In this work, we provide another application of HHL algorithm in cubic spline interpolation problem. In this problem, the condition number is small, the Hamiltonian simulation is efficient and quantum state preparation is efficient. So the quantum algorithm obtained by HHL algorithm toward this problem actually achieves an exponential speedup with no restrictions. This will be another application of HHL algorithm besides the work of Clader et al. \cite{clader} to the electromagnetic scattering cross-section problem with no caveats.

We propose an incident direction free wave propagation generated by unidirectional destructive interference, which is a consequence of the appropriate match of synthetic magnetic flux and the incident wave vector. Single-direction lasing and one-way propagation are feasible without breaking reciprocity or introducing nonlinearity. Unidirectional destructive interference enables a unidirectional laser and a unidirectional perfect absorber. When they are combined in a parity-time symmetric manner, the spectral singularities vanish with bounded reflection and transmission. Our findings provide insights into light modulation and will shed light on the exploration of desirable asymmetric features of non-Hermitian systems in fundamental research and practical applications.

The intersection between the fields of machine learning and quantum information processing is proving to be a fruitful field for the discovery of new quantum algorithms, which potentially offer an exponential speed-up over their classical counterparts. However, many such algorithms require the ability to produce states proportional to vectors stored in quantum memory. Even given access to quantum databases which store exponentially long vectors, the construction of which is considered a one-off overhead, it has been argued that the cost of preparing such amplitude-encoded states may offset any exponential quantum advantage. Here we argue that specifically in the context of machine learning applications it suffices to prepare a state close to the ideal state only in the $\infty$-norm, and that this can be achieved with only a constant number of memory queries.

Two dimensional heterostructures are likely to provide new avenues for the manipulation of magnetization that is crucial for spintronics or magnetoelectronics. Here, we demonstrate that optical spin pumping can generate a large effective magnetic field in two dimensional MoSe2/WSe2 heterostructures. We determine the strength of the generated field by polarization-resolved measurement of the interlayer exciton photoluminescence spectrum: the measured splitting exceeding 10 milli-electron volts (meV) between the emission originating from the two valleys corresponds to an effective magnetic field of ~ 30 T. The strength of this optically induced field can be controlled by the excitation light polarization. Our finding opens up new possibilities for optically controlled spintronic devices based on van der Waals heterostructures.

Shortcuts to adiabaticity (STA) provide control protocols to guide the dynamics of a quantum system through an adiabatic reference trajectory in an arbitrary prescheduled time. Designing STA proves challenging in complex quantum systems when the dynamics of the degrees of freedom span different time scales. We introduce Counterdiabatic Born-Oppenheimer Dynamics (CBOD) as a framework to design STA in systems with a large separation of energy scales. CBOD exploits the Born-Oppenheimer approximation to separate the Hamiltonian into effective fast and slow degrees of freedom and calculate the corresponding counterdiabatic drivings for each subsystem. We show the validity of the CBOD technique via an example of coupled harmonic oscillators, which can be solved exactly for comparison.

Today, further downscaling of mobile electronic devices poses serious problems, such as energy consumption and local heat dissipation. In this context, spin wave majority gates made of very thin ferromagnetic films may offer a viable alternative. However, similar downscaling of magnetic thin films eventually enforces the latter to operate as quasi-two dimensional magnets, the magnetic properties of which are not yet fully understood, especially those related to anisotropies and external magnetic fields in arbitrary directions. To this end, we have investigated the behaviour of an easy-plane and easy-axis anisotropic ferromagnet -- both in two and three dimensions -- subjected to a uniform magnetic field, applied along an arbitrary direction. In this paper, a spin-1/2 Heisenberg Hamiltonian with anisotropic exchange interactions is solved using double-time temperature-dependent Green's functions and the Tyablikov decoupling approximation. We determine various magnetic properties such as the Curie temperature and the magnetization as a function of temperature and the applied magnetic field, discussing the impact of the system's dimensionality and the type of anisotropy. The magnetic reorientation transition taking place in anisotropic Heisenberg ferromagnets is studied in detail. Importantly, spontaneous magnetization is found to be absent for easy-plane two-dimensional spin systems with short range interactions.

We consider a large number $N$ of quantum particles coupled via a mean field interaction to another quantum system (reservoir). Our main result is an expansion for the averages of observables, both of the particles and of the reservoir, in inverse powers of $\sqrt{N}$. The analysis is based directly on the Dyson series expansion of the propagator. We analyze the dynamics, in the limit $N\rightarrow\infty$, of observables of a fixed number $n$ of particles, of extensive particle observables and their fluctuations, as well as of reservoir observables. We illustrate our results on the infinite mode Dicke model and on various energy conserving models.

We consider a massive particle of arbitrary spin and the basis vectors that carry the unitary, irreducible representations of the Poincar\'e group. From the complex coefficients in normalizable superpositions of these basis vectors, we identify momentum/spin-component probability amplitudes with the same interpretation as in the nonrelativistic theory. We find the relativistic transformations of these amplitudes, which are unitary in that they preserve the modulus-squared of scalar products from frame to frame. Space inversion and time reversal are also treated. We reconsider the Newton- Wigner construction of eigenvectors of position and the position operator. Position/spin-component probability amplitudes are also identified and their relativistic, unitary, transformations derived. Again, space inversion and time reversal are considered. For reference, we show how to construct positive energy solutions of the Klein-Gordon and Dirac equations in terms of probability amplitudes. We find the boost transformation of the position operator in the spinless case and present some results on the relativity of position measurements. We consider issues surrounding the classical concept of causality as it applies in quantum mechanics. We briefly examine the relevance of the results presented here for theories of interaction.

As one of the most intriguing features of quantum mechanics, Einstein-Podolsky-Rosen (EPR) steering is a useful resource for secure quantum networks. Greenberger-Horne-Zeilinger (GHZ) state plays important role in quantum communication network. By reconstructing the covariance matrix of a continuous variable tripartite GHZ state, we fully quantify the amount of bipartite steering under Gaussian measurements. We demonstrate that the (1+1)-mode steerability is not exist in the tripartite GHZ state, only the collectively steerability exist between the (1+2)-mode and (2+1)-mode partitions. These properties confirm that the tripartite GHZ state is a perfect resource for quantum secret sharing protocol. We also demonstrate one-way EPR steering of the GHZ state under Gaussian measurements, and experimentally verify the introduced monogamy relations for Gaussian steerability. Our experiment provides reference for using EPR steering in Gaussian GHZ states as a valuable resource for multiparty quantum information tasks.

A mathematical proposition with a trainable pair, operator and quantum circuit, are introduced to approximate functions expressed as cubic Taylor polynomials, numerical simulations illustrate three cases.

We show that a non-Hermitian zero mode can exhibit an unusual behavior at the transition between extended and localized regimes: it displays a linearly decreasing amplitude as a function of space in a weakly coupled non-Hermitian reservoir. Through the discussion of a linear homogeneous recurrence relation, we attribute this phenomenon to the underlying non-Hermitian particle-hole symmetry and the zeroness of its energy eigenvalue. We also show that linear localization bears a strong resemblance to critical damping, even though the latter does not display linear temporal dynamics.

The current generation of quantum computing technologies call for quantum algorithms that require a limited number of qubits and quantum gates, and which are robust against errors. A suitable design approach are variational circuits where the parameters of gates are learnt, an approach that is particularly fruitful for applications in machine learning. In this paper, we propose a low-depth variational quantum algorithm for supervised learning. The input feature vectors are encoded into the amplitudes of a quantum system, and a quantum circuit of parametrised single and two-qubit gates together with a single-qubit measurement is used to classify the inputs. This circuit architecture ensures that the number of learnable parameters is poly-logarithmic in the input dimension. We propose a quantum-classical training scheme where the analytical gradients of the model can be estimated by running several slightly adapted versions of the variational circuit. We show with simulations that the circuit-centric quantum classifier performs well on standard classical benchmark datasets while requiring dramatically fewer parameters than other methods. We also evaluate sensitivity of the classification to state preparation and parameter noise, introduce a quantum version of dropout regularisation and provide a graphical representation of quantum gates as highly symmetric linear layers of a neural network.

We give a protocol for producing certifiable randomness from a single untrusted quantum device that is polynomial-time bounded. The randomness is certified to be statistically close to uniform from the point of view of any computationally unbounded quantum adversary, that may share entanglement with the quantum device. The protocol relies on the existence of post-quantum secure trapdoor claw-free functions, and introduces a new primitive for constraining the power of an untrusted quantum device. We then show how to construct this primitive based on the hardness of the learning with errors (LWE) problem.

The randomness protocol can also be used as the basis for an efficiently verifiable quantum supremacy proposal, thus answering an outstanding challenge in the field.

Hardy's nonlocality is a "nonlocality proof without inequalities": it exemplifies that quantum correlations can be qualitatively stronger than classical correlations. This paper introduces variants of Hardy's nonlocality in the CHSH scenario which are realized by the PR-box, but not by quantum correlations. Hence this new kind of Hardy-type nonlocality is a proof without inequalities showing that superquantum correlations can be qualitatively stronger than quantum correlations.

We study uncertainty relations for pairs of conjugate variables like number and angle, of which one takes integer values and the other takes values on the unit circle. The translation symmetry of the problem in either variable implies that measurement uncertainty and preparation uncertainty coincide quantitatively, and the bounds depend only on the choice of two metrics used to quantify the difference of number and angle outputs, respectively. For each type of observable we discuss two natural choices of metric, and discuss the resulting optimal bounds with both numerical and analytic methods. We also develop some simple and explicit (albeit not sharp) lower bounds, using an apparently new method for obtaining certified lower bounds to ground state problems.

The BEC regime of a cold fermi gas is characterised by coupled atoms (dimers) which, superficially, look like elementary bosons. We examine how simply-bosonic they really are; firstly, in the Bogoliubov approximation and further, through new actions for the BEC regime in which dimers are represented by coupled Gross-Pitaevskii fields. We find identity at the level of the Bogoliubov approximation in the deep BEC regime, permitting a simple Gross-Pitaevskii description. This fails rapidly as we move towards the BCS regime. However, even in the deep BEC regime there is an intrinsic difference if we go beyond the Bogoliubov approximation. To exemplify this we construct vortex solutions.

Proof of security of cryptographic protocols theoretically establishes the strength of a protocol and the constraints under which it can perform, it does not take into account the overall design of the protocol. In the past model checking has been successfully applied to classical cryptographic protocols to weed out design flaws which would have otherwise gone unnoticed. Quantum cryptographic protocols differ from their classical counterparts, in their ability to detect the presence of an eavesdropper. Although unconditional security has been proven for both BB84 and B92 protocols, in this paper we show that identifying an eavesdropper's presence is constrained on the number of qubits exchanged. We first model the protocols in CQP and then explain the mechanism by which we have translated this into a PRISM model. We mainly focus on the protocols' ability to detect an active eavesdropper and the extent to which an eavesdropper can retrieve the shared key without being detected by either party. We then conclude by comparing the performance of the protocols.

In this work we discuss the dynamical response of heavy quantum impurities immersed in a Fermi gas at zero and at finite temperature. Studying both the frequency and the time domain allows one to identify interaction regimes that are characterized by distinct many-body dynamics. From this theoretical study a picture emerges in which impurity dynamics is universal on essentially all time scales, and where the high-frequency few-body response is related to the long-time dynamics of the Anderson orthogonality catastrophe by Tan relations. Our theoretical description relies on different and complementary approaches: functional determinants give an exact numerical solution for time- and frequency-resolved responses, bosonization provides analytical expressions at low temperatures, and the theory of Toeplitz determinants allows one to analytically predict response up to high temperatures. Using these approaches we predict the thermal decoherence rate and prove that within the considered model the fastest rate of long-time decoherence is given by $\gamma=\pi k_BT/4$. We show that Feshbach resonances in cold atomic systems give access to new interaction regimes where quantum effects prevail even in the thermal regime of many-body dynamics. The key signature of this phenomenon is a crossover between exponential decay rates of the real-time Ramsey signal. It is shown that the physics of the orthogonality catastrophe is experimentally observable up to temperatures $T/T_F\lesssim 0.2$ where it leaves its fingerprint in a power-law temperature dependence of thermal spectral weight and we review how this phenomenon is related to the physics of heavy ions in liquid $^3$He and the formation of Fermi polarons. The presented results are in excellent agreement with recent experiments on LiK mixtures, and we predict several phenomena that can be tested using currently available experimental technology.

We introduce and experimentally demonstrate a method for realising a quantum channel using the measurement-based model. Using a photonic setup and modifying the bases of single-qubit measurements on a four-qubit entangled cluster state, representative channels are realised for the case of a single qubit in the form of amplitude and phase damping channels. The experimental results match the theoretical model well, demonstrating the successful performance of the channels. We also show how other types of quantum channels can be realised using our approach. This work highlights the potential of the measurement-based model for realising quantum channels which may serve as building blocks for simulations of realistic open quantum systems.

We study the problem of communication over a compound quantum channel in the presence of entanglement. Classically such channels are modeled as a collection of conditional probability distributions wherein neither the sender nor the receiver is aware of the channel being used for transmission, except for the fact that it belongs to this collection. We provide near optimal achievability and converse bounds for this problem in the one-shot quantum setting in terms of quantum hypothesis testing divergence. We also consider the case of informed sender, showing a one-shot achievability result that converges appropriately in the asymptotic and i.i.d. setting. Our achievability proof is similar in spirit to its classical counterpart. To arrive at our result, we use the technique of position-based decoding along with a new approach for constructing a union of two projectors, which can be of independent interest. We give another application of the union of projectors to the problem of testing composite quantum hypotheses.