QUROPE Quantum Information Processing and Communication in Europe

In this review, we describe the current landscape of emergent quantum materials for quantum photonic applications. We focus on three specific solid-state platforms: single emitters in monolayers of transition metal dichalcogenides, defects in hexagonal boron nitride, and colloidal quantum dots in perovskites. These platforms share a unique technological accessibility, enabling the rapid implementation of testbed quantum applications, all while being on the verge of becoming technologically mature enough for a first generation of real-world quantum applications.

The review begins with a comprehensive overview of the current state-of-the-art for relevant single-photon sources in the solid-state, introducing the most important performance criteria and experimental characterization techniques along the way. We then benchmark progress for each of the three novel materials against more established (yet complex) platforms, highlighting performance, material-specific advantages, and giving an outlook on quantum applications. This review will thus provide the reader with a snapshot on latest developments in the fast-paced field of emergent single-photon sources in the solid-state, including all the required concepts and experiments relevant to this technology.

This study investigates the thermal properties of the repulsive Fermi-Hubbard model with chemical potential using variational quantum algorithms, crucial in comprehending particle behaviour within lattices at high temperatures in condensed matter systems. Conventional computational methods encounter challenges, especially in managing chemical potential, prompting exploration into Hamiltonian approaches. Despite the promise of quantum algorithms, their efficacy is hampered by coherence limitations when simulating extended imaginary time evolution sequences. To overcome such constraints, this research focuses on optimising variational quantum algorithms to probe the thermal properties of the Fermi-Hubbard model. Physics-inspired circuit designs are tailored to alleviate coherence constraints, facilitating a more comprehensive exploration of materials at elevated temperatures. Our study demonstrates the potential of variational algorithms in simulating the thermal properties of the Fermi-Hubbard model while acknowledging limitations stemming from error sources in quantum devices and encountering barren plateaus.

The factorization method of Schrodinger shows us how to determine the energy eigenstates without needing to determine the wavefunctions in position or momentum space. A strategy to convert the energy eigenstates to wavefunctions is well known for the one-dimensional simple harmonic oscillator by employing the Rodrigues formula for the Hermite polynomials in position or momentum space. In this work, we illustrate how to generalize this approach in a representation-independent fashion to find the wavefunctions of other problems in quantum mechanics that can be solved by the factorization method. We examine three problems in detail: (i) the one-dimensional simple harmonic oscillator; (ii) the three-dimensional isotropic harmonic oscillator; and (iii) the three-dimensional Coulomb problem. This approach can be used in either undergraduate or graduate classes in quantum mechanics.

Wait-time distributions for the $n$th photo-detection at a detector illuminated by a stationary light beam are studied. Both unconditional measurements, initiated at an arbitrary instant, and conditional measurements, initiated upon a photo-detection, are considered. Simple analytic expressions are presented for several classical and quantum sources of light and are used to quantify and compare photon sequences generated by them. These distributions can be measured in photon counting experiments and are useful in characterizing and generating photon sequences with prescribed statistics. Effects of non-unit detection efficiency are also discussed, and curves are presented to illustrate the behavior.

We develop a microscopic calculation scheme for the excitation spectrum of a single-electron atom localized near a dielectric nanostructure. The atom originally has an arbitrary degenerate structure of its Zeeman sublevels on its closed optical transition and we follow how the excitation spectrum would be modified by its radiative coupling with a mesoscopicaly small dielectric sample of arbitrary shape. The dielectric medium is modeled by a dense ensemble of $V$-type atoms having the same dielectric permittivity near the transition frequency of the reference atom. Our numerical simulations predict strong coupling for some specific configurations and then suggest promising options for quantum interface and quantum information processing at the level of single photons and atoms. In particular, the strong resonance interaction between atom(s) and light, propagating through a photonic crystal waveguide, justifies as realistic the scenario of a signal light coupling with a small atomic array consisting of a few atoms. As a potential implication, the directional one-dimensional resonance scattering, expected in such systems, could provide a quantum bus by entangling distant atoms integrated into a quantum register.

Grover's algorithm is a well-known unstructured quantum search algorithm run on quantum computers. It constructs an oracle and calls the oracle O($\sqrt N$) times to locate specific data out of N unsorted data. This represents a quadratic speedup compared to the classical unstructured data sequential search algorithm, which requires to call the oracle O(N) times. We are currently in the noisy intermediate-scale quantum (NISQ) era in which quantum computers have a limited number of qubits, short decoherence time, and low gate fidelity. It is thus desirable to design quantum components with three good properties: (i) a reduced number of qubits, (ii) shorter quantum depth, and (iii) fewer gates. This paper utilizes novel quantum counters with the above-mentioned three good properties to construct the oracle of Grover's algorithm to efficiently solve the dominating set problem (DSP), as defined below. For a given graph G=(V, E), a dominating set (DS) D is a subset of the vertex set V, such that every vertex is in D or has an adjacent vertex in D. The DSP is to decide for a given graph G and an integer k whether there exists a DS with size k. Algorithms solving the DSP have many applications. For example, they can be applied to check whether k routers suffice to connect all computers in a computer network. The DSP is an NP-complete problem, indicating that no classical algorithm exists to solve the DSP with polynomial time complexity in the worst case. Therefore, using quantum algorithms, such as Grover's algorithm, to exploit the potent computational capabilities of quantum computers to solve the DSP is highly promising. We execute the whole quantum circuit of Grover's algorithm using novel quantum counters through the IBM Quantum Lab service to validate that the circuit can solve the DSP efficiently and correctly.

All quantum field theories that describe interacting bosonic elementary particles, share the feature that the zeroth order perturbation expansion describes non-interacting harmonic oscillators. This is explained in the paper. We then indicate that introducing interactions still leads to classical theories that can be compared with the quantum theories, but only if we terminate the expansion somewhere. `Quantum effects' typically occur when some of the classical variables fluctuate too rapidly to allow a conventional description, so that these are described exclusively in terms of their energy eigen modes; these do not commute with the standard classical variables. Perturbation expansions are not fundamentally required in classical theories, and this is why classical theories are more precisely defined than the quantum theories. Since the expansion parameters involve the fundamental constants of nature, such as the finestructure constant, we suggest that research in these classical models may lead to new clues concerning the origin of these constants.

We propose a method to dynamically decouple every magnetically sensitive hyperfine sublevel of a trapped ion from magnetic field noise, simultaneously, using integrated circuits to adiabatically rotate its local quantization field. These integrated circuits allow passive adjustment of the effective polarization of any external (control or noise) field. By rotating the ion's quantization direction relative to this field's polarization, we can perform `passive' dynamical decoupling (PDD), inverting the linear Zeeman sensitivity of every hyperfine sublevel. This dynamically decouples the entire ion, rather than just a qubit subspace. Fundamentally, PDD drives the transition $m_{F}\rightarrow -m_{F}$ for every magnetic quantum number $m_{F}$ in the system--with only one operation--indicating it applies to qudits with constant overhead in the dimensionality of the qudit. We show how to perform pulsed and continuous PDD, weighing each technique's insensitivity to external magnetic fields versus their sensitivity to diabaticity and control errors. Finally, we show that we can tune the sinusoidal oscillation of the quantization axis to a motional mode of the crystal in order to perform a laser-free two qubit gate that is insensitive to magnetic field noise.

We propose a conceptual model of a toroidal flux qubit, which consists of a quantized toroidal magnetic flux coupled to a charged particle on a quantum ring through field-free interaction. Scaling the system to two or more flux qubits results in emergent field-free coupling between them. We show that the topological and nonlocal aspects of this system can have profound applications in quantum information. We illustrate it with examples of nonlocal operations on these flux qubits which are protected from environmental noise, including creating entanglement and ``teleporting'' excitation energy between the flux qubits.

Electronic topological phases are renowned for their unique properties, where conducting surface states exist on the boundary of an insulating three-dimensional bulk. While the transport response of the surface states has been extensively studied, the response of the topological hinge modes remains elusive. Here, we investigate a layered topological insulator $\alpha$-Bi$_4$Br$_4$, and provide the first evidence for quantum transport in gapless topological hinge states existing within the insulating bulk and surface energy gaps. Our magnetoresistance measurements reveal pronounced h/e periodic (where h denotes Planck's constant and e represents the electron charge) Aharonov-Bohm oscillation. The observed periodicity, which directly reflects the enclosed area of phase-coherent electron propagation, matches the area enclosed by the sample hinges, providing compelling evidence for the quantum interference of electrons circumnavigating around the hinges. Notably, the h/e oscillations evolve as a function of magnetic field orientation, following the interference paths along the hinge modes that are allowed by topology and symmetry, and in agreement with the locations of the hinge modes according to our scanning tunneling microscopy images. Remarkably, this demonstration of quantum transport in a topological insulator can be achieved using a flake geometry and we show that it remains robust even at elevated temperatures. Our findings collectively reveal the quantum transport response of topological hinge modes with both topological nature and quantum coherence, which can be directly applied to the development of efficient quantum electronic devices.

Multipartite entanglement holds great importance in quantum information processing. The distribution of entanglement among subsystems can be characterized by monogamy relations. Based on the $\beta$th power of concurrence and negativity, we provide two new monogamy inequalities. Through detailed examples, we demonstrate that these inequalities are tighter than previous results.

Monogamy and polygamy of quantum correlations are the fundamental properties of quantum systems. We study the monogamy and polygamy relations satisfied by any quantum correlations in multipartite quantum systems. General monogamy relations are presented for the $\alpha$th $(0\leq\alpha \leq\gamma$, $\gamma\geq2)$ power of quantum correlation, and general polygamy relations are given for the $\beta$th $(\beta\geq \delta$, $0\leq\delta\leq1)$ power of quantum correlation. We show that these newly derived monogamy and polygamy inequalities are tighter than the existing ones. By applying these results to specific quantum correlations such as concurrence and the square of convex-roof extended negativity of assistance (SCRENoA), the corresponding new classes of monogamy and polygamy relations are obtained, which include the existing ones as special cases. Detailed examples are given to illustrate the advantages of our results.

The solution of large systems of nonlinear differential equations is needed for many applications in science and engineering. In this study, we present three main improvements to existing quantum algorithms based on the Carleman linearisation technique. First, by using a high-precision technique for the solution of the linearised differential equations, we achieve logarithmic dependence of the complexity on the error and near-linear dependence on time. Second, we demonstrate that a rescaling technique can considerably reduce the cost, which would otherwise be exponential in the Carleman order for a system of ODEs, preventing a quantum speedup for PDEs. Third, we provide improved, tighter bounds on the error of Carleman linearisation. We apply our results to a class of discretised reaction-diffusion equations using higher-order finite differences for spatial resolution. We show that providing a stability criterion independent of the discretisation can conflict with the use of the rescaling due to the difference between the max-norm and 2-norm. An efficient solution may still be provided if the number of discretisation points is limited, as is possible when using higher-order discretisations.

In this paper, we investigate steered quantum coherence, i.e., the $l_1$ norm of steered coherence and the relative entropy of steered coherence, and the quantum Fisher information in the Gibbs state of two-qubit $XXZ$ systems. Their variations with respect to the temperature, external magnetic field, and interaction intensities are analyzed both analytically and numerically in detail. The similar behaviors among these three quantum measures in the $XXZ$ model are presented.

In materials informatics, searching for chemical materials with desired properties is challenging due to the vastness of the chemical space. Moreover, the high cost of evaluating properties necessitates a search with a few clues. In practice, there is also a demand for proposing compositions that are easily synthesizable. In the real world, such as in the exploration of chemical materials, it is common to encounter problems targeting black-box objective functions where formalizing the objective function in explicit form is challenging, and the evaluation cost is high. In recent research, a Bayesian optimization method has been proposed to formulate the quadratic unconstrained binary optimization (QUBO) problem as a surrogate model for black-box objective functions with discrete variables. Regarding this method, studies have been conducted using the D-Wave quantum annealer to optimize the acquisition function, which is based on the surrogate model and determines the next exploration point for the black-box objective function. In this paper, we address optimizing a black-box objective function containing discrete variables in the context of actual chemical material exploration. In this optimization problem, we demonstrate results obtaining parameters of the acquisition function by sampling from a probability distribution with variance can explore the solution space more extensively than in the case of no variance. As a result, we found combinations of substituents in compositions with the desired properties, which could only be discovered when we set an appropriate variance.

Quantum machine learning is an important application of quantum computing in the era of noisy intermediate-scale quantum devices. Domain adaptation is an effective method for addressing the distribution discrepancy problem between the training data and the real data when the neural network model is deployed. In this paper, a variational quantum domain adaptation method is proposed by using a quantum convolutional neural network, together with a gradient reversal module, and two quantum fully connected layers, named variational quantum domain adaptation(VQDA). The simulations on the local computer and IBM Quantum Experience (IBM Q) platform by Qiskit show the effectiveness of the proposed method. The results demonstrate that, compared to its classical corresponding domain adaptation method, VQDA achieves an average improvement of 4% on the accuracy for MNIST to USPS domain transfer under the same parameter scales. Similarly, for SYNDigits to SVHN domain transfer, VQDA achieves an average improvement of 2% on the accuracy under the same parameter scales.

Atom optics demonstrates optical phenomena with coherent matter waves, providing a foundational connection between light and matter. Significant advances in optics have followed the realisation of structured light fields hosting complex singularities and topologically non-trivial characteristics. However, analogous studies are still in their infancy in the field of atom optics. Here, we investigate and experimentally create knotted quantum wavefunctions in spinor Bose--Einstein condensates which display non-trivial topologies. In our work we construct coordinated orbital and spin rotations of the atomic wavefunction, engineering a variety of discrete symmetries in the combined spin and orbital degrees of freedom. The structured wavefunctions that we create map to the surface of a torus to form torus knots, M\"obius strips, and a twice-linked Solomon's knot. In this paper we demonstrate striking connections between the symmetries and underlying topologies of multicomponent atomic systems and of vector optical fields--a realization of topological atom-optics.

Accurate and robust estimation of quantum process properties is crucial for quantum information processing and quantum many-body physics. Combining classical shadow tomography and randomized benchmarking, Helsen et al. introduced a method to estimate the linear properties of quantum processes. In this work, we focus on the estimation protocols of nonlinear process properties that are robust to state preparation and measurement errors. We introduce two protocols, both utilizing random gate sequences but employing different post-processing methods, which make them suitable for measuring different nonlinear properties. The first protocol offers a robust and sound method to estimate the out-of-time-ordered correlation, as demonstrated numerically in an Ising model. The second protocol estimates unitarity, effectively characterizing the incoherence of quantum channels. We expect the two protocols to be useful tools for exploring quantum many-body physics and characterizing quantum processes.

Circuit cutting, the partitioning of quantum circuits into smaller independent fragments, has become a promising avenue for scaling up current quantum-computing experiments. Here, we introduce a scheme for joint cutting of two-qubit rotation gates based on a virtual gate-teleportation protocol. By that, we significantly lower the previous upper bounds on the sampling overhead and prove optimality of the scheme. Furthermore, we show that no classical communication between the circuit partitions is required. For parallel two-qubit rotation gates we derive an optimal ancilla-free decomposition, which include CNOT gates as a special case.

We study heat radiation and radiative heat transfer for nanoparticles in the presence of an infinitely long cylinder in different geometrical configurations, based on its electromagnetic Green's tensor. The heat radiation of a single particle can be enhanced by placing it close to a nanowire, and this enhancement can be much larger as compared to placing it close to plate of same material. The heat transfer along a cylinder decays much slower than through empty vacuum, being especially long ranged in case of a perfectly conducting nanowire, and showing nonmonotonic behavior in case of a SiC cylinder. Exploring the dependence on the relative azimuthal angle of the nanoparticles, we find that the results are insensitive to small angles, but they can be drastically different when the angle is large, depending on the material. Finally, we demonstrate that a cylinder can either enhance or block the heat flux when placed perpendicular to the interparticle distance line, where especially the blocking is strongly enhanced compared to the geometry of a sphere of same radius.