Related papers: Enhanced Perturbative Continuous Unitary Transform…
Continuous unitary transformations are a powerful tool to extract valuable information out of quantum many-body Hamiltonians, in which the so-called flow equation transforms the Hamiltonian to a diagonal or block-diagonal form in second…
Directly evaluated enhanced perturbative continuous unitary transformations (deepCUTs) are used to calculate non-perturbatively extrapolated numerical data for the ground-state energy and the energy gap. The data coincides with the…
We use a novel parameterization of the flowing Hamiltonian to show that the flow equations based on continuous unitary transformations, as proposed by Wegner, can be implemented through a nonlinear partial differential equation involving…
The quantum quartic oscillator is investigated in order to test the many-body technique of the continuous unitary transformations. The quartic oscillator is sufficiently simple to allow a detailed study and comparison of various…
One-way measurement based quantum computations (1WQC) may describe unitary transformations, via a composition of CPTP maps which are not all unitary themselves. This motivates the following decision problems: Is it possible to determine…
Due to existence of periodic windows, chaotic systems undergo numerous bifurcations as system parameters vary, rendering it hard to employ an analytic continuation, which constitutes a major obstacle for its effective analysis or…
We identify a fundamental challenge for non-perturbative linked cluster expansions (NLCEs) resulting from the reduced symmetry on graphs, most importantly the breaking of translational symmetry, when targeting the properties of excited…
We present a robust scheme to derive effective models non-perturbatively for quantum lattice models when at least one degree of freedom is gapped. A combination of graph theory and the method of continuous unitary transformations (gCUTs) is…
Unitarity serves as a fundamental concept for characterizing linear and conservative wave phenomena in both classical and quantum systems. Developing platforms that perform unitary operations on light waves in a uni-versal and programmable…
Photon-Counting Computed Tomography (PCCT) is a novel imaging modality that simultaneously acquires volumetric data at multiple X-ray energy levels, generating separate volumes that capture energy-dependent attenuation properties.…
This paper addresses the problem of designing universal quantum circuits to transform $k$ uses of a $d$-dimensional unitary input-operation into a unitary output-operation in a probabilistic heralded manner. Three classes of protocols are…
This study addresses the predictive limitation of probabilistic circuits and introduces transformations as a remedy to overcome it. We demonstrate this limitation in robotic scenarios. We motivate that independent component analysis is a…
Linear optical elements are pivotal instruments in the manipulation of classical and quantum states of light. The vast progress in integrated quantum photonic technology enables the implementation of large numbers of such elements on chip…
Quantum control in large dimensional Hilbert spaces is essential for realizing the power of quantum information processing. For closed quantum systems the relevant input/output maps are unitary transformations, and the fundamental challenge…
We develop variational continuous unitary transformations (VCUTs), which integrate Wegner-Wilson flow equations with tensor network techniques to approximately diagonalize many-body localized (MBL) Hamiltonians. The diagonalizing unitary is…
Starting from a semiclassical approach recently developed for spectral correlation functions of quantum systems whose classical dynamics is chaotic, we focus on the case of broken time-reversal symmetry, the so-called unitary class. We…
The technique of continuous unitary transformations has recently been used to provide physical insight into a diverse array of quantum mechanical systems. However, the question of how to best numerically implement the flow equations has…
This article reviews unitarization methods essential for extending Effective Field Theories (EFTs) beyond their perturbative limits, particularly in hadronic and electroweak (EW) sectors. Perturbative EFTs, like Chiral Perturbation Theory…
Transformers achieve strong performance across diverse domains but implicitly assume Euclidean geometry in their attention mechanisms, limiting their effectiveness on data with non-Euclidean structure. While recent extensions to hyperbolic…
In this paper we analyze a recent application of perturbation theory by the moment method to a family of two-dimensional anharmonic oscillators. By means of straightforward unitary transformations we show that two of the models studied by…