Related papers: Quantum Hamiltonians with weak random abstract per…
Pseudorandom circuits generate quantum states and unitary operators which are approximately distributed according to the unitarily invariant Haar measure. We explore how several design parameters affect the efficiency of pseudo-random…
Learning the structure of the entanglement Hamiltonian (EH) is central to characterizing quantum many-body states in analog quantum simulation. We describe a protocol where spatial deformations of the many-body Hamiltonian, physically…
Precision measurements of frequency are critical to accurate timekeeping, and are fundamentally limited by quantum measurement uncertainties. While for time-independent quantum Hamiltonians, the uncertainty of any parameter scales at best…
A model Hamiltonian dynamical system has been derived to study frequency cascades in the cubic defocusing nonlinear Schr\"odinger equation on the torus. Here, we explore the framework for exploring a canonical ensemble formulation of the…
Recent advances in analog and digital quantum-simulation platforms have enabled exploration of the spectrum of entanglement Hamiltonians via variational algorithms. In this work we analyze the convergence properties of the variationally…
We develop a variational principle to determine the quantum controls and initial state which optimizes the quantum Fisher information, the quantity characterizing the precision in quantum metrology. When the set of available controls is…
We develop further the approach to upper and lower bounds in quantum dynamics via complex analysis methods which was introduced by us in a sequence of earlier papers. Here we derive upper bounds for non-time averaged outside probabilities…
The goal of this paper is to review several qualitative properties of well-known eigenvalue problems using a different perspective based on the theory of effective Hamiltonians, working exclusively on the Hopf-Cole transform of the…
We study the entanglement Hamiltonian for finite intervals in infinite quantum chains for two different free-particle systems: coupled harmonic oscillators and fermionic hopping models with dimerization. Working in the ground state, the…
We propose a quantum algorithm to compute low-energy expectation values of a quantum Hamiltonian by sampling a partition function associated with the average energy of that Hamiltonian. For any given quantum circuit-Hamiltonian pair, there…
Harnessing the full power of nascent quantum processors requires the efficient management of a limited number of quantum bits with finite lifetime. Hybrid algorithms leveraging classical resources have demonstrated promising initial results…
The article surveys quantization schemes for metric graphs with spin. Typically quantum graphs are defined with the Laplace or Schrodinger operator which describe particles whose intrinsic angular momentum (spin) is zero. However, in many…
We ask to what extent an isolated quantum system can eventually "contract" to be contained within a given Hilbert subspace. We do this by starting with an initial random state, considering the probability that all the particles will be…
Understanding the mechanisms responsible for the equilibration of isolated quantum many-body systems is a long-standing open problem. In this work we obtain a statistical relationship between the equilibration properties of Hamiltonians and…
In \cite{BK} Parseval frames were used to define bounded Hamiltonians, both in finite and in infinite dimesional Hilbert spaces. Here we continue this analysis, with a particular focus on the discrete spectrum of Hamiltonian operators…
We establish Lieb-Thirring type inequalities for non self-adjoint relatively compact perturbations of certain operators of mathematical physics. We apply our results to quantum Hamiltonians of Schr{\"o}dinger and Pauli with constant…
Non-leptonic kaon decays are often described through an effective chiral weak Hamiltonian, whose couplings ("low-energy constants") encode all non-perturbative QCD physics. It has recently been suggested that these low-energy constants…
After analyzing Dirac's equation, one can suggest that a well-known quantum-mechanical momentum operator is associated with relativistic momentum, rather than with non-relativistic one. Consideration of relativistic energy and momentum…
Quantum measurements are our eyes to the quantum systems consisting of a multitude of microscopic degrees of freedom. However, the intrinsic uncertainty of quantum measurements and the exponentially large Hilbert space pose natural barriers…
We consider one particle confined to a deformed one-dimensional wire. The quantum mechanical equivalent of the classical problem is not uniquely defined. We describe several possible hamiltonians and corresponding solutions for a finite…