Julio Alberto Lopez-Saldivar

In connection with the International Year of Quantum Science and Technology, a review of joint works of the Lebedev Institute and the Mexican research group at UNAM is presented, especially related to solving the old problem of the state description, not only by wave functions but also by conventional probability distributions analogous to quasiprobability distributions, like the Wigner function. Also, explicit expressions of tomographic representations describing the quantum states of particles moving in known potential wells are obtained and briefly discussed. In particular, we present the examples of the tomographic distributions for the free evolution, finite and infinite potential wells, and the Morse potential. Additional to this, an extension of the Peres–Horodecki separability criteria for momentum probability distributions is presented in the case of bipartite, asymmetrical, real states.

In connection with the International Year of Quantum Science and Technology, a review of joint works of the Lebedev Institute and different Mexican research groups is presented; specially related to solving the old problem of the state description not only by wave functions but also by conventional probability distributions analogous to quasiprobability distributions like the Wigner function. Also, explicit expressions of tomographic representations describing the quantum states of particles moving in known potential wells are obtained and briefly discussed. In particular, we present the examples of the tomographic distributions for the free evolution, finite and infinite potential wells, and the Morse potential. Additional to this, an extension of the Peres--Horodecki separability criteria for momentum probability distributions is presented in the case of bipartite, asymmetrical, real states.

We discuss in general the geometric properties of qudit systems, with a particular interest in thermal states. The principle of maximum entropy is used to study the geometric properties of an ensemble of finite dimensional Hamiltonian systems with known average energy. These geometric characterizations are given in terms of the generalized diagonal Bloch vectors and the invariants of the special unitary group in n dimensions. As examples, Hamiltonians written in terms of linear and quadratic generators of the angular momentum algebra are considered and explicitly visualized with J = 1 and J = 3/2. For these cases, paths as functions of the temperature are established in the corresponding simplex representations, which show first- and second-order quantum phase transitions, as well as the adiabatic evolution of the interaction strengths (control parameters) of the Hamiltonian models. For the Lipkin-Meshkov-Glick Hamiltonian the quantum phase diagram is explicitly shown for different temperature values in parameter space.

We present a continuous monitoring system for intermediate-scale quantum processors that allows extracting estimates of noisy native gate and read-out measurements based on the set of executed quantum circuits and resulting measurement outcomes. In contrast to standard approaches for calibration and benchmarking quantum processors, the executed circuits, which are input to the monitoring system, are assumed to be out of any control. We provide the results of applying our system to the synthetically generated data obtained from a quantum emulator, as well as to the experimental data collected from a publicly accessible cloud-based quantum processor. In both cases, we demonstrate that the developed approach provides valuable results about inherent noises of emulators and processors. Considering that our approach uses only already accessible data from implemented circuits without the need to run additional algorithms, the monitoring system can complement existing approaches. We expect that our monitoring system can become a useful tool for various quantum computers in the near-term horizon, including publicly accessible cloud-based platforms, and reduce resources that are required for their benchmarking and calibration.

The Wigner and tomographic representations of thermal Gibbs states for one- and two-mode quantum systems described by a quadratic Hamiltonian are obtained. This is done by using the covariance matrix of the mentioned states. The area of the Wigner function and the width of the tomogram of quantum systems are proposed to define a temperature scale for this type of states. This proposal is then confirmed for the general one-dimensional case and for a system of two coupled harmonic oscillators. The use of these properties as measures for the temperature of quantum systems is mentioned.