Related papers: Quantum Surface of Section Method: Eigenstates and…
Motivated by understanding the power of quantum computation with restricted number of qubits, we give two complete characterizations of unitary quantum space bounded computation. First we show that approximating an element of the inverse of…
There has been substantial calculational progress in the last few years for gauge theory amplitudes which involve massless four dimensional particles. One of the central ingredients in this has been the ability to keep precise track of the…
The semiclassical Wigner function for a Bohr-quantized energy eigenstate is known to have a caustic along the corresponding classical closed phase space curve in the case of a single degree of freedom. Its Fourier transform, the…
We consider the problem of computing exact sums of squares (SOS) decompositions for certain classes of non-negative multivariate polynomials, relying on semidefinite programming (SDP) solvers. We provide a hybrid numeric-symbolic algorithm…
The dynamics of M-site, N-particle Bose-Hubbard systems is described in quantum phase space constructed in terms of generalized SU(M) coherent states. These states have a special significance for these systems as they describe fully…
Hamiltonian representations based on the sum-of-squares (SOS) hierarchy provide rigorous lower bounds on ground-state energies and facilitate the design of efficient classical and quantum simulation algorithms. This work presents a unified…
Generic low-dimensional Hamiltonian systems feature a structured, mixed classical phase-space. The traditional Percival classification of quantum spectra into regular states supported by quasi-integrable regions and irregular states…
We undertake a thorough investigation into the phenomenology of quantum eigenstates, in the three-particle FPUT model. Employing different Husimi functions, our study focuses on both the $\alpha$-type, which is canonically equivalent to the…
We study the statistical properties of the spectrum of a quantum dynamical system whose classical counterpart has a mixed phase space structure consisting of two regular regions separated by a chaotical one. We make use of a simple symmetry…
Polarisation is described by an $SU(2)$ wavefunction due to macroscopic coherence of photons emitted from a ubiquitous laser source, and thus, a laser pulse is expected to behave as a macroscopic quantum bit (qubit), i.e., a qubit realised…
A study on a method for the establishment of a phase space representation of quantum theory is presented. The approach utilizes the properties of Gaussian distribution, the properties of Hermite polynomials, Fourier analysis and the current…
Large-scale quantum computation is likely to require massive quantum error correction (QEC). QEC codes and circuits are described via the stabilizer formalism, which represents stabilizer states by keeping track of the operators that…
We provide (partial) reconstruction formulas and discrete Fourier transforms for wave functions in standard Fock-Bargmann (holomorphic) phase-number representation from a finite number $N$ of phase samples $\{\theta_k=2\pi…
Recently, it has been demonstrated that asymptotic states of open quantum system can undergo qualitative changes resembling pitchfork, saddle-node, and period doubling classical bifurcations. Here, making use of the periodically modulated…
While quantum state tomography (QST) remains the gold standard for benchmarking and verifying quantum devices, it requires an exponentially large number of measurements and classical computational resources for generic quantum many-body…
Coherent states in a projected Hilbert space have many useful properties. When there are conserved quantities, a representation of the entire Hilbert space is not necessary. The same issue arises when conditional observations are made with…
The moment-sum-of-squares (moment-SOS) hierarchy is one of the most celebrated and widely applied methods for approximating the minimum of an n-variate polynomial over a feasible region defined by polynomial (in)equalities. A key feature of…
Quantum systems with a finite number of states at all times have been a primary element of many physical models in nuclear and elementary particle physics, as well as in condensed matter physics. Today, however, due to a practical demand in…
For the representation of eigenstates on a Poincar\'e section at the boundary of a billiard different variants have been proposed. We compare these Poincar\'e Husimi functions, discuss their properties and based on this select one…
We investigate eigenstate localization in the phase space of the Bunimovich mushroom billiard, a paradigmatic mixed-phase-space system whose piecewise-$C^{1}$ boundary yields a single clean separatrix between one regular and one chaotic…