Related papers: Quantum quasi-Lie systems: properties and applicat…
There are two classes of quantum integrable systems on a manifold with quadratic integrals, the Liouville and the Lie integrable systems as it happens in the classical case. The quantum Liouville quadratic integrable systems are defined on…
Every quantum physical system can be considered the ''shadow'' of a special kind of classical system. The system proposed here is classical mainly because each observable function has a well precise value on each state of the system: an…
In this paper we consider Hamiltonian systems on the quantum plane and we show that the set of Q-meromorphic Hamiltonians is a Virasoro algebra with central charge zero and the set of Hamiltonian derivations of the algebra of $Q$-analytic…
A general quantum adiabatic theorem with and without the time-dependent orthogonalization is proven, which can be applied to understand the origin of activation energies in chemical reactions. Further proofs are also developed for the…
Quantum communication is often investigated in scenarios where only the dimension of Hilbert space is known. However, assigning a precise dimension is often an approximation of what is actually a higher-dimensional process. Here, we…
We analyze some crucial questions regarding the practical feasibility of quantum simulation for lattice gauge models. Our analysis focuses on two models suitable for the quantum simulation of the Schwinger Hamiltonian, or QED in 1+1…
Strongly-coupled gauge theories far from equilibrium may exhibit unique features that could illuminate the physics of the early universe and of hadron and ion colliders. Studying real-time phenomena has proven challenging with…
We study mirror symmetry (A-side vs B-side) in the framework of quantum differential systems. We focuse on the logarithmic and non-resonant case, which describes the geometric situation. We show that quantum differential systems provide a…
The Whitham approach is a well-studied method to describe non-linear integrable systems. Although approximate in nature, its results may predict rather accurately the time evolution of such systems in many situations given initial…
We introduce a general method for the construction of quasiprobability representations for arbitrary notions of quantum coherence. Our technique yields a nonnegative probability distribution for the decomposition of any classical state.…
It is shown that quantum walks on one-dimensional arrays of special linear-optical units allow the simulation of discrete-time Hamiltonian systems with distinct topological phases. In particular, a slightly modified version of the…
The dynamics of a quantum nonlinear oscillator is studied in terms of its quasi-flow, a dynamical mapping of the classical phase plane that represents the time-evolution of the quantum observables. Explicit expressions are derived for the…
A characteristical property of a classical physical theory is that the observables are real functions taking an exact outcome on every (pure) state; in a quantum theory, at the contrary, a given observable on a given state can take several…
The 1+1D Ising model is an ideal benchmark for quantum algorithms, as it is very well understood theoretically. This is true even when expanding the model to include complex coupling constants. In this work, we implement quantum algorithms…
Construction of explicit quantum circuits follows the notion of the "standard circuit model" introduced in the solid and profound analysis of elementary gates providing quantum computation. Nevertheless the model is not always optimal (e.g.…
Quantum systems with constraints are often considered in modern theoretical physcics. All realistic field models based on the idea of gauge symmetry are of this type. A partial case of constraints being linear in coordinate and momenta…
We introduce a general statistical learning theory for processes that take as input a classical random variable and output a quantum state. Our setting is motivated by the practical situation in which one desires to learn a quantum process…
The relation between the dynamical properties of a coupled quasiparticle-oscillator system in the mixed quantum-classical and fully quantized descriptions is investigated. The system is considered to serve as a model system for applying a…
Interpretability of artificial intelligence (AI) methods, particularly deep neural networks, is of great interest. This heightened focus stems from the widespread use of AI-backed systems. These systems, often relying on intricate neural…
We introduce a smooth mapping of some discrete space-time symmetries into quasi-continuous ones. Such transformations are related with q-deformations of the dilations of the Euclidean space and with the non-commutative space. We work out…