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Quantum mechanics requires the operation of quantum computers to be unitary, and thus makes it important to have general techniques for developing fast quantum algorithms for computing unitary transforms. A quantum routine for computing a…
In this second in a series of four articles we create a mathematical formalism sufficient to represent nontrivial hamiltonian quantum dynamics, including resonances. Some parts of this construction are also mathematically necessary. The…
Quasiparticle (QP) excitations are extremely important for understanding and predicting charge transfer and transport in molecules, nanostructures and extended systems. Since density functional theory (DFT) within the Kohn-Sham (KS)…
To set up a self-consistent quantum field theory of degenerate systems, the unperturbed state should be described by a density matrix instead of a pure state. This increases the combinatorial complexity of the many-body equations. Hopf…
We present an approach for GW calculations of quasiparticle energies with quasi-quadratic scaling by approximating high-energy contributions to the Green's function in its Lehmann representation with effective stochastic vectors. The method…
Classical {\W}$_3$ transformations are discussed as restricted diffeomorphism transformations (\W-Diff) in two-dimensional space. We formulate them by using Riemannian geometry as a basic ingredient. The extended {\W}$_3$ generators are…
A self-consistent many-body approach is proposed to build a first-principles crystal field theory, where crystal field parameters are calculated ab initio. Many-body theory is used to write the energy of the interacting system as a function…
The Schrodinger equation with a two-dimensional delta-function potential is a simple example of an asymptotically free theory that undergoes dimensional transmutation. Renormalization requires the introduction of a mass scale, which can be…
The Quantum Singular Value Transformation (QSVT) is a technique that provides a unified framework for describing many of the quantum algorithms discovered to date. We implement a noise-free simulation of the technique to investigate how it…
In this article we present a new C*-algebraic deformation of the Lorentz group. It is obtained by means of the Rieffel deformation applied to SL(2,C). We give a detailed description of the resulting quantum group in terms of generators -…
We give a systematic treatment of the quantum mechanics of a spin zero particle in a combined electromagnetic field and a weak gravitational field, which is produced by a slow moving matter source. The analysis is based on the Klein-Gordon…
We rewrite the Klein-Gordon (KG) equation in an arbitrary space-time transforming it into a generalized Schr\"odinger equation. Then we take the weak field limit and show that this equation has some differences with the traditional…
Quantum few-body systems are deceptively simple. Indeed, with the notable exception of a few special cases, their associated Schrodinger equation cannot be solved analytically for more than two particles. One has to resort to approximation…
A perturbative renormalization group is formulated for the study of Hamiltonian light-front field theory near a critical Gaussian fixed point. The only light-front renormalization group transformations found that can be approximated by…
Discussed is kinematics and dynamics of bodies with affine degrees of freedom, i.e., homogeneously deformable "gyroscopes". The special stress is laid on the status and physical justification of affine dynamical invariance. On the basis of…
Quantum simulation provides a powerful route for exploring many-body phenomena beyond the capabilities of classical computation. Existing approaches typically proceed in the forward direction: a model Hamiltonian is specified, implemented…
We present a comprehensive quantum many body theory for kq deformed particles, offering a novel framework that relates particle statistics directly to effective interaction strength. Deformed by the parameters k and q, these particles…
We introduce a way of implementing Wilson renormalization within the context of the theory of effective Hamiltonians. Our renormalization scheme involves manipulations at the level of the generalized $G$--matrix and is independent of any…
Quantum circuits have been widely used as a platform to simulate generic quantum many-body systems. In particular, random quantum circuits provide a means to probe universal features of many-body quantum chaos and ergodicity. Some such…
We study a qDRIFT-type randomized method to simulate Lindblad dynamics by decomposing its generator into an ensemble of Lindbladians, $\mathcal{L} = \sum_{a \in \mathcal{A}} \mathcal{L}_a$, where each $\mathcal{L}_a$ comprises a simple…