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The magnetic dipole field geometry of subatomic elementary particles like the electron differs from the classical macroscopic field imprint of a bar magnet. It resembles more like an eight figure or else joint double quantum-dots instead of the classical, spherical more uniform field of a bar magnet. This actual subatomic quantum magnetic field of an electron at rest, is called Quantum Magnet or else a Magneton. Normally, a macroscale bar magnet should behave like a relative giant Quantum Magnet with identical magnetic dipole field imprint since all of its individual magnetons collectively inside the material, dipole moments are uniformly aligned forming the total net field of the magnet. However due to Quantum Decoherence (QDE) phenomenon at the macroscale and macroscopic magnetic field imaging sensors limitations which cannot pickup these rapid quantum magnetization fluctuations, this field is masked and not visible at the macroscale. By using the relative inexpensive submicron resolution Ferrolens quantum magnetic optical sensor and method, we can actually make this net magneton field visible on macroscale magnets. We call this net total field herein, Quantum Field of Magnet (QFM) differentiating it therefore from the field of the single subatomic magneton thus quantum magnet. Additionally, the unique potential of the Ferrolens device to display also the magnetic flux lines of this macroscopically projected giant Magenton gives us the unique opportunity to study the individual magnetic flux lines geometrical pattern that of a single subatomic magneton. We describe this particular magnetic flux of the magneton observed, quantum magnetic flux. Therefore a novel observation has been made that the QFM of the Magnet-Magneton consists of a dipole vortex shaped magnetic flux geometrical pattern responsible for creating the classical macroscopic N-S field of the magnet.

To characterize the generic behavior of open quantum systems, we consider random, purely dissipative Liouvillians with a notion of locality. We find that the positivity of the map implies a sharp separation of the relaxation timescales according to the locality of observables. Specifically, we analyze a spin-1/2 system of size $\ell$ with up to $n$-body Lindblad operators, which are $n$-local in the complexity-theory sense. Without locality ($n=\ell$), the complex Liouvillian spectrum densely covers a "lemon"-shaped support, in agreement with recent findings [Phys. Rev. Lett. 123, 140403;arXiv:1905.02155]. However, for local Liouvillians ($n<\ell$), we find that the spectrum is composed of several dense clusters with random matrix spacing statistics, each featuring a lemon-shaped support wherein all eigenvectors correspond to $n$-body decay modes. This implies a hierarchy of relaxation timescales of $n$-body observables, which we verify to be robust in the thermodynamic limit.

We present a formal analysis and convergence proofs for an autonomous adaptive learning algorithm useful for the tuneup and stabilization of quantum computing architectures. We focus on the specific application of spatial noise mapping in a "spectator" qubit paradigm, in which these qubits act as sensors to provide information useful for decoherence mitigation on proximal data qubits. In earlier work, the authors introduced and experimentally demonstrated this framework, Noise Mapping for Quantum Architectures (NMQA), as applied in autonomous adaptive scheduling of sensor-qubit measurements across multi-qubit architectures. This methodology has several unique features: a classical measurement model that incorporates discretized single-qubit projective measurements, and a two-layered particle filtering structure to facilitate adaptive information sharing between qubits in small spatial regions. In this work, we formalize the NMQA problem definition and build direct links to conventional non-linear filtering theory. Taking into account NMQA's departure from existing literature, we show that NMQA satisfies axioms of theorems for asymptotic convergence in specific parameter regimes. Outside of these parameter regimes, we augment our theoretical analysis with numerical studies to estimate rates of convergence for NMQA. We find that these numerical estimates match our theoretical expectations for a variety of physical configurations. Our work ensures that the methodology encapsulated by NMQA permits comparative analysis with existing filtering techniques in the literature, while highlighting unique directions for future automation of quantum computer tuneup, calibration, and stabilization.

Quantum error correction is vital for implementing universal quantum computing. A key component is the encoding circuit that maps a product state of physical qubits into the encoded multipartite entangled logical state. Known methods are typically not optimal either in terms of the circuit depth (and therefore the error burden) or the specifics of the target platform, i.e. the native gates and topology of a system. This work introduces a variational compiler for efficiently finding the encoding circuit of general quantum error correcting codes with given quantum hardware. Focusing on the noisy intermediate scale quantum regime, we show how to systematically compile the circuit so that either it has the minimal number of noisy operations that are allowed by the noisy quantum hardware or it can achieve the highest fidelity of the encoded state with noisy gates. We demonstrate our method by deriving novel encoders for logic states of the five qubit code and the seven qubit Steane code. Our method is applicable quite generally for compiling the encoding circuits of quantum error correcting codes.

Detection and manipulation of excitations with non-Abelian statistics, such as Majorana fermions, are essential for creating topological quantum computers. To this end, we show the connection between the existence of such localized particles and the phenomenon of unitary subharmonic response (SR) in periodically driven systems. In particular, starting from highly non-equilibrium initial states, the unpaired Majorana modes exhibit spin oscillations with twice the driving period, are localized, and can have exponentially long lifetimes in clean systems. While the lifetime of SR is limited in translationally invariant systems, we show that disorder can be engineered to stabilize the subharmonic response of Majorana modes. A viable observation of this phenomenon can be achieved using modern multi-qubit hardware, such as superconducting circuits and cold atomic systems.

Sometimes, mathematical oddities crowd in upon one another, and the exceptions to one classification scheme reveal themselves as fellow-travelers with the exceptions to a quite different taxonomy.

We show that the motion of a cold trapped ion can be squeezed by modulating the intensity of a phase-stable optical lattice placed inside the trap. As this method is reversible and state selective it effectively implements a controlled-squeeze gate. We show how to use this resource, that can be useful for quantum information processing with continuous variables, in order to prepare coherent superpositions of states which are squeezed along complementary quadratures. We show that these states, which we denote as "${\mathcal X}$-states", exhibit high sensitivity to small displacements along two complementary quadratures which make them useful for quantum metrology.

We investigate whether the entropic regularisation of the strictly-correlated-electrons problem can be used to build approximations for the kinetic correlation energy functional at large coupling strengths and, more generally, to gain new insight in the problem of describing and understanding strong correlation within Density Functional Theory.

We propose a spatial analog of the Berry's phase mechanism for the coherent manipulation of states of non-relativistic massive particles moving in a two-dimensional landscape. In our construction the temporal modulation of the system Hamiltonian is replaced by a gentle modulation of the confining potential along the transverse direction of the particle propagation. By properly tuning the model parameters the resulting scattering input-output relations exhibit a Wilczek-Zee non-abelian phase shift contribution that is intrinsically geometrical, hence insensitive to the specific details of the potential landscape. A theoretical derivation of the effect is provided together with practical examples.

The basic thermodynamic quantities for a non-interacting scalar field in a periodic potential composed of either a one-dimensional chain of Dirac $\delta$-$\delta^\prime$ functions or a specific potential with extended support are calculated. First, we consider the representation in terms of real frequencies (or one-particle energies). Then we turn the axis of frequency integration towards the imaginary axis by a finite angle, which allows for easy numerical evaluation, and finally turn completely to the imaginary frequencies and derive the corresponding Matsubara representation, which this way appears also for systems with band structure. In the limit case $T \to 0$ we confirm earlier results on the vacuum energy. We calculate for the mentioned examples the free energy and the entropy and generalize earlier results on negative entropy.

We report on an emergent dynamical phase of a strongly-correlated light-matter system, which is governed by dimerization processes due to short-range and long-range two-body interactions. The dynamical phase is characterized by the spontaneous symmetry breaking of the translational invariance and appears in an intermediate regime of light-matter interaction between the resonant and dispersive cases. We describe the quench dynamics from an initial state with integer filling factor of a finite-sized array of coupled resonators, each doped with a two-level system, by using an effective Hilbert space that accounts for resonant polaritonic states. This procedure allows us to demonstrate and characterize the emergent dynamical phase through time-averaged quantities such as fluctuations in the number of polaritons per site and linear entropy. Our findings reveal that intrinsic two-body dynamics dominates the emergent dynamical phase.

Nanofabrication techniques for superconducting qubits rely on resist-based masks patterned by electron-beam or optical lithography. We have developed an alternative nanofabrication technique based on free-standing silicon shadow masks fabricated from silicon-on-insulator wafers. These silicon shadow masks not only eliminate organic residues associated with resist-based lithography, but also provide a pathway to better understand and control surface-dielectric losses in superconducting qubits by decoupling mask fabrication from substrate preparation. We have successfully fabricated aluminum 3D transmon superconducting qubits with these shadow masks, and demonstrated energy relaxation times on par with state-of-the-art values.

We in theory proposed a hybrid system consisting of a mechanical resonator, an optical Fabry-P\'erot cavity, and two superconducting microwave circuits to generate stationary continuous-variable quantum entanglement between two microwave modes. We show that the hybrid system can also achieve quantum entanglement of other bipartite subsystems in experimentally accessible parameter regimes, which has the potential to be useful in quantum information processing and quantum illumination radar.

In superconducting circuit architectures for quantum computing, microwave resonators are often used both to isolate qubits from the electromagnetic environment and to facilitate qubit state readout. We analyze the full counting statistics of photons emitted from such driven readout resonators both in and beyond the dispersive approximation. We calculate the overlap between emitted-photon distributions for the two qubit states and explore strategies for its minimization with the purpose of increasing fidelity of intensity-sensitive readout techniques. In the dispersive approximation and at negligible qubit relaxation, both distributions are Poissonian, and the overlap between them can be easily made arbitrarily small. Nondispersive terms of the Hamiltonian generate squeezing and the Purcell decay with the latter effect giving the dominant contribution to the overlap between two distributions.

Quantum optics experiments, involving the measurement of low-probability photon events, are known to be extremely time-consuming. We present a new methodology for accelerating such experiments using simple statistical learning techniques such as Bayesian maximum a posteriori estimation based on few-shot data. We show that it is possible to reconstruct time-dependent data using a small number of detected photons, allowing for fast estimates in under a minute and providing a one-to-two order of magnitude speed up in data acquisition time. We test our approach using real experimental data to retrieve the second order intensity correlation function, $G^{(2)}(\tau)$, as a function of time delay $\tau$ between detector counts, for thermal light as well as anti-bunched light emitted by a quantum dot driven by periodic laser pulses. The proposed methodology has a wide range of applicability and has the potential to impact the scientific discovery process across a multitude of domains.

Certification of quantum systems and operations is a central task in quantum information processing. Most current schemes rely on a tomography with fully characterised devices, while this may not be met in real experiments. Device characterisations can be removed with device-independent tests, it is technically challenging at the moment, though. In this letter, we investigate the problem of certifying entangled states and measurements via semi-quantum games, a type of non-local quantum games with well characterised quantum inputs, balancing practicality and device-independence. We first design a specific bounded-dimensional measurement-device-independent game, with which we simultaneously certify any pure entangled state and Bell state measurement operators. Afterwards via a duality treatment of state and measurement, we interpret the dual form of this game as a source-independent bounded-dimensional entanglement swapping protocol and show the whole process, including any entangled projector and Bell states, can be certified with this protocol. In particular, our results do not require a complete Bell state measurement, which is beneficial for experiments and practical use.

Photon interference and bunching are widely studied quantum effects that have also been proposed for high precision measurements. Here we construct a theoretical description of photon-interferometry on rotating platforms, specifically exploring the relation between non-inertial motion, relativity, and quantum mechanics. On the basis of this, we then propose an experiment where photon entanglement can be revealed or concealed solely by controlling the rotational motion of an interferometer, thus providing a route towards studies at the boundary between quantum mechanics and relativity.

We discuss and review in this chapter the developing field of research of quantum simulation of gauge theories with ultracold atoms.

We investigate the quench dynamics of an open quantum system involving a quantum phase transition. In the isolated case, the quench dynamics involving the phase transition exhibits a number of scaling relations with the quench rate as predicted by the celebrated Kibble-Zurek mechanism. In contact with an environment however, these scaling laws breakdown and one may observe an anti-Kibble-Zurek behavior: slower ramps lead to less adiabatic dynamics, increasing thus non-adiabatic effects with the quench time. In contrast to previous works, we show here that such anti-Kibble-Zurek scaling can acquire a universal form in the sense that it is determined by the equilibrium critical exponents of the phase transition, provided the excited states of the system exhibit singular behavior, as observed in fully-connected models. This demonstrates novel universal scaling laws granted by a system-environment interaction in a critical system. We illustrate these findings in two fully-connected models, namely, the quantum Rabi and the Lipkin-Meshkov-Glick models. In addition, we discuss the impact of non-linear ramps and finite-size systems.