Related papers: Simplified diagrammatic expansion for effective op…
For many-particle systems defined on lattices we investigate the global structure of effective Hamiltonians and observables obtained by means of a suitable basis transformation. We study transformations which lead to effective Hamiltonians…
One of the useful and practical methods for solving quantum-mechanical many-body systems is to recast the full problem into a form of the effective interaction acting within a model space of tractable size. Many of the effective-interaction…
Electronic structure simulation is an anticipated application for quantum computers. Due to high-dimensional quantum entanglement in strongly correlated systems, the quantum resources required to perform such simulations are far beyond the…
Accurately describing properties of challenging problems in physical sciences often requires complex mathematical models that are unmanageable to tackle head-on. Therefore, developing reduced dimensionality representations that encapsulate…
We propose an adiabatic-elimination formalism in the dispersive regime based on a transition-centric perturbation theory. The perturbative expansion is recast into a diagrammatic framework, while adiabatic elimination is implemented through…
Effective interaction operators usually act on a restricted model space and give the same energies (for Hamiltonian) and matrix elements (for transition operators etc.) as those of the original operators between the corresponding true…
We prove the existence of a unitary transformation that enables two arbitrarily given Hamiltonians in the same Hilbert space to be transformed into one another. The result is straightforward yet, for example, it lays the foundation to…
Recent advances in the field of adiabatic quantum computing and the closely related field of quantum annealers has centered around using more advanced and novel Hamiltonian representations to solve optimization problems. One of these…
We decompose the Hilbert space of wave functions into two subspaces, and assign to a given observable two effective representatives that act in the model space. The first serves to determine some of the eigenvalues of the full observable,…
The dynamics of classical and quantum systems which are driven by a high frequency ($\omega$) field is investigated. For classical systems the motion is separated into a slow part and a fast part. The motion for the slow part is computed…
We present an effective operator formalism for open quantum systems. Employing perturbation theory and adiabatic elimination of excited states for a weakly driven system, we derive an effective master equation which reduces the evolution to…
The quantum mechanical motion of the atomic nuclei is considered over a single- or a multi-dimensional subspace of electronic states which is separated by a gap from the rest of the electronic spectrum over the relevant range of nuclear…
Additional information about the eigenvalues and eigenvectors of a physical system demands extension of the effective Hamiltonian in use. In this work we extend the effective Hamiltonian that describes partially a physical system so that…
The Variational Quantum Eigensolver approach to the electronic structure problem on a quantum computer involves measurement of the Hamiltonian expectation value. Formally, quantum mechanics allows one to measure all mutually commuting or…
We show here that the Hamiltonian for an electronic system may be written exactly in terms of fluctuation operators that transition constituent fragments between internally correlated states, accounting rigorously for inter-fragment…
Quantum optimization algorithms hold the promise of solving classically hard, discrete optimization problems in practice. The requirement of encoding such problems in a Hamiltonian realized with a finite -- and currently small -- number of…
The characteristic polynomial of the effective Hamiltonian for a general model has been discussed. It is found that, compared with the associated energy eigenvalues, this characteristic polynomial generally has better analytical properties…
In the field of quantum control, effective Hamiltonian engineering is a powerful tool that utilises perturbation theory to mitigate or enhance the effect that a variation in the Hamiltonian has on the evolution of the system. Here, we…
An effective Hamiltonian describing interaction between generic "fast" and a "slow" systems is obtained in the strong interaction limit. The result is applied for studying the effect of quantum phase transition as a bifurcation of the…
We present a systematic scheme for optimization of quantum simulations. Specifically, we show how polychromatic driving can be used to significantly improve the driving of Raman transitions in the Lambda system, which opens new…