QUROPE Quantum Information Processing and Communication in Europe

Quantum computers have been proposed to solve a number of important problems such as discovering new drugs, new catalysts for fertilizer production, breaking encryption protocols, optimizing financial portfolios, or implementing new artificial intelligence applications. Yet, to date, a simple task such as multiplying 3 by 5 is beyond existing quantum hardware. This article examines the difficulties that would need to be solved for quantum computers to live up to their promises. I discuss the whole stack of technologies that has been envisioned to build a quantum computer from the top layers (the actual algorithms and associated applications) down to the very bottom ones (the quantum hardware, its control electronics, cryogeny, etc.) while not forgetting the crucial intermediate layer of quantum error correction.

Optically accessible spin-active nanomaterials are promising as quantum nanosensors for probing biological samples. However, achieving bioimaging-level brightness and high-quality spin properties for these materials is challenging and hinders their application in quantum biosensing. Here, we demonstrate ultrabright fluorescent nanodiamonds (NDs) containing 0.6-1.3-ppm nitrogen-vacancy (NV) centers by spin-environment engineering via enriching spin-less 12C-carbon isotopes and reducing substitutional nitrogen spin impurities. The NDs, readily introduced into cultured cells, exhibited substantially narrow optically detected magnetic resonance (ODMR) spectra, requiring 16-times less microwave excitation power to give an ODMR depth comparable to that of conventional type-Ib NDs. They show average spin-relaxation times of T1 = 0.68 ms and T2 = 1.6 us (1.6 ms and 2.7 us maximum) that were 5- and 10-fold longer than those of type-Ib, respectively. The bulk-like NV spin properties and bright fluorescence demonstrated in this study significantly improve the sensitivity of ND-based quantum sensors for biological applications.

To quantify the entanglement of bipartite systems in terms of some entanglement measure is a challenging problem in general, and it is much worse when the information about the system is less. In this manuscript, based on two classes of entanglement criteria, we present a method to obtain the lower bounds of the entanglement measures, concurrence, entanglement of formation, and geometrical entanglement measure.

We examine the emergence of periodicity in a non-interacting steady-state quantum system without external drive inspired by quantum time crystals' spontaneous time-translation symmetry breaking. Specifically, we consider a lattice ring of non-interacting electrons undergoing weak local position measurements. Our analysis uncovers time-periodic structures in steady-state two-time correlation functions, with periodicity linked to the system's group velocity. This study demonstrates a measurement-induced clock mechanism, highlighting periodic behaviors in two-time correlators of a non-equilibrium steady state, contributing to understanding time-periodic phenomena in minimally interactive quantum systems.

In Si/SiGe heterostructures, the low-lying excited valley state seriously limit operability and scalability of electron spin qubits. For characterizing and understanding the local variations in valley splitting, fast probing methods with high spatial and energy resolution are lacking. Leveraging the spatial control granted by conveyor-mode spin-coherent electron shuttling, we introduce a method for two-dimensional mapping of the local valley splitting by detecting magnetic field dependent anticrossings of ground and excited valley states using entangled electron spin-pairs as a probe. The method has sub-{\mu}eV energy accuracy and a nanometer lateral resolution. The histogram of valley splittings spanning a large area of 210 nm by 18 nm matches well with statistics obtained by the established but time-consuming magnetospectroscopy method. For the specific heterostructure, we find a nearly Gaussian distribution of valley splittings and a correlation length similar to the quantum dot size. Our mapping method may become a valuable tool for engineering Si/SiGe heterostructures for scalable quantum computing.

Bosonic and fermionic statistics are well known to give rise to antinomic behaviors, most notably boson bunching vs. fermion antibunching. Here, we establish a fundamental relation that combines bosonic and fermionic multiparticle interferences in an arbitrary linear interferometer. The bosonic and fermionic transition probabilities appear together in a same equation which constrains their values, hence expressing a boson-fermion complementarity that is independent of the details of the interaction. For two particles in any interferometer, for example, it implies that the average of the bosonic and fermionic probabilities must coincide with the probability obeyed by classical particles. Incidentally, this fundamental relation also provides a heretofore unknown mathematical identity connecting the squared moduli of the permanent and determinant of arbitrary complex matrices.

We provide a mechanism to imprint local temporal correlations in photon streams which have the same character as spatial correlations in liquids. Usual single-photon emitters correspond, in this picture, to a (temporal) gas while uncorrelated light is the ideal gas. We argue that good single-photon sources are those that exhibit such temporal liquid features, i.e., with a plateau for their short-time correlations (as opposed to a linear dependence) and oscillations at later times, which is a direct manifestation of photon time-ordering. We obtain general, closed-form analytical expressions for the second-order coherence function of a broad family of "liquid light" which can be arbitrarily correlated, though never completely crystallized.

We investigate the possibility of reproducing the continuum physics of 2d SU(N) gauge theory coupled to a single flavor of massless Dirac fermions using qubit regularization. The continuum theory is described by N free fermions in the ultraviolet (UV) and a coset Wess-Zumino-Witten (WZW) model in the infrared (IR). In this work, we explore how well these features can be reproduced using the Kogut-Susskind Hamiltonian with a finite-dimensional link Hilbert space and a generalized Hubbard coupling. Using strong coupling expansions, we show that our model exhibits a gapped dimer phase and another phase described by a spin-chain. Furthermore, for N=2, using tensor network methods, we show that there is a second-order phase transition between these two phases. The critical theory at the transition can be understood as an SU(2)_1 WZW model, using which we determine the phase diagram of our model quantitatively. Using the confinement properties of the model we argue how the UV physics of free fermions could also emerge, but may require further modifications to our model.

High-dimensional quantum information processing has emerged as a promising avenue to transcend hardware limitations and advance the frontiers of quantum technologies. Harnessing the untapped potential of the so-called qudits necessitates the development of quantum protocols beyond the established qubit methodologies. Here, we present a robust, hardware-efficient, and extensible approach for operating multidimensional solid-state systems using Raman-assisted two-photon interactions. To demonstrate its efficacy, we construct a set of multi-qubit operations, realize highly entangled multidimensional states including atomic squeezed states and Schr\"odinger cat states, and implement programmable entanglement distribution along a qudit array. Our work illuminates the quantum electrodynamics of strongly driven multi-qudit systems and provides the experimental foundation for the future development of high-dimensional quantum applications.

For quantum computers to successfully solve real-world problems, it is necessary to tackle the challenge of noise: the errors which occur in elementary physical components due to unwanted or imperfect interactions. The theory of quantum fault tolerance can provide an answer in the long term, but in the coming era of `NISQ' machines we must seek to mitigate errors rather than completely remove them. This review surveys the diverse methods that have been proposed for quantum error mitigation, assesses their in-principle efficacy, and then describes the hardware demonstrations achieved to date. We identify the commonalities and limitations among the methods, noting how mitigation methods can be chosen according to the primary type of noise present, including algorithmic errors. Open problems in the field are identified and we discuss the prospects for realising mitigation-based devices that can deliver quantum advantage with an impact on science and business.

Utilizing the framework of $\mathbb{Z}_2$ lattice gauge theories in the context of Pauli stabilizer codes, we present methodologies for simulating fermions via qubit systems on a two-dimensional square lattice. We investigate the symplectic automorphisms of the Pauli module over the Laurent polynomial ring. This enables us to systematically increase the code distances of stabilizer codes while fixing the rate between encoded logical fermions and physical qubits. We identify a family of stabilizer codes suitable for fermion simulation, achieving code distances of $d=2,3,4,5,6,7$, allowing correction of any $\lfloor \frac{d-1}{2} \rfloor$-qubit error. In contrast to the traditional code concatenation approach, our method can increase the code distances without decreasing the (fermionic) code rate. In particular, we explicitly show all stabilizers and logical operators for codes with code distances of $d=3,4,5$. We provide syndromes for all Pauli errors and invent a syndrome-matching algorithm to compute code distances numerically.

Physicists dating back to Feynman have lamented the difficulties of applying the variational principle to quantum field theories. In non-relativistic quantum field theories, the challenge is to parameterize and optimize over the infinitely many $n$-particle wave functions comprising the state's Fock space representation. Here we approach this problem by introducing neural-network quantum field states, a deep learning ansatz that enables application of the variational principle to non-relativistic quantum field theories in the continuum. Our ansatz uses the Deep Sets neural network architecture to simultaneously parameterize all of the $n$-particle wave functions comprising a quantum field state. We employ our ansatz to approximate ground states of various field theories, including an inhomogeneous system and a system with long-range interactions, thus demonstrating a powerful new tool for probing quantum field theories.

We characterize quantum correlations encoded in a three-flavor oscillating neutrino system by using both plane-wave and wave-packet approach. By means of the Complete Complementarity Relations we study the trade off of predictability, local coherence and non local correlations in terms of the relevant parameters, chosen from recent neutrino experiments. Although the CCR describe very well the contributions associated to bipartite correlations, an attempt of promoting these relations to include the genuine tripartite contributions in the pure state case leads to a not completely meaningful result. However, we provide an analysis of the genuine tripartite contributions both for the pure instance and for the mixed case, independently of CCR.

We present an exactly solvable toy model for the continuous dissipative dynamics of permutation-invariant graph states of $N$ qubits. Such states are locally equivalent to an $N$-qubit Greenberger-Horne-Zeilinger (GHZ) state, a fundamental resource in many quantum information processing setups. We focus on the time evolution of the state governed by a Lindblad master equation with the three standard single-qubit jump operators, the Hamiltonian part being set to zero. Deriving analytic expressions for the expectation values of observables expanded in the Pauli basis at all times, we analyze the nontrivial intermediate-time dynamics. Using a numerical solver based on matrix product operators, we simulate the time evolution for systems with up to 64 qubits and verify a numerically exact agreement with the analytical results. We find that the evolution of the operator space entanglement entropy of a bipartition of the system manifests a plateau whose duration increases logarithmically with the number of qubits, whereas all Pauli-operator products have expectation values decaying at most in constant time.

Spin network systems can be used to achieve quantum state transfer with high fidelity and to generate entanglement. A new approach to design spin-chain-based spin network systems, for shortrange quantum information processing and phase-sensing, has been proposed recently in [1]. In this paper, we investigate the scalability of such systems, by designing larger spin network systems that can be used for longer-range quantum information tasks, such as connecting together quantum processors. Furthermore, we present more complex spin network designs, which can produce different types of entangled states. Simulations of disorder effects show that even such larger spin network systems are robust against realistic levels of disorder.

The paper analyzes the probability distribution of the occupancy numbers and the entropy of a system at the equilibrium composed by an arbitrary number of non-interacting bosons. The probability distribution is derived both by tracing out the environment from a bosonic eigenstate of the union of environment and system of interest (the empirical approach) and by tracing out the environment from the mixed state of the union of environment and system of interest (the Bayesian approach). In the thermodynamic limit, the two coincide and are equal to the multinomial distribution. Furthermore, the paper proposes to identify the physical entropy of the bosonic system with the Shannon entropy of the occupancy numbers, fixing certain contradictions that arise in the classical analysis of thermodynamic entropy. Finally, by leveraging an information-theoretic inequality between the entropy of the multinomial distribution and the entropy of the multivariate hypergeometric distribution, Bayesianism and empiricism are integrated into a common ''infomechanical'' framework.

Finding groups of similar image blocks within an ample search area is often necessary in different applications, such as video compression, image clustering, vector quantization, and nonlocal noise reduction. A block-matching algorithm that uses a dissimilarity measure can be applied in such scenarios. In this work, a measure that utilizes the quantum Fourier transform or the Swap test based on the Euclidean distance is proposed. Experiments on small cases with ideal and noisy simulations are implemented. In the case of the Swap test, the IBM and IonQ quantum devices have been used, demonstrating potential for future near-term applications.

In this article, we investigate Ehrenfest's theorem from the Dirac equation in a noncommutative phase-space where we calculate the time derivative of the position and the kinetic momentum operators for Dirac particles in interaction with electromagnetic field and within a noncommutative setting. This allows examining the effect of the phase-space noncommutativity on Ehrenfest's theorem. Knowing that with both the linear Bopp-Shift and Moyal-Weyl product, the noncommutativity is inserted.

The need of near-surface color centers in diamond for quantum technologies motivates the controlled doping of specific extrinsic impurities into the crystal lattice. Recent experiments have shown that this can be achieved by momentum transfer from a surface precursor via ion implantation, an approach known as ``recoil implantation.'' Here, we extend this technique to incorporate dielectric precursors for creating nitrogen-vacancy (NV) and silicon-vacancy (SiV) centers in diamond. Specifically, we demonstrate that gallium focused-ion-beam exposure to a thin layer of silicon nitride or silicon dioxide on the diamond surface results in the introduction of both extrinsic impurities and carbon vacancies. These defects subsequently give rise to near-surface NV and SiV centers with desirable optical properties after annealing.

A generalization of associated Legendre functions is proposed and used to describe the scattering states of the Rosen-Morse potential. The functions are then given explicit formulas in terms of the hypergeometric function, their asymptotic behavior is examined and shown to match the requirements for states in the regions of total and partial reflection. Elementary expressions are given for reflection and transmission coefficients, and an integral identity for the generalized Legendre functions is proven, allowing the calculation of the spectral measure of the induced integral transform for the scattering states. These methods provide a complete classical solution to the potential, without need of path integral techniques.