Related papers: Universal Quantum Hamiltonians
New status in quantum mechanics is connected with recent achievements in the inverse problem. With its help instead of about ten exactly solvable models which serve as a basis of the contemporary education there are infinite (!) number,…
Hamiltonians with inverse square interaction potential occur in the study of a variety of physical systems and exhibit a rich mathematical structure. In this talk we briefly mention some of the applications of such Hamiltonians and then…
Several completely integrable, indeed solvable, Hamiltonian many-body problems are exhibited, characterized by Newtonian equations of motion ("acceleration equal force"), with linear and cubic forces, in N-dimensional space (N being an…
Nowadays, quantum simulation schemes come in two flavours. Either they are continuous-time discrete-space models (a.k.a Hamiltonian-based), pertaining to non-relativistic quantum mechanics. Or they are discrete-spacetime models (a.k.a…
We construct a class of exact eigenstates of the Hamiltonian obtained by projecting the Hubbard interaction term onto the flat band subspace of a generic lattice model. These exact eigenstates are many body states in which an arbitrary…
We present a scalable framework for accurately modeling many-body interactions in surface-code quantum processor units (QPUs). Combining a concise diagrammatic formalism with high-precision numerical methods, our approach efficiently…
Quantum computing employs controllable interactions to perform sequences of logical gates and entire algorithms on quantum registers. This paradigm has been widely explored, e.g., for simulating dynamics of manybody systems by decomposing…
Quantum chaos is a quantum many-body phenomenon that is associated with a number of intricate properties, such as level repulsion in energy spectra or distinct scalings of out-of-time ordered correlation functions. In this work, we…
We propose a general framework of quantum kinetic Monte Carlo algorithm, based on a stochastic representation of a series expansion of the quantum evolution. Two approaches have been developed in the context of quantum many-body spin…
Simulating non-equilibrium phenomena in strongly-interacting quantum many-body systems, including thermalization, is a promising application of near-term and future quantum computation. By performing experiments on a digital quantum…
We investigate whether quantum theory can be understood as the continuum limit of a mechanical theory, in which there is a huge, but finite, number of classical 'worlds', and quantum effects arise solely from a universal interaction between…
We explore the effectiveness of variational quantum circuits in simulating the ground states of quantum many-body Hamiltonians. We show that generic high-depth circuits, performing a sequence of layer unitaries of the same form, can…
We present a class of one-dimensional generic spinless fermion lattice Hamiltonians that express quasi-Fermi liquid physics, manifesting both Luttinger and Fermi liquid features due to solely irrelevant interactions. Using infinite matrix…
We prove that quantum many-body systems on a one-dimensional lattice locally relax to Gaussian states under non-equilibrium dynamics generated by a bosonic quadratic Hamiltonian. This is true for a large class of initial states - pure or…
In this thesis we present new results relevant to two important problems in quantum information science: the development of a theory of entanglement and the exploration of the use of controlled quantum systems to the simulation of quantum…
We develop a method to deduce the symmetry properties of many-body Hamiltonians when they are prepared in Jordan-Wigner form for evaluation on quantum computers. Symmetries, such as point-group symmetries in molecules, are apparent in the…
A crucial milestone in the field of quantum simulation and computation is to demonstrate that a quantum device can compute certain tasks that are impossible to reproduce by a classical computer with any reasonable resources. Such a…
We present a symmetry-adapted extension of sample-based quantum diagonalization (SQD) that rigorously embeds space-group symmetry into the many-body subspace sampled by quantum hardware. The method is benchmarked on the two-leg ladder…
Hamiltonian quantum simulation of bosons on digital quantum computers requires truncating the Hilbert space to finite dimensions. The method of truncation and the choice of basis states can significantly impact the complexity of the quantum…
Modelling the electrical response of multi-level quantum systems at finite frequency has been typically performed in the context of two incomplete paradigms: (i) input-output theory, which is valid at any frequency but neglects dynamic…