5varepsilon2+ fract_mixmu_min (1-gamma)$ up to some logarithmic factor.
  arXiv  Detail & Related papers  (2020-06-04T17:51:00Z)
• Anisotropy-mediated reentrant localization [62.997667081978825]
  We consider a 2d dipolar system, $d=2$, with the generalized dipole-dipole interaction $sim r-a$, and the power $a$ controlled experimentally in trapped-ion or Rydberg-atom systems. We show that the spatially homogeneous tilt $beta$ of the dipoles giving rise to the anisotropic dipole exchange leads to the non-trivial reentrant localization beyond the locator expansion.
  arXiv  Detail & Related papers  (2020-01-31T19:00:01Z)

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.