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We study analytically and numerically the effects of various imperfections in a quantum computation of a simple dynamical model based on the Quantum Wavelet Transform (QWT). The results for fidelity timescales, obtained for a large range of…
Towards better understanding of how to design efficient adiabatic quantum algorithms, we study how the adiabatic gap depends on the spectra of the initial and final Hamiltonians in a natural family of test-bed examples. We show that perhaps…
A statistical analysis of the prime numbers indicates possible traces of quantum chaos. We have computed the nearest neighbor spacing distribution, number variance, skewness, and excess for sequences of the first N primes for various values…
We study the statistical and dynamical properties of the quantum triangle map, whose classical counterpart can exhibit ergodic and mixing dynamics, but is never chaotic. Numerical results show that ergodicity is a sufficient condition for…
We predict that continuously monitored quantum dynamics can be chaotic. The optimal paths between past and future boundary conditions can diverge exponentially in time when there is time-dependent evolution and continuous weak monitoring.…
We study numerically the effects of static imperfections and residual couplings between qubits for the quantum phase estimation algorithm with two qubits. We show that the success probability of the algorithm is affected significantly more…
Quantum state tomography is a core task in quantum system identification. Real experimental conditions often deviate from nominal designs, introducing errors in both the measurement devices and the Hamiltonian governing the system's…
Random matrix theory (RMT) provides a successful model for quantum systems, whose classical counterpart has a chaotic dynamics. It is based on two assumptions: (1) matrix-element independence, and (2) base invariance. Last decade witnessed…
Quantum chaos plays a significant role in understanding several important questions of recent theoretical and experimental studies. Here, by focusing on the localization properties of eigenstates in phase space (by means of Husimi…
We perform a detailed numerical study of energy-level and wavefunction statistics of a deformable quantum billiard focusing on properties relevant to semiconductor quantum dots. We consider the family of Robnik billiards generated by simple…
We assume that the level spectra of quantum systems in the initial phase of transition from integrability to chaos are approximated by superpositions of independent sequences. Each individual sequence is modeled by a random matrix ensemble.…
We show on the example of the Arnold cat map that classical chaotic systems can be simulated with exponential efficiency on a quantum computer. Although classical computer errors grow exponentially with time, the quantum algorithm with…
We propose to analyse the statistical properties of a sequence of vectors using the spectrum of the associated Gram matrix. Such sequences arise e.g. by the repeated action of a deterministic kicked quantum dynamics on an initial condition…
We experimentally and numerically investigate the quantum accelerator mode dynamics of an atom optical realization of the quantum delta-kicked accelerator, whose classical dynamics are chaotic. Using a Ramsey-type experiment, we observe…
There is a newly emerging understanding that in the chaotic domain of isolated finite interacting many particle systems smoothed densities define the statistical description of these systems and these densities follow from embedded…
Quantum chaotic dynamics is obtained for a tight-binding model in which the energies of the atomic levels at the boundary sites are chosen at random. Results for the square lattice indicate that the energy spectrum shows a complex behavior…
Ergodicity and chaos play an integral role in the dynamical behavior of many-particle systems and are crucial to the formulation of statistical mechanics. Still, a general understanding of how randomness and chaos emerge in the dynamical…
We analyze the interplay of chaos, entanglement and decoherence in a system of qubits whose collective behaviour is that of a quantum kicked top. The dynamical entanglement between a single qubit and the rest can be calculated from the mean…
Following a recent work (briefly reviewed below) we consider temporal fluctuations in the reduced density matrix elements for a coupled system involving a pair of kicked rotors as also one made up of a pair of Harper Hamiltonians. These…
Simulating the dynamics and the non-equilibrium steady state of an open quantum system are hard computational tasks on conventional computers. For the simulation of the time evolution, several efficient quantum algorithms have recently been…