Initialization of composite quantum systems into highly entangled states is usually a must to allow their use for quantum technologies. However, the presence of unavoidable noise in the preparation stage makes the system state mixed, thus limiting the possibility of achieving this goal. Here we address this problem in the context of identical particle systems. We define the entanglement of formation for an arbitrary state of two identical qubits within the operational framework of spatially localized operations and classical communication (sLOCC). We then introduce an entropic measure of spatial indistinguishability under sLOCC as an information resource. We show that spatial indistinguishability, even partial, may shield entanglement from noise, guaranteeing Bell inequality violations. These results prove the fundamental role of particle identity as a control for efficient noise-protected entanglement generation.

A design of LEGO-like construction set that allows assembling of different linear arrays of three-dimensional (3D) cavities and qubits for circuit quantum electrodynamics (cQED) experiments has been developed. A study of electromagnetic properties of qubit-3D cavity arrays has been done by using high frequency structure simulator (HFSS). A technique for estimation of inter-qubit coupling strength between qubits embedded in different cavities of cavity array, which combines Hamiltonian description of the system with simple HFSS simulations, has been proposed. A good agreement between inter-qubit coupling strengths, which were obtained by using this technique and directly from simulation, demonstrates the suitability of the method for more complex qubit-cavity arrays where usage of finite-element electromagnetic simulators is limited.

In this article we propose a novel method to accelerate adiabatic passage in a two-level system with only longitudinal field (detuning) control, while the transverse field is kept constant. The suggested method is a modification of the Roland-Cerf protocol, during which the parameter quantifying local adiabaticity is held constant. Here, we show that with a simple ``on-off" modulation of this local adiabaticity parameter, a perfect adiabatic passage can be obtained for every duration larger than the lower bound $\pi/\Omega$, where $\Omega$ is the constant transverse field. For a fixed maximum amplitude of the local adiabaticity parameter, the timings of the ``on-off" pulse-sequence which achieves perfect fidelity in minimum time are obtained using optimal control theory. The corresponding detuning control is continuous and monotonic, a significant advantage compared to the detuning variation at the quantum speed limit which includes non-monotonic jumps. The proposed methodology can be applied in several important core tasks in quantum computing, for example to the design of a high fidelity controlled-phase gate, which can be mapped to the adiabatic quantum control of such a qubit. Additionally, it is expected to find applications across all Physics disciplines which exploit the adiabatic control of such a two-level system.

We investigate a classical statistical model and show that Mermin's version of a Bell inequality is violated. We get this violation, if the measurement modifies the ensemble, a feature, which is also characteristic for measurement processes for quantum systems.

In this work we calculate the Cram\'{e}r-Rao, the Fisher-Shannon and the L\'{o}pez-Ruiz-Mancini-Calbert (LMC) complexity measures for eigenstates of a deformed Schr\"{o}dinger equation, being this intrinsically linked with position-dependent mass (PDM) systems. The formalism presented is illustrated with a particle confined in an infinite potential well. Abrupt variation of the complexity near to the asymptotic value of the PDM-function $m(x)$ and erasure of its asymmetry along with negative values of the entropy density in the position space, are reported as a consequence of the interplay between the deformation and the complexity.

Detailed measurements of the cosmic microwave background indicate the large-scale homogeneity of the universe. On very small scales, we observe however inhomogeneities such as galaxies, stars, planets and ourselves. In the context of hot Big-Bang cosmology, these inhomogeneities are often explained as the remains of quantum fluctuations at very early times, enlarged to observable scales through the process of inflation. In this dissertation, I examine two important questions surrounding this scenario: a) How do inherently quantal fluctuations transition to the observed inhomogeneities, which behave classically? ; and b) If the initial state of the universe was symmetric, how can the currently observed state? This dissertation is organized in three parts. Part one first introduces the slow-roll inflation model and then discusses the behavior of small (scalar) perturbations to this model. The second part investigates various answers provided to the questions above, starting with some general observations on the classical limit of quantum mechanics with special attention given to the inverted harmonic oscillator. The formalisms of `squeezing' and decoherence are discussed and weak points are pointed out. In the final part, I examine in detail the pilot-wave approach to the problem, discussing in detail the classical limit of the theory and how pilot-wave theory addresses both questions above. Numerical results for pilot-wave trajectories are presented, illustrating directly the classical limit.

In this paper we consider the problems of testing isomorphism of tensors, $p$-groups, cubic forms, algebras, and more, which arise from a variety of areas, including machine learning, group theory, and cryptography. These problems can all be cast as orbit problems on multi-way arrays under different group actions. Our first two main results are:

1. All the aforementioned isomorphism problems are equivalent under polynomial-time reductions, in conjunction with the recent results of Futorny-Grochow-Sergeichuk (Lin. Alg. Appl., 2019).

2. Isomorphism of $d$-tensors reduces to isomorphism of 3-tensors, for any $d \geq 3$.

Our results suggest that these isomorphism problems form a rich and robust equivalence class, which we call Tensor Isomorphism-complete, or TI-complete. We then leverage the techniques used in the above results to prove two first-of-their-kind results for Group Isomorphism (GpI):

3. We give a reduction from GpI for $p$-groups of exponent $p$ and small class ($c < p$) to GpI for $p$-groups of exponent $p$ and class 2. The latter are widely believed to be the hardest cases of GpI, but as far as we know, this is the first reduction from any more general class of groups to this class.

4. We give a search-to-decision reduction for isomorphism of $p$-groups of exponent $p$ and class 2 in time $|G|^{O(\log \log |G|)}$. While search-to-decision reductions for Graph Isomorphism (GI) have been known for more than 40 years, as far as we know this is the first non-trivial search-to-decision reduction in the context of GpI.

Our main technique for (1), (3), and (4) is a linear-algebraic analogue of the classical graph coloring gadget, which was used to obtain the search-to-decision reduction for GI. This gadget construction may be of independent interest and utility. The technique for (2) gives a method for encoding an arbitrary tensor into an algebra.

Quantum error-correcting codes are used to protect qubits involved in quantum computation. This process requires logical operators, acting on protected qubits, to be translated into physical operators (circuits) acting on physical quantum states. We propose a mathematical framework for synthesizing physical circuits that implement logical Clifford operators for stabilizer codes. Circuit synthesis is enabled by representing the desired physical Clifford operator in $\mathbb{C}^{N \times N}$ as a partial $2m \times 2m$ binary symplectic matrix, where $N = 2^m$. We state and prove two theorems that use symplectic transvections to efficiently enumerate all binary symplectic matrices that satisfy a system of linear equations. As a corollary of these results, we prove that for an $[\![ m,k ]\!]$ stabilizer code every logical Clifford operator has $2^{r(r+1)/2}$ symplectic solutions, where $r = m-k$, up to stabilizer degeneracy. The desired physical circuits are then obtained by decomposing each solution into a product of elementary symplectic matrices, that correspond to elementary circuits. This enumeration of all physical realizations enables optimization over the ensemble with respect to a suitable metric. Furthermore, we show that any circuit that normalizes the stabilizer of the code can be transformed into a circuit that centralizes the stabilizer, while realizing the same logical operation. Our method of circuit synthesis can be applied to any stabilizer code, and this paper discusses a proof of concept synthesis for the $[\![ 6,4,2 ]\!]$ CSS code. Programs implementing the algorithms in this paper, which includes routines to solve for binary symplectic solutions of general linear systems and our overall LCS (logical circuit synthesis) algorithm, can be found at: https://github.com/nrenga/symplectic-arxiv18a

Entropic Dynamics is a framework for deriving the laws of physics from entropic inference. In an (ED) of particles, the central assumption is that particles have definite yet unknown positions. By appealing to certain symmetries, one can derive a quantum mechanics of scalar particles and particles with spin, in which the trajectories of the particles are given by a stochastic equation. This is much like Nelson's stochastic mechanics which also assumes a fluctuating particle as the basis of the microstates. The uniqueness of ED as an entropic inference of particles allows one to continuously transition between fluctuating particles and the smooth trajectories assumed in Bohmian mechanics. In this work we explore the consequences of the ED framework by studying the trajectories of particles in the continuum between stochastic and Bohmian limits in the context of a few physical examples, which include the double slit and Stern-Gerlach experiments.

We present computational chemistry data for small molecules ($CO$, $HCl$, $F_2$, $NH_4^+$, $CH_4$, $NH_{3}$, $H_3O^+$, $H{_2}O$, $BeH_{2}$, $LiH$, $OH^-$, $HF$, $HeH^+$, $H_2$), obtained by implementing the Unitary Coupled Cluster method with Single and Double excitations (UCCSD) on a quantum computer simulator. We have used the Variational Quantum Eigensolver (VQE) algorithm to extract the ground state energies of these molecules. This energy data represents the expected ground state energy that a quantum computer will produce for the given molecules, on the STO-3G basis. Since there is a lot of interest in the implementation of UCCSD on quantum computers, we hope that our work will serve as a benchmark for future experimental implementations.

In this manuscript, we investigate the effect of the white and color noise on a accelerated two-qubit system, where different initial state setting are considered. The behavior of the survival amount of entanglement is quantified for this accelerated system by means of the concurrence. We show that, the color noise enhances the generated entanglement between the two particles even for small values of the initial purity of the accelerated state. However, the larger values of the white noise strength improve the generated entanglement. The initial parameters that describe this system are estimated by using Fisher information, where two forms are considered, namely by using a single and two-qubit forms. It is shown that, by using the two-qubit form, the estimation degree of these parameters is larger than that displayed by using a single-qubit form.

We theoretically investigate the quantum phase transition in the collective systems of qubits in a high-quality cavity, which is driven by a squeezed light. We show that the squeezed light induced symmetry breaking can result in quantum phase transition without the ultrastrong coupling requirement. Using the standard mean field theory, we derive the condition of the quantum phase transition. Surprisingly, we show that there exists a tricritical point where the first- and second-order phase transitions meet. With specific atom-cavity coupling strengths, both the first- and second-order phase transition can be controlled by the squeezed light, leading to an optical switching from the normal phase to the superradiant phase by just increasing the squeezed light intensity. The signature of these phase transitions can be observed by detecting the phase space Wigner function distribution with different profiles controlled by the squeezed light intensity. Such superradiant phase transition can be implemented in various quantum systems, including atoms, quantum dots and ions in optical cavities as well as the circuit quantum electrodynamics system.

The fastest known classical algorithm deciding the $k$-colorability of $n$-vertex graph requires running time $\Omega(2^n)$ for $k\ge 5$. In this work, we present an exponential-space quantum algorithm computing the chromatic number with running time $O(1.9140^n)$ using quantum random access memory (QRAM). Our approach is based on Ambainis et al's quantum dynamic programming with applications of Grover's search to branching algorithms. We also present a polynomial-space quantum algorithm not using QRAM for the graph $20$-coloring problem with running time $O(1.9575^n)$. In the polynomial-space quantum algorithm, we essentially show $(4-\epsilon)^n$-time classical algorithms that can be improved quadratically by Grover's search.

We study properties of localized effective spins induced in gapped quantum spin chains by local inhomogeneities of the lattice. As a prototype, we study effective spins induced in impunity sites doped AKLT model by constructing the exact ground state in a matrix product state (MPS) form. We characterize their responses to external fields by studying an extended Zeeman interaction. We also study the antiferromagnetic bond-alternating Heisenberg chain with defect structures. For this model, an MPS representation similar to that for the AKLT model, "a uniform MPS with windows", is constructed, and it gives a good approximation of the ground state. We discuss the trade-off relation between the window length and the precision of the MPS ansatz. The effective exchange interaction between the induced spins is also investigated by using this representation.

Experimental searches for the electron electric dipole moment, $d_e$, probe new physics beyond the Standard Model. Recently, the ACME Collaboration set a new limit of $|d_e| <1.1\times 10^{-29}$ $e\cdot \textrm{cm}$ [Nature $\textbf{562}$, 355 (2018)], constraining time reversal symmetry (T) violating physics in the 3-100 TeV energy scale. ACME extracts $d_e$ from the measurement of electron spin precession due to the thorium monoxide (ThO) molecule's internal electric field. This recent ACME II measurement achieved an order of magnitude increased sensitivity over ACME I by reducing both statistical and systematic uncertainties in the measurement of the electric dipole precession frequency. The ACME II statistical uncertainty was a factor of 1.7 above the ideal shot-noise limit. We have since traced this excess noise to timing imperfections. When the experimental imperfections are eliminated, we show that shot noise limit is attained by acquiring noise-free data in the same configuration as ACME II.

In this paper, we study the effect of classical driving field on the spontaneous emission spectrum of a qubit embedded in a dissipative cavity. Furthermore, we monitor the entanglement dynamics of the driven qubit with its radiative decay under the action of the classical field. Afterwards, we carry out an investigation on the possibility of entanglement swapping between two such distinct driven qubits. The swapping will be feasible with the aid of a Bell state measurement performing on the photons leaving the cavities. It is demonstrated that the classical driving field has a beneficial effect on the prolonging of the swapped entanglement.

Three-qubit mixed states are used as channel for controlled quantum teleportation (CQT) of single qubit states. The connection between different channel parameters to achieve maximum controlled teleportation fidelity is investigated. We show that for a given multipartite entanglement and mixedness, a new class of non-maximally entangled mixed $X$ states (X-NMEMS) achieve optimum controlled quantum teleportation fidelity, interestingly a class of maximally entangled mixed X states (X-MEMS) fails to do so. This demonstrates, for a given spectrum and mixedness, X-MEMS is not sufficient to attain optimum controlled quantum teleportation fidelity, which is in contradiction with the traditional quantum teleportation of single qubits. In addition, we show that biseparable X-NMEMS for certain range of mixedness are useful as a resource to attain high controlled quantum teleportation fidelity, which essentially lower the requirements of quantum channels for CQT.

This work deals with quantum graphs, focusing on the transmission properties they engender. We first select two simple graphs, in which the vertices are all of degree 3, and investigate their transmission coefficients. In particular, we identified regions in which the transmission is fully suppressed. We also considered the transmission coefficients of some series and parallel arrangements of the two basic graphs, with the vertices still preserving the degree 3 condition, and then identified specific series and parallel compositions that allow for windows of no transmission. Inside some of these windows, we found very narrow peaks of full transmission, which are consequences of constructive quantum interference. Possibilities of practical use, as the experimental construction of devices of current interest to control and manipulate quantum information are also discussed.

We study the dynamic properties of a thermal autonomous machine made up of two quantum Brownian particles, each of which is in contact with an environment at different temperature and moves on a periodic sinusoidal track. When such tracks are shifted, the center of mass of the system exhibits a non-vanishing velocity, for which we provide an exact expression in the limit of small track undulations. We discuss the role of the broken spatial symmetry in the emergence of directed motion in thermal machines. We then consider the case in which external deterministic forces are applied to the system, and characterize its steady state velocity. If the applied external force opposes the system motion, work can be extracted from such a steady state thermal machine, without any external cyclic protocol. When the two particles are not interacting, our results reduce to those of refs. [1,2] for a single particle moving in a periodic tilted potential. We finally use our results for the motor velocity to check the validity of the quantum molecular dynamics algorithm in the non--linear, non--equilibrium regime.

We derive the analytical expression of local quantum uncertainty for three-qubit X-states. We give also the expressions of quantum discord and the negativity. A comparison of these three quantum correlations quantifiers is discussed in the special cases of mixed GHZ states and Bell-type states. We find that local quantum uncertainty gives the same amount of non-classical correlations as are measured by entropic quantum discord and goes beyond negativity. We also discuss the dynamics of non-classical correlations under the effect of phase damping, depolarizing and phase reversal channels. We find the local quantum uncertainty shows more robustness and exhibits, under phase reversal effect, revival and frozen phenomena. The monogamy property of local quantum uncertainty is also discussed. It is shown that it is monogamous for three-qubit states.