Universal quantum computers are potentially an ideal setting for simulating many-body quantum dynamics that is out of reach for classical digital computers. We use state-of-the-art IBM quantum computers to study paradigmatic examples of condensed matter physics -- we simulate the effects of disorder and interactions on quantum particle transport, as well as correlation and entanglement spreading. Our benchmark results show that the quality of the current machines is below what is necessary for quantitatively accurate continuous time dynamics of observables and reachable system sizes are small comparable to exact diagonalization. Despite this, we are successfully able to demonstrate clear qualitative behaviour associated with localization physics and many-body interaction effects.

The relationship between quantum physics and discrete mathematics is reviewed in this article. The Boolean functions unitary representation is considered. The relationship between Zhegalkin polynomial, which defines the algebraic normal form of Boolean function, and quantum logic circuits is described. It is shown that quantum information approach provides simple algorithm to construct Zhegalkin polynomial using truth table. Developed methods and algorithms have arbitrary Boolean function generalization with multibit input and multibit output. Such generalization allows us to use many-valued logic (k-valued logic, where k is a prime number). Developed methods and algorithms can significantly improve quantum technology realization. The presented approach is the baseline for transition from classical machine logic to quantum hardware.

The quantum measurement procedure based on the Lorentz transformation formalism and weak perturbation of the system is considered. In the simple case of a single-qubit it turns out that one can perform 4-dimension pseudo-rotation along with ordinary 3-dimension rotations on the Bloch sphere. These pseudo-rotations are similar to the Lorentz transformation in special relativity theory. The extension of the Lorentz transformation for many-qubit systems is also considered. The quantum measurement protocols based on the Lorentz transformation are proposed. It has been shown that these protocols cease to form the decomposition of unity and could be superefficient providing the fidelity higher than any POVM-measurement protocol. However, one can perform the complement of the Lorentz protocol to POVM-protocol by an additional measurement operator. If the initial mixed state is close to the pure one this operator corresponds to weak perturbation of the state while the original Lorentz protocol sets the strong perturbations. As the result, the feedback provides an effective control of a quantum system introducing weak perturbations to the quantum state. The results of this research are essential for the development of methods for the control of quantum information technologies.

The work is devoted to the theoretical and experimental study of quantum states of light conditionally prepared by subtraction of a random number of photons from the initial multimode thermal state. A fixed number of photons is subtracted from a multimode quantum state, but only a subsystem of a lower number of modes is registered, in which the number of subtracted photons turns out to be a non-fixed random variable. It is shown that the investigation of multiphoton subtracted multimode thermal states provides a direct study of the fundamental quantum-statistical properties of bosons using a simple experimental implementation. The developed experimental setup plays a role of a specific boson lototron, which is based on the fundamental link between the statistics of boson systems and the Polya distribution. It is shown that the calculation of the photon number distribution based on the Polya urn scheme is equivalent to a calculation using statistical weights for boson systems. A mathematical model based on the composition of the Polya distribution and thermal state is developed and verified. The experimental results are in a good agreement with the developed theory.

We apply the scattering approach to the Casimir interaction between two dielectric half-spaces separated by an electrolyte solution. We take the nonlocal electromagnetic response of the intervening medium into account, which results from the presence of movable ions in solution. In addition to the usual transverse modes, we consider longitudinal channels and their coupling by reflection at the surface of the local dielectric. The Casimir interaction energy is calculated from the matrix describing a round-trip of coupled transverse and longitudinal waves between the interacting surfaces. The nonzero-frequency contributions are approximately unaffected by the presence of ions. We find, at zero frequency, a contribution from longitudinal channels, which is screened over a distance of the order of the Debye length, alongside an unscreened term arising from transverse-magnetic modes. The latter defines the long-distance asymptotic limit for the interaction.

Clifford gates play a role in the optimisation of Clifford+T circuits. Reducing the count and the depth of Clifford gates, as well as the optimal scheduling of T gates, influence the hardware and the time costs of executing quantum circuits. This work focuses on circuits protected by the surface quantum error-correcting code. The result of compiling a quantum circuit for the surface code is called a topological assembly. We use queuing theory to model a part of the compiled assemblies, evaluate the models, and make the empiric observation that at least for certain Clifford+T circuits (e.g. adders), the assembly's execution time does not increase when the available hardware is restricted. This is an interesting property, because it shows that T gate scheduling and Clifford gate optimisation have the potential to save both hardware and execution time.

Based on a generic quantum open system model, we study the geometric nature of decoherence by defining a complex-valued geometric phase through stochastic pure states describing non-unitary, non-cyclic and non-adiabatic evolutions. The ensemble average of the complex geometric phases for the pure stochastic states yields a conventional geometric phase together with an amplitude factor. We show that the decoherence process described by the decaying amplitude can be a geometric quantity independent of the system's dynamics. It is a remarkable fact that the geometric phase of a quantum system can serve as an ideal realisation of quantum gates due to its robustness against dynamical errors, however, in this paper we show that, for some open quantum systems, a desirable geometric phase may be accompanied by an unwanted robust geometric decoherence factor. Two exactly solvable models are studied to demonstrate that, while the decoherence is a purely dynamical effect for a dephasing two-level model, the decoherence in a dissipative two-level model can be a geometric process. Finally, we show that such a geometric decoherence effect may be eliminated by a non-perturbative control scheme.

We present a general approach to the classical dynamical systems simulation. This approach is based on classical systems extension to quantum states. The proposed theory can be applied to analysis of multiple (including non-Hamiltonian) dissipative dynamical systems. As examples, we consider the logistic model, the Van der Pol oscillator, dynamical systems of Lorenz, R\"ossler (including R\"ossler hyperchaos) and Rabinovich-Fabrikant. Developed methods and algorithms integrated in quantum simulators will allow us to solve a wide range of problems with scientific and practical significance.

In this report we present a general approach for estimating quantum circuits by means of measurements. We apply the developed general approach for estimating the quality of superconducting and optical quantum chips. Using the methods of quantum states and processes tomography developed in our previous works, we have defined the adequate models of the states and processes under consideration.

We present rigorous and intuitive master equation models to study on-demand single photon sources from pulse-excited quantum dots coupled to cavities. We consider three methods of source excitation: resonant pi-pulse, off-resonant phonon-assisted inversion, and two-photon excitation of a biexciton-exciton cascade, and investigate the effect of the pulse excitation process on the quantum indistinguishability, efficiency, and purity of emitted photons. By explicitly modelling the time-dependent pulsed excitation process in a manner which captures non-Markovian effects associated with coupling to photon and phonon reservoirs, we find that photons of near-unity indistinguishability can be emitted with over 90% efficiency for all these schemes, with the off-resonant schemes not necessarily requiring polarization filtering due to the frequency separation of the excitation pulse, and allowing for very high single photon purities. Furthermore, the off-resonant methods are shown to be robust over certain parameter regimes, with less stringent requirements on the excitation pulse duration in particular. We also derive a semi-analytical simplification of our master equation for the off-resonant drive, which gives insight into the important role that exciton-phonon decoupling for a strong drive plays in the off-resonant phonon-assisted inversion process

Emission and absorption of light lie at the heart of light-matter interaction. Although the emission and absorption rates are regarded as intrinsic properties of atoms and molecules, various ways to modify these rates have been sought in critical applications such as quantum information processing, metrology and light-energy harvesting. One of the promising approaches is to utilize collective behavior of emitters as in superradiance. Although superradiance has been observed in diverse systems, its conceptual counterpart in absorption has never been realized. Here, we demonstrate superabsorption, enhanced cooperative absorption, by correlated atoms of phase-matched superposition state. By implementing an opposite-phase-interference idea on a superradiant state or equivalently a time-reversal process of superradiance, we realized the superabsorption with its absorption rate much faster than that of the ordinary ground-state absorption. The number of photons completely absorbed for a given time interval was measured to be proportional to the square of the number of atoms. Our approach, breaking the limitation of the conventional absorption, can help weak-signal sensing and advance efficient light-energy harvesting as well as light-matter quantum interfaces.

We study quantum anomaly detection with density estimation and multivariate Gaussian distribution. Both algorithms are constructed using the standard gate-based model of quantum computing. Compared with the corresponding classical algorithms, the resource complexities of our quantum algorithm are logarithmic in the dimensionality of quantum states and the number of training quantum states. We also present a quantum procedure for efficiently estimating the determinant of any Hermitian operators $\mathcal{A}\in\mathcal{R}^{N\times N}$ with time complexity $O(poly\log N)$ which forms an important subroutine in our quantum anomaly detection with multivariate Gaussian distribution. Finally, our results also include the modified quantum kernel principal component analysis (PCA) and the quantum one-class support vector machine (SVM) for detecting classical data.

We probe electric-field noise in a surface ion trap for ion-surface distances $d$ between 50 and 300 $\mu\mathrm{m}$ in the normal and planar directions. We find the noise distance dependence to scale as $d^{-2.6}$ in our trap and a frequency dependence which is consistent with $1/f$ noise. Simulations of the electric-field noise specific to our trap geometry provide evidence that we are not limited by technical noise sources. Our distance scaling data is consistent with a noise correlation length of about 100 $\mu\mathrm{m}$ at the trap surface, and we discuss how patch potentials of this size would be modified by the electrode geometry.

Generalising the concept of Bell nonlocality to networks leads to novel forms of correlations, the characterization of which is however challenging. Here we investigate constraints on correlations in networks under the two natural assumptions of no-signaling and independence of the sources. We consider the ``triangle network'', and derive strong constraints on correlations even though the parties receive no input, i.e. each party performs a fixed measurement. We show that some of these constraints are tight, by constructing explicit local models (i.e. where sources distribute classical variables) that can saturate them. However, we also observe that other constraints can apparently not be saturated by local models, which opens the possibility of having nonlocal (but non-signaling) correlations in the triangle network.

Scalable integration of bright emitters in quantum photonic structures is an important step in the broader quest to generate and manipulate single photons via compact solid-state devices. Unfortunately, implementations relying on material platforms that also serve as the emitter host often suffer from a trade-off between the desired emitter properties and the photonic system practicality and performance. Here, we demonstrate 'pick and place' integration of a Silicon Nitride microdisk optical resonator with a bright emitter host in the form of 20nm thick hexagonal boron nitride (hBN).The film folds around the microdisk maximizing contact to ultimately form a composite hBN/Si3N4 structure. The local strain that develops in the hBN film at the resonator circumference deterministically activates a low density of SPEs within the whispering gallery mode volume of the microdisk. These conditions allow us to demonstrate cavity-mediated out-coupling and Purcell enhancement of emission from hBN color centers through the microdisk cavity modes. Our results pave the route toward the development of scalable quantum photonic circuits with independent emitter/resonator optimization for active and passive functionalities.

We suggest a near deterministic compact model of a photonic CNOT gate based on a quantum dot trapped in a double sided optical microcavity and a universal cloner. Our design surpasses the cloner optimal limit of 5/6 and we show that it provides fidelity around 91 % in the weak coupling regime.

Extracting as much information as possible about an object when probing with a limited number of photons is an important goal with applications from biology and security to metrology. Imaging with a few photons is a challenging task as the detector noise and stray light are then predominant, which precludes the use of conventional imaging methods. Quantum correlations between photon pairs has been exploited in a so called 'heralded imaging scheme' to eliminate this problem. However these implementations have so-far been limited to intensity imaging and the crucial phase information is lost in these methods. In this work, we propose a novel quantum-correlation enabled Fourier Ptychography technique, to capture high-resolution amplitude and phase images with a few photons. This is enabled by the heralding of single photons combined with Fourier ptychographic reconstruction. We provide experimental validation and discuss the advantages of our technique that include the possibility of reaching a higher signal to noise ratio and non-scanning Fourier Ptychographic acquisition.

The method of many body Green's functions is used to describe an arbitrary system of electrons and nuclei in a rigorous manner given the Hamiltonian of Coulombic interactions and kinetic energies. The theory given resolves the problem arising from the translational and rotational invariance of the Hamiltonian afflicting the existing theory based on the same technique. As a result, we derive a coupled set of exact equations for the electron and nuclei Green's functions giving a systematic way to potentially compute various properties of a rather arbitrary many-body systems of electrons and nuclei beyond Born-Oppenheimer approximation, including molecules and solids. We discuss a special case of crystalline solids in more detail.

Recently, the study of non-Hermitian physics has attracted considerable attention. The modified bulk-boundary correspondence has been proposed to understand topological edge states in non-Hermitian static systems. Here we report a new experimental observation of edge states in non-Hermitian periodically driven systems. Some unconventional edge states are found not to be satisfied with the bulk-boundary correspondence when the system belongs to the broken parity-time (PT) symmetric phase. The experiments are performed in our constructed non-Hermitian light quantum walk platform with left and right boundaries, where the beams outside system boundary are blocked subtly at the end of each step. The robust properties of these edge states against to static perturbations and disorder have also been demonstrated experimentally. The finding of robust edge states in broken PT-symmetric phase inspires us to explore a robust transport channel in ubiquitously complex systems with strong dissipation.

In practical implementation of quantum key distributions (QKD), it requires efficient, real-time feedback control to maintain system stability when facing disturbance from either external environment or imperfect internal components. Usually, a "scanning-and-transmitting" program is adopted to compensate physical parameter variations of devices, which can provide accurate compensation but may cost plenty of time in stopping and calibrating processes, resulting in reduced efficiency in key transmission. Here we for the first propose to employ a well known machine learning model, i.e., the Long Short-Term Memory Network (LSTM), to predict those physical parameter variations in advance and actively perform real-time control on corresponding QKD devices. Experimentally, we take the phase-coding scheme as an example and run the LSTM model based QKD system for more than 10 days. Experimental results show that we can keep the same level of quantum-bit error rate as the traditional "scanning-and-transmitting" program by employing our new machine learning method, but dramatically reducing the scanning time and resulting in significantly enhanced key transmission efficiency. Furthermore, our present machine learning model should also be applicable to any other QKD systems using any coding scheme or QKD protocols, and thus seems a very promising candidate in large-scale application of quantum communication network in the near future.