Related papers: Quasi-classical alternatives in quantum chemistry
Quantum Machine Learning algorithms based on Variational Quantum Circuits (VQCs) are important candidates for useful application of quantum computing. It is known that a VQC is a linear model in a feature space determined by its…
This paper presents a renormalization approach to many-particle systems. By starting from a bare Hamiltonian ${\cal H}= {\cal H}_0 +{\cal H}_1$ with an unperturbed part ${\cal H}_0$ and a perturbation ${\cal H}_1$,we define an effective…
Lie-algebraic and quantum-algebraic techniques are used in the analysis of thermodynamic properties of molecules and solids. The local anharmonic effects are described by a Morse-like potential associated with the $su(2)$ algebra. A…
Variational quantum algorithms involve training parameterized quantum circuits using a classical co-processor. An important variational algorithm, designed for combinatorial optimization, is the quantum approximate optimization algorithm.…
We present a general framework for finding the time-optimal evolution and the optimal Hamiltonian for a quantum system with a given set of initial and final states. Our formulation is based on the variational principle and is analogous to…
Solving combinatorial optimization problems on current noisy quantum devices is currently being advocated for (and restricted to) binary polynomial optimization with equality constraints via quantum heuristic approaches. This is achieved…
Quantum algorithms for simulating large and complex molecular systems are still in their infancy, and surpassing state-of-the-art classical techniques remains an ever-receding goal post. A promising avenue of inquiry in the meanwhile is to…
The main goal of this thesis is to quantize the Einstein-Hilbert action extended by the quadratic curvature terms within the canonical quantization approach, thus formulating quantum geometrodynamics of the higher derivative theories. The…
We provide an introduction to deformation quantisation and discuss the application of the formalism in solving the evolution problem for many-body systems in terms of semiclassical expansion. In any fixed order of expansion over the…
Through recent progress in hardware development, quantum computers have advanced to the point where benchmarking of (heuristic) quantum algorithms at scale is within reach. Particularly in combinatorial optimization - where most algorithms…
To study electronic transport through chaotic quantum dots, there are two main theoretical approachs. One involves substituting the quantum system with a random scattering matrix and performing appropriate ensemble averaging. The other…
While it seems possible that quantum computers may allow for algorithms offering a computational speed-up over classical algorithms for some problems, the issue is poorly understood. We explore this computational speed-up by investigating…
Variational quantum algorithms are poised to have significant impact on high-dimensional optimization, with applications in classical combinatorics, quantum chemistry, and condensed matter. Nevertheless, the optimization landscape of these…
We propose a method for constructing $\texttt{PREPARE}$ circuits for quantum phase estimation of a molecular Hamiltonian in quantum chemistry by using variational optimization of quantum circuits solely on classical computers. The…
Quantum annealing (QA) has the potential to significantly improve solution quality and reduce time complexity in solving combinatorial optimization problems compared to classical optimization methods. However, due to the limited number of…
Hamiltonian theory of hybrid quantum-classical systems is used to study dynamics of the classical subsystem coupled to different types of quantum systems. It is shown that the qualitative properties of orbits of the classical subsystem…
We formulate a conceptually new model in which quantum mechanics emerges from classical mechanics. Given a local Hamiltonian $H$ acting on $n$ qubits, we define a local classical model with an additional spatial dimension whose boundary…
The emergent semiclassical time approach to resolving the problem of time in quantum gravity involves heavy slow degrees of freedom providing via an approximately Hamilton-Jacobi equation an approximate timestandard with respect to which…
Quantum chemistry is a key target for quantum computing, but benchmarking quantum algorithms for large molecular systems remains challenging due to the lack of exactly solvable yet structurally realistic models. In particular, molecular…
The Hamiltonian conservative system of two interacting particles has been considered both in classical and quantum description. The quantum model has been realized using a symmetrized two-particle basis reordered in the unperturbed energy.…