Related papers: Chaotic quantum dots with strongly correlated elec…
In this article, using the principles of Random Matrix Theory (RMT), we give a measure of quantum chaos by quantifying Spectral From Factor (SFF) appearing from the computation of two-point Out of Time Order Correlation function (OTOC)…
There have been several algorithms designed to optimise matrix multiplication. From schoolbook method with complexity $O(n^3)$ to advanced tensor-based tools with time complexity $O(n^{2.3728639})$ (lowest possible bound achieved), a lot of…
We investigate the distribution of roots of polynomials of high degree with random coefficients which, among others, appear naturally in the context of "quantum chaotic dynamics". It is shown that under quite general conditions their roots…
Quantum state tomography (QST), the process of reconstructing some unknown quantum state $\hat\rho$ from repeated measurements on copies of said state, is a foundationally important task in the context of quantum computation and simulation.…
A linearly coupled chain of spin-polarized quantum dots is investigated under the condition that the number of electrons is equal to or less than the number of the dots. The chemical potential of the system, $\mu_{N}=E(N)-E(N-1)$,…
As a cornerstone of automated reasoning, equational reasoning finds equivalences between symbolic expressions and fuels advances across scientific disciplines. Yet, its potential remains limited by the exponential growth of equivalent…
Computations with a future quantum computer will be implemented through the operations by elementary quantum gates. It is now well known that the collection of 1-bit and 2-bit quantum gates are universal for quantum computation, i.e., any…
Quantum chaotic systems are conjectured to display a spectrum whose fine-grained features (gaps and correlations) are well described by Random Matrix Theory (RMT). We propose and develop a complementary version of this conjecture: quantum…
A tool for the identification of the shape of quantum dots is developed. By preparing a two-electron quantum dot, the response of the low-lying excited states to a homogeneous magnetic field, i.e. their spin and parity oscillations, is…
We adapt the transfer matrix ($\T$-matrix) method originally designed for one-dimensional quantum mechanical problems to solve the circularly symmetric two-dimensional problem of graphene quantum dots. In similarity to one-dimensional…
In this work we present a general mathematical framework to deal with Quantum Networks, i.e. networks resulting from the interconnection of elementary quantum circuits. The cornerstone of our approach is a generalization of the Choi…
Several topics on the implementation of spin qubits in quantum dots are reviewed. We first provide an introduction to the standard model of quantum computing and the basic criteria for its realization. Other alternative formulations such as…
The observed IR and the spectator UV particles of a regulated, cutoff quantum field theory are entangled by their interactions; hence, the IR sector can be described by the help of the density matrix only. The tree-level renormalized…
We summarize recent work showing that the $1/r^2$ model of interacting particles in 1-dimension is a universal Hamiltonian for quantum chaotic systems. The problem is analyzed in terms of random matrices and of the evolution of their…
A molecular description for magic-number configurations of interacting electrons in a quantum dot in high magnetic fields developed by one of the authors has been elaborated for four, five and six electron dots. For four electrons, the…
Using the vehicle of resolving an apparent paradox, a discussion of quantum interference is presented. The understanding of a number of different physical phenomena can be unified, in this context. These range from the neutral kaon system…
The electrostatic energy of an additional electron on a conducting grain blocks the flow of current through the grain, an effect known as the Coulomb blockade. Current can flow only if two charge states of the grain have the same energy; in…
The random-phase approximation has been used to compute the properties of parabolic two-dimensional quantum dots beyond the mean-field approximation. Special emphasis is put on the ground state correlation energy, the symmetry restoration…
We present a complete classification of the electron-electron interaction in chaotic quantum dots based on expansion in inverse powers of $1/M$, the number of the electron states in the Thouless window, $M \simeq k_F R$. This classification…
A system consisting of two independently contacted quantum dots with strong electrostatic interaction shows interdot Coulomb blockade when the dots are weakly tunnel coupled to their leads. It is studied experimentally how the blockade can…