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The hopes for scalable quantum computing rely on the "threshold theorem": once the error per qubit per gate is below a certain value, the methods of quantum error correction allow indefinitely long quantum computations. The proof is based…
One of the most promising applications of quantum computing is simulating quantum many-body systems. However, there is still a need for methods to efficiently investigate these systems in a native way, capturing their full complexity. Here,…
For a system of N identical particles in a random pure state, there is a threshold k_0 = k_0(N) ~ N/5 such that two subsystems of k particles each typically share entanglement if k > k_0, and typically do not share entanglement if k < k_0.…
Scalable quantum computers hold the promise to solve hard computational problems, such as prime factorization, combinatorial optimization, simulation of many-body physics, and quantum chemistry. While being key to understanding many…
Non-Abelian geometric phases form the foundation of fault-tolerant holonomic quantum computation. An "all-geometric" approach leveraging these phases enables robust unitary operations in condensed matter systems. Photonics, with rich…
Non-Gaussian entangled states play a crucial role in harnessing quantum advantage in continuous-variable quantum information. However, how to fully characterize N-partite (N > 3) non-Gaussian entanglement without quantum state tomography…
Quantum computing crucially relies on the ability to efficiently characterize the quantum states output by quantum hardware. Conventional methods which probe these states through direct measurements and classically computed correlations…
Quantum tunneling across double potential barriers is studied. With the assumption that the real space is a continuum, it is rigorously proved that large barriers of arbitrary shapes can be penetrated by low-energy particles with a…
Quantum state tomography (QST) aims at estimating a quantum state from averaged quantum measurements made on copies of the state. Most quantum algorithms rely on QST at some point and it is a well explored topic in the literature, mostly…
Typical quantum computing schemes require transformations (gates) to be targeted at specific elements (qubits). In many physical systems, direct targeting is difficult to achieve; an alternative is to encode local gates into globally…
This review is focused on various properties of quantum phase transitions (QPTs) in the Interacting Boson Model (IBM) of nuclear structure. The model in its infinite-size limit exhibits shape-phase transitions between spherical, deformed…
The capability to generate and manipulate quantum states in high-dimensional Hilbert spaces is a crucial step for the development of quantum technologies, from quantum communication to quantum computation. One-dimensional quantum walk…
In many systems, the time scales of the microscopic dynamics and macroscopic dynamics of interest are separated by many orders of magnitude. Examples abound, for instance nucleation, protein folding, and chemical reactions. For these…
Gradient-based optimization is a key ingredient of variational quantum algorithms, with applications ranging from quantum machine learning to quantum chemistry and simulation. The parameter-shift rule provides a hardware-friendly method for…
Quantum Process Tomography (QPT) methods aim at identifying, i.e. estimating, a quantum process. QPT is a major quantum information processing tool, since it especially allows one to experimentally characterize the actual behavior of…
A conventional quantum phase transition (QPT) can be accessed by varying a real parameter at absolute zero temperature. Motivated by the discovery of the pseudo-Hermiticity of non-Hermitian systems, we explore the QPT in non-Hermitian…
The eigenvalue absorption for a many-particle Hamiltonian depending on a parameter is analyzed in the framework of non--relativistic quantum mechanics. The long--range part of pair potentials is assumed to be pure Coulomb and no restriction…
Quantum phase transition is interpreted as an evolution, at the end of which a parameter-dependent Hamiltonian $H(g)$ loses its observability. In the language of mathematics, such a quantum catastrophe occurs at an exceptional point of…
We propose a probabilistic quantum protocol to realize a nonlinear transformation of qutrit states, which by iterative applications on ensembles can be used to distinguish two types of pure states. The protocol involves single-qutrit and…
Equilibrium phase transitions usually emerge from the microscopic behavior of many-body systems and are associated to interesting phenomena such as the generation of long-range order and spontaneous symmetry breaking. They can be defined…