The suppression of chaos in quantum reality is evident in quantum scars, i.e., in enhanced probability densities along classical periodic orbits, providing opportunities in controlling quantum trans- port in nanoscale quantum systems. Here, we focus on the energy level statistics of perturbed two-dimensional quantum systems exhibiting recently discovered, strong perturbation-induced quantum scarring. In particular, we study the effect of local perturbations and an external magnetic field on the eigenvalue statistics and scarring. Energy spectra are analyzed to investigate the chaoticity of the quantum system in the context of the Bohigas-Giannoni-Schmidt conjecture. We demonstrate that perturbation-induced scarring is strong in classically fully chaotic systems that, however, represent mixed eigenvalue statistics in the quantum case.

We study the dynamical behavior of a non-Hermitian moire superlattice system, which consists of two-coupled SSH chains with staggered imaginary on-site potentials. There are two main spatial regions, in which systems are in unbroken symmetric phases with fully real spectrum, appearing periodically along the ladder. We show that the two quantum phases are dimerized and tetramerized, which determine the distinct dynamical behaviors. Dirac probability can oscillate periodically, increase quadratically and increase exponentially, which correspond to the unbroken phase, exceptional point and the broken phase of the tetramerized region. In comparison, the Dirac probability can exhibit high-frequency oscillation in the dimerized region. These phenomena demonstrate the dynamical signature and provide insightful information of the moire pattern in the non-Hermitian regime.

We present a systematic formulation of scattering theory for nonlinear interactions in one dimension and develop a nonlinear generalization of the transfer matrix that has a composition property similar to its linear analog's. We offer alternative characterizations of spectral singularities, unidirectional reflectionlessness and invisibility, and nonreciprocal transmission for nonlinear scattering systems, and examine the application of our general results in addressing the scattering problem for nonlinear single- and double-$\delta$-function potentials.

We consider the Molecular Opto-mechanical systems in back-action amplification of single molecule Raman imaging. Surface Enhanced Raman Scattering (SERS) is mapped into the dissipative cavity opto-mechanics system of coupled resonators. We investigate the plasmon molecular vibration interactions in strong coupling regimes of cavity opto-mechanics in the presence of impurities. Eigenfunction spectrum is analyzed for the normal mode splitting of photonic and mechanical hybrid system. Back-action transduction of photons into mechanical modes is investigated by avoided crossing due to the nonlinear interactions and Casimir forces in the presence of virtual photons and radiation pressure. In input-output coupled cavity scheme, both cavity and driving fields are analyzed for the absorption and dissipation of heat in weak and strong coupling regimes of the cascaded cavity setup. In terms of the second order coherence functions, thermodynamic work and heat engine are investigated via phonon lasing of mechanical mode in opto-mechanical implementation of Brownian motors by tuning the competing coupling strengths of impurities and nonlinearities.

The impossibility of ascribing definite states to the constituents of an entangled system restricts the scope of Pauli's principle in this context. We analyze the conceptual and physical aspects of the problem by studying the actual scope of the principle and the possibility of extending the concept of exclusion in correlated systems. When the entanglement is weak, as in the archetypical case of the Helium atom, the principle can be applied in an approximated way. The concept of non-complete set of properties plays a crucial role in the argument, which also clarifies the physical meaning of the atomic quantum numbers; they are a multi-particle property, not an one-electron one. In contrast, for strong entanglement the excluded states are independent of the principle. We describe some of these states, many times determined by symmetries of the multi-fermion state.

We introduce a novel generalization of the Clauser-Horne-Shimony-Holt (CHSH) game to a multiplayer setting, i.e., Hypercube game, where all $m$ players are required to assign values to vertices on corresponding facets of an $m$-dimensional hypercube. The players win if and only if their answers satisfy both parity and consistency conditions. We completely characterize the maximum winning probabilities (game value) under classical, quantum and no-signalling strategies, respectively. In contrast to the original CHSH game designed to demonstrate the superiority of quantumness, we find that the quantum advantages in the Hypercube game significantly decrease as the number of players increase. Notably, the quantum value decays exponentially fast to the classical value as $m$ increases, while the no-signalling value always remains to be one.

The Superconducting Quantum Computing (SQC) is one of the most promising quantum computing techniques. The SQC requires precise control and acquisition to operate the superconducting qubits. The ultra-precision DC source is used to provide a DC bias for the qubit to work at its operation point. With the development of the multi-qubit processor, to use the commercial precise DC source device is impossible for its large volume occupation. We present our ultra-precision DC source which is designed for SQC experiments in this paper. The DC source contains 12 channels in 1U 19~inch crate. The performances of our DC source strongly beat the commercial devices. The output rang is -7~V to +7~V with 20~mA maximum output current. The Vpp of the output noise is 3~uV, and the standard deviation is 0.497~uV. The temperature coefficient is less than 1~ppm/$^{\circ}$C in 14~V range. The primary results show that the total drift of the output within 48h at an A/C room temperature environment is 40~uV which equal to 2.9~ppm/48h. We are still trying to optimize the channel density and long-term drift / stability.

Transition metal dichalcogenides have been the primary materials of interest in the field of valleytronics for their potential in information storage, yet the limiting factor has been achieving long valley decoherence times. We explore the dynamics of four monolayer TMDCs (MoS$_2$, MoSe$_2$, WS$_2$, WSe$_2$) using ab initio calculations to describe electron-electron and electron-phonon interactions. By comparing calculations which both omit and include relativistic effects, we isolate the impact of spin-resolved spin-orbit coupling on transport properties. In our work, we find that spin-orbit coupling increases carrier lifetimes at the valence band edge by an order of magnitude due to spin-valley locking, with a proportional increase in the hole mobility at room temperature. At temperatures of 50~K, we find intervalley scattering times on the order of 100 ps, with a maximum value ~140 ps in WSe$_2$. Finally, we calculate excited-carrier generation profiles which indicate that direct transitions dominate across optical energies, even for WSe$_2$ which has an indirect band gap. Our results highlight the intriguing interplay between spin and valley degrees of freedom critical for valleytronic applications. Further, our work points towards interesting quantum properties on-demand in transition metal dichalcogenides that could be leveraged via driving spin, valley and phonon degrees of freedom.

The exact solution of the one-dimensional Schr\"odinger equation with symmetric trigonometric double-well potential (DWP) is obtained via angular oblate spheroidal function. The results of stringent analytic calculation for the ground state splitting of ring-puckering vibration in the 1,3-dioxole (as an example of the case when the ground state tunneling doublet is well below the potential barrier top) and 2,3-dihydrofuran (as an example of the case when the ground state tunneling doublet is close to the potential barrier top) are compared with several variants of approximate semiclassical (WKB) ones. This enables us to verify the accuracy of various WKB formulas suggested in the literature: 1. ordinary WKB, i.e., the formula from the Landau and Lifshitz textbook; 2. Garg's formula; 3. instanton approach. We show that for the former case all three variants of WKB provide good accuracy while for the latter one they are very inaccurate. The results obtained provide a new theoretical tool for describing relevant experimental data on IR spectroscopy of ring-puckering vibrations.

Improving accuracy of quantum operations is an indispensable task for realizing a practical quantum computer. A reliable method for characterizing quantum operations is a useful tool toward further improvements of the accuracy. Quantum tomography and randomized benchmarking protocols are current standard methods for evaluating accuracies of quantum operations, but they lack reliability of estimates because of high sensitivity to state preparation and measurement (SPAM) errors or they use multiple approximations. Here we propose a self-consistent quantum tomographic method. First, we derive a sufficient condition on experiments for characterizing quantum operations except for the gauge degrees of freedom. Second, we propose a new self-consistent estimator. We mathematically prove that, when the sufficient condition is satisfied, the estimator provides estimates that is always physical and converges to the gauge-equivalent class of the quantum operations of interest at the limit of data size going to infinity. These results theoretically guarantee that the method makes it possible to reliably characterize accurate quantum operations.

We canonically quantize a spin-less non-relativistic point particle in a rigidly rotating cylinder symmetric reference system. The resulting quantum mechanics is investigated in the case of both a two-dimensional cylindrical shell and in the case of the full rotating cylinder; in both cases energy eigenstates exist which exhibit rotation induced negative energies. Based on a reanalysis of the classical Sagnac effect a novel way to compute the quantum Sagnac phase shift is deduced. It is pointed out that certain states on both the cylindrical shell and in the bulk give rise to a novel anomalous quantum Sagnac effect.

Quantum processors with sizes in the 10-100 qubit range are now increasingly common. However, with increased size comes increased complexity for benchmarking. The effectiveness of a given device may vary greatly between different tasks, and will not always be easy to predict from single and two qubit gate fidelities. For this reason, it is important to assess processor quality for a range of important tasks. In this work we propose and implement tests based on random quantum circuits. These are used to evaluate multiple different superconducting qubit devices, with sizes from 5 to 19 qubits, from two hardware manufacturers: IBM Research and Rigetti. The data is analyzed to give a quantitive description of how the devices perform. We also describe how it can be used for a qualititive description accessible to the layperson, by being played as a game.

We derive a Magnus expansion for a frequency chirped quantum two-level system. We obtain a time-independent effective Hamiltonian which generates a stroboscopic time evolution. At lowest order the according dynamics is identical to results from using a rotating wave approximation. We determine, furthermore, also the next higher order corrections within our expansion scheme in correspondence to the Bloch-Siegert shifts for harmonically driven systems. Importantly, our scheme can be extended to more complicated systems, i.e. even many-body systems.

We explore the question as to whether quantum effects can yield a speedup of the non-equilibrium evolution of spin systems towards a classical thermal state. In our approach we exploit the fact that the thermal state of a spin system can be mapped onto a node-free quantum state whose coefficients are given by thermal weights. This perspective permits the construction of a dissipative -- yet quantum -- dynamics which encodes in its stationary state the thermal state of the original problem. We show for the case of an all-to-all connected Ising spin model that an appropriate transformation of this dissipative dynamics allows to interpolate between a regime in which the order parameter obeys the classical equations of motion under Glauber dynamics, to a quantum regime with an accelerated approach to stationarity. We show that this effect enables in principle a speedup of pattern retrieval in a Hopfield neural network.

Quantum simulation presents itself as one of the biggest advantages of developing quantum computers. Simulating a quantum system classically is almost impossible beyond a certain system size whereas a controllable quantum system inherently has the resources and computing space to simulate another system. Analog quantum simulation is one of the ways of quantum simulation through which a known system mimics an unknown system. A key aspect of this is the ability to generate the target Hamiltonian using control operations which is referred to as Hamiltonian engineering. One way of doing this is to apply pulse sequences over a length of time such that the average Hamiltonian over this period is the desired one. In this thesis, we discuss the method of filtered Hamiltonian engineering which works in a similar fashion. Using this technique, we create a star topology from a general network of spins.

Quantum communication between two parties is an important task for its applications in information theory as well as for its use in a quantum computer. A typical solution to this is using teleportation through the means of shared entangled qubits. Teleportation is not ideal for short-range communication such as between two units in a quantum computer. It has been shown that information can be transported from one node of a quantum spin network to another by natural evolution of the system over time. Such networks are better suited for solid-state based computing architectures as well as for short-range communication. The Hamiltonian that permits such transport however places stringent requirements on the parameters of the network. While individual control of spins cannot be avoided in most cases, excess control can introduce noise. In this thesis, we work on a few models of spin networks that permit information transport with minimal requirements on the parameters of the network.

The Exact Factorization framework is extended and utilized to introduce the electronic-states of correlated electron-photon systems. The formal definitions of an exact scalar potential and an exact vector potential that account for the electron-photon correlation are given. Inclusion of these potentials to the Hamiltonian of the uncoupled electronic system leads to a purely electronic Schr\"odinger equation that uniquely determines the electronic states of the complete electron-photon system. For a one-dimensional asymmetric double-well potential coupled to a single photon mode with resonance frequency, we investigate the features of the exact scalar potential. In particular, we discuss the significance of the step-and-peak structure of the exact scalar potential in describing the phenomena of photon-assisted delocalization and polaritonic squeezing of the electronic excited-states. In addition, we develop an analytical approximation for the scalar potential and demonstrate how the step-and-peak features of the exact scalar potential are captured by the proposed analytical expression.

Quantum registers that combine the attractive properties of different types of qubits are useful for many different applications. They also pose a number of challenges, often associated with the large differences in coupling strengths between the different types of qubits. One example is the non-resonant effect that alternating electromagnetic fields have on the transitions of qubits that are not targeted by the specific gate operation. The example being studied here is known as Bloch-Siegert shift. Unless these shifts are accounted for and, if possible, compensated, they can completely destroy the information contained in the quantum register. Here we study this effect quantitatively in the important example of the nitrogen vacancy (NV) center in diamond and demonstrate how it can be eliminated.

We show that one can quantum simulate the dynamics of a Sachdev-Ye-Kitaev model with $N$ Majorana modes for time $t$ to precision $\epsilon$ with gate complexity $O(N^{7/2} t + N \log(1 / \epsilon) / \log\log(1/\epsilon))$. In addition to scaling sublinearly in the number of Hamiltonian terms, this gate complexity represents an exponential improvement in $1/\epsilon$ and large polynomial improvement in $N$ and $t$ over prior state-of-the-art algorithms which scale as $O(N^{10} t^2 / \epsilon)$. Our approach involves a variant of the qubitization technique in which we encode the Hamiltonian $H$ as an asymmetric projection of a signal oracle $U$ onto two different signal states prepared by state oracles, $A\left\vert{0}\right\rangle \mapsto \left\vert{A}\right\rangle$ and $B \left\vert{0}\right\rangle \mapsto \left\vert{B}\right\rangle$, such that $H = \left\langle{B}\right\vert U\left\vert{A}\right\rangle$. Our strategy for applying this method to the Sachdev-Ye-Kitaev model involves realizing $B$ using only Hadamard gates and realizing $A$ as a random quantum circuit.

We investigate magnetically tunable Feshbach resonances between ultracold europium atoms and between europium and alkali-metal atoms using multichannel quantum scattering calculations. For ultracold gases of europium atoms both homonuclear $^{153}$Eu+$^{153}$Eu and heteronuclear $^{151}$Eu+$^{153}$Eu systems are studied. Calculations for mixtures of europium and alkali-metal atoms are carried out for prototype systems of $^{153}$Eu+$^{87}$Rb and $^{153}$Eu+$^7$Li. We analyze the prospects for the control of scattering properties, observation of quantum chaotic behavior, and magnetoassociation into ultracold polar and paramagnetic molecules. We show that favorable resonances can be expected at experimentally feasible magnetic field strengths below 1000$\,$G for all investigated atomic combinations. For Eu atoms, a rich spectrum of resonances is expected as a result of the competition between relatively weak short-range spin-exchange and strong long-range magnetic dipole-dipole interactions, where the dipolar interaction induces measurable resonances. A high density of resonances is expected at magnetic field strengths below 200$\,$G without pronounced quantum chaos signatures. The present results may be useful for the realization and application of dipolar atomic and molecular quantum gases based on europium atoms in many-body physics.

The color code is both an interesting example of an exactly solved topologically ordered phase of matter and also among the most promising candidate models to realize fault-tolerant quantum computation with minimal resource overhead. The contributions of this work are threefold. First of all, we build upon the abstract theory of boundaries and domain walls of topological phases of matter to comprehensively catalog the objects realizable in color codes. Together with our classification we also provide lattice representations of these objects which include three new types of boundaries as well as a generating set for all 72 color code twist defects. Our work thus provides an explicit toy model that will help to better understand the abstract theory of domain walls. Secondly, we discover a number of interesting new applications of the cataloged objects for quantum information protocols. These include improved methods for performing quantum computations by code deformation, a new four-qubit error-detecting code, as well as families of new quantum error-correcting codes we call stellated color codes, which encode logical qubits at the same distance as the next best color code, but using approximately half the number of physical qubits. To the best of our knowledge, our new topological codes have the highest encoding rate of local stabilizer codes with bounded-weight stabilizers in two dimensions. Finally, we show how the boundaries and twist defects of the color code are represented by multiple copies of other phases. Indeed, in addition to the well studied comparison between the color code and two copies of the surface code, we also compare the color code to two copies of the three-fermion model. In particular, we find that this analogy offers a very clear lens through which we can view the symmetries of the color code which gives rise to its multitude of domain walls.