QUROPE Quantum Information Processing and Communication in Europe

Many problems in linear algebra -- such as those arising from non-Hermitian physics and differential equations -- can be solved on a quantum computer by processing eigenvalues of the non-normal input matrices. However, the existing Quantum Singular Value Transformation (QSVT) framework is ill-suited to this task, as eigenvalues and singular values are different in general. We present a Quantum EigenValue Transformation (QEVT) framework for applying arbitrary polynomial transformations on eigenvalues of block-encoded non-normal operators, and a related Quantum EigenValue Estimation (QEVE) algorithm for operators with real spectra. QEVT has query complexity to the block encoding nearly recovering that of the QSVT for a Hermitian input, and QEVE achieves the Heisenberg-limited scaling for diagonalizable input matrices. As applications, we develop a linear differential equation solver with strictly linear time query complexity for average-case diagonalizable operators, as well as a ground state preparation algorithm that upgrades previous nearly optimal results for Hermitian Hamiltonians to diagonalizable matrices with real spectra. Underpinning our algorithms is an efficient method to prepare a quantum superposition of Faber polynomials, which generalize the nearly-best uniform approximation properties of Chebyshev polynomials to the complex plane. Of independent interest, we also develop techniques to generate $n$ Fourier coefficients with $\mathbf{O}(\mathrm{polylog}(n))$ gates compared to prior approaches with linear cost.

Photonic integrated circuits with second-order ($\chi^{(2)}$) nonlinearities are rapidly scaling to remarkably low powers. At this time, state-of-the-art devices achieve saturated nonlinear interactions with thousands of photons when driven by continuous-wave lasers, and further reductions in these energy requirements enabled by the use of ultrafast pulses may soon push nonlinear optics into the realm of single-photon nonlinearities. This tutorial reviews these recent developments in ultrafast nonlinear photonics, discusses design strategies for realizing few-photon nonlinear interactions, and presents a unified treatment of ultrafast quantum nonlinear optics using a framework that smoothly interpolates from classical behaviors to the few-photon scale. These emerging platforms for quantum optics fundamentally differ from typical realizations in cavity quantum electrodynamics due to the large number of coupled optical modes. Classically, multimode behaviors have been well studied in nonlinear optics, with famous examples including soliton formation and supercontinuum generation. In contrast, multimode quantum systems exhibit a far greater variety of behaviors, and yet closed-form solutions are even sparser than their classical counterparts. In developing a framework for ultrafast quantum optics, we will identify what behaviors carry over from classical to quantum devices, what intuition must be abandoned, and what new opportunities exist at the intersection of ultrafast and quantum nonlinear optics. While this article focuses on establishing connections between the classical and quantum behaviors of devices with $\chi^{(2)}$ nonlinearities, the frameworks developed here are general and are readily extended to the description of dynamical processes based on third-order ($\chi^{(3)}$) nonlinearities.

A promising strategy to protect quantum information from noise-induced errors is to encode it into the low-energy states of a topological quantum memory device. However, readout errors from such memory under realistic settings is less understood. We study the problem of decoding quantum information encoded in the groundspaces of topological stabilizer Hamiltonians in the presence of generic perturbations, such as quenched disorder. We first prove that the standard stabilizer-based error correction and decoding schemes work adequately well in such perturbed quantum codes by showing that the decoding error diminishes exponentially in the distance of the underlying unperturbed code. We then prove that Quantum Neural Network (QNN) decoders provide an almost quadratic improvement on the readout error. Thus, we demonstrate provable advantage of using QNNs for decoding realistic quantum error-correcting codes, and our result enables the exploration of a wider range of non-stabilizer codes in the near-term laboratory settings.

Quantum channel, as the information transmitter, is an indispensable tool in quantum information theory. In this paper, we study a class of special quantum channels named the mixed-permutation channels. The properties of these channels are characterized. The mixedpermutation channels can be applied to give a lower bound of quantum coherence with respect to any coherence measure. In particular, the analytical lower bounds for l1-norm coherence and the relative entropy of coherence are shown respectively. The extension to bipartite systems is presented for the actions of the mixed-permutation channels.

Image denoising is essential for removing noise in images caused by electric device malfunctions or other factors during image acquisition. It helps preserve image quality and interpretation. Many convolutional autoencoder algorithms have proven effective in image denoising. Owing to their promising efficiency, quantum computers have gained popularity. This study introduces a quantum convolutional autoencoder (QCAE) method for improved image denoising. This method was developed by substituting the representative latent space of the autoencoder with a quantum circuit. To enhance efficiency, we leveraged the advantages of the quantum approximate optimization algorithm (QAOA)-incorporated parameter-shift rule to identify an optimized cost function, facilitating effective learning from data and gradient computation on an actual quantum computer. The proposed QCAE method outperformed its classical counterpart as it exhibited lower training loss and a higher structural similarity index (SSIM) value. QCAE also outperformed its classical counterpart in denoising the MNIST dataset by up to 40% in terms of SSIM value, confirming its enhanced capabilities in real-world applications. Evaluation of QAOA performance across different circuit configurations and layer variations showed that our technique outperformed other circuit designs by 25% on average.

In photonic quantum applications, optical routers are required to handle single photons with low loss, high speed, and preservation of their quantum states. Single-photon routing with maintained polarization states is particularly important for utilizing them as qubits. Here, we demonstrate a polarization-maintaining electro-optic router compatible with single photons. Our custom electro-optic modulator is embedded in a configuration of a Mach-Zehnder interferometer, where each optical component achieves polarization-maintaining operation. We observe the performance of the router with 2-4% loss, 20 dB switching extinction ratio, 2.9 ns rise time, and $>$ 99% polarization process fidelity to an ideal identity operation.

Time series prediction (TSP) has been widely used in various fields, such as life sciences and finance, to forecast future trends based on historical data. However, to date, there has been relatively little research conducted on the TSP for quantum physics. In this paper, we explore the potential application of TSP in forecasting the dynamical evolution of open quantum systems. We employ deep learning techniques to train a TSP model and evaluate its performance by comparison with exact solution. We use the ratio of the prediction step length and the sequence length to define short and long-term forecasting. Our results show that the trained model has the ability to effectively capture the inherent characteristics of time series for both short-term and long-term forecasting. Accurate predictions for different coupling intensities and initial states are obtained. Furthermore, we use our method to train another model and find that it can successfully predict the steady state of the system. These findings suggests that TSP is a valuable tool for the prediction of the dynamics in open quantum systems.

Electrodynamical coupled cluster (CC) methodologies have been formulated employing standard QED Hamiltonian that is written in Coulomb gauge while using the DF and the MCDF pictures of the matter field for closed-shell and open-shell cases respectively. The general methodology employs a radiative cluster, pure matter clusters and their pair modifications, and a number state distribution of photons in thermal equilibrium. The closed-shell treatment relies on the customary CC approach. For open shells, QED and electron correlation through CC are treated on the same footing. An averaging over the radiation state is done to generate Lamb, Breit and hyperfine interactions from the radiative cluster. Because of the thermal distribution, it leaves a residual transverse interaction that may modify the static correlation in open shells. Dynamical correlation effects are determined next by using the exponential matter cluster in traditional ways of single- and multi-reference CC. When the matter cluster is extended to include de-excitations to negative-energy levels, vacuum polarization effects are generated from the pair part of Coulomb interaction. The dynamical correlation energy includes relativistic corrections as well as QED contributions, namely, Lamb, Breit, hyperfine and pair energy. This work has three novelties: (i) QED interactions (Lamb, Breit and hyperfine) are obtained from a single procedure based on the radiative cluster; (ii) pair energy is determined from an extended matter cluster formalism; and (iii) additional correlation energy can be had from radiative effects and pair terms, while the option for higher order pair energy in high-Z atoms is kept open. The open-shell formalism has one more novelty in finding an additional static correlation in certain cases when the radiation is not isotropic.

We propose and analyze a scheme for manipulating the propagation of single photon pulses with two polarization components in a Rydberg atomic gas via double electromagnetically induced transparency. We show that by storing a gate photon in a Rydberg state a deep and tunable potential for a photon polarization qubit can be achieved based on strong Rydberg interaction. We also show that the scheme can be used to realize all-optical switch in dissipation regime and generate a large phase shift in dispersion regime for the photon polarization qubit. Moreover, we demonstrate that such a scheme can be utilized to detect weak magnetic fields. The results reported here are not only beneficial for understanding the quantum optical property of Rydberg atomic gases, but also promising for designing novel devices for quantum information processing.

Topological quantum optics, an emerging area of study, holds the potential to bring about substantial enhancements for integrated quantum devices. Here we propose integrated topological quantum devices performing various functions including optical parametric amplification, frequency division, and frequency entangled biphoton generation. We show two distinct edge modes corresponding to different frequency ranges in both sandwich kagome and honeycomb topological designs that emulate the quantum valley Hall effect. These two topological edge modes enable two types of optical parametric processes through four-wave mixing, specifically inter-band and intra-band cases. The devices emulating photonic valley-Hall insulators allow the frequency division of two transverse modes, and furthermore, enable the separation of two quantum functionalities - optical parametric amplification and frequency entangled biphoton state generation. More importantly, the parametric processes are inborn topological protected, showing robustness against sharp bends and disorders. Our proposal significantly widens the possibilities for robust, multifunctional topological quantum devices on-chip, which may find applications in quantum information processing.

Quantum computation promises to advance a wide range of computational tasks. However, current quantum hardware suffers from noise and is too small for error correction. Thus, accurately utilizing noisy quantum computers strongly relies on noise characterization, mitigation, and suppression. Crucially, these methods must also be efficient in terms of their classical and quantum overhead. Here, we efficiently characterize and mitigate crosstalk noise, which is a severe error source in, e.g., cross-resonance based superconducting quantum processors. For crosstalk characterization, we develop a simplified measurement experiment. Furthermore, we analyze the problem of optimal experiment scheduling and solve it for common hardware architectures. After characterization, we mitigate noise in quantum circuits by a noise-aware qubit routing algorithm. Our integer programming algorithm extends previous work on optimized qubit routing by swap insertion. We incorporate the measured crosstalk errors in addition to other, more easily accessible noise data in the objective function. Furthermore, we strengthen the underlying integer linear model by proving a convex hull result about an associated class of polytopes, which has applications beyond this work. We evaluate the proposed method by characterizing crosstalk noise for a complete 27 qubit chip and leverage the resulting data to improve the approximation ratio of the Quantum Approximate Optimization Algorithm by up to 10 % compared to other established noise-aware routing methods. Our work clearly demonstrates the gains of including noise data when mapping abstract quantum circuits to hardware native ones.

The great scientific and technological advances that are being carried out in the field of quantum communications, accompanied by large investment programs such as EuroQCI, are driving the deployment of quantum network throughout the world. One of the final long-term objectives is to achieve the development of a quantum internet that provides greater security in its services and new functionalities that the current internet does not have. This article analyzes the possible integration strategies of already deployed networks or in the process of being deployed in order to reach a future global quantum network. Two strategies based on the SDN paradigm are proposed, based on a hierarchical controller scheme and on a distributed model. Each of these approaches shows pros and cons and could be applicable in different use cases. To define these strategies, the most relevant deployments of quantum communications networks carried out to date has been analyzed, as well as the different approaches for a quantum network architecture and topology, and the various proposed definitions of what quantum internet is and what are the components that would make it up in an ideal scenario. Finally, several detected opportunities and challenges regarding security and technological aspects are presented.

In the standard Bell scenario, when making a local projective measurement on each system component, the amount of randomness generated is restricted. However, this limitation can be surpassed through the implementation of sequential measurements. Nonetheless, a rigorous definition of random numbers in the context of sequential measurements is yet to be established, except for the lower quantification in device-independent scenarios. In this paper, we define quantum intrinsic randomness in sequential measurements and quantify the randomness in the Collins-Gisin-Linden-Massar-Popescu (CGLMP) inequality sequential scenario. Initially, we investigate the quantum intrinsic randomness of the mixed states under sequential projective measurements and the intrinsic randomness of the sequential positive-operator-valued measure (POVM) under pure states. Naturally, we rigorously define quantum intrinsic randomness under sequential POVM for arbitrary quantum states. Furthermore, we apply our method to one-Alice and two-Bobs sequential measurement scenarios, and quantify the quantum intrinsic randomness of the maximally entangled state and maximally violated state by giving an extremal decomposition. Finally, using the sequential Navascues-Pironio-Acin (NPA) hierarchy in the device-independent scenario, we derive lower bounds on the quantum intrinsic randomness of the maximally entangled state and maximally violated state.

Coherent spin resonance methods, such as nuclear magnetic resonance and electron spin resonance spectroscopy, have led to spectrally highly sensitive, non-invasive quantum imaging techniques. Here, we propose a pump-probe spin resonance spectroscopy approach, designed for electron microscopy, based on microwave pump fields and electron probes. We investigate how quantum spin systems couple to electron matter waves through their magnetic moments and how the resulting phase shifts can be utilized to gain information about the states and dynamics of these systems. Notably, state-of-the-art transmission electron microscopy provides the means to detect phase shifts almost as small as that due to a single electron spin. This could enable state-selective observation of spin dynamics on the nanoscale and indirect measurement of the environment of the examined spin systems, providing information, for example, on the atomic structure, local chemical composition and neighboring spins.

Algebraic quantum field theory (AQFT) puts forward three "causal axioms" that aim to characterize the theory as one that implements relativistic causation: the spectrum condition, microcausality, and primitive causality. In this paper, I aim to show, in a minimally technical way, that none of them fully explains the notion of causation appropriate for AQFT because they only capture some of the desiderata for relativistic causation I state or because it is often unclear how each axiom implements its respective desideratum. After this diagnostic, I will show that a fourth condition, local primitive causality (LPC), fully characterizes relativistic causation in the sense of fulfilling all the relevant desiderata. However, it only encompasses the virtues of the other axioms because it is implied by them, as I will show from a construction by Haag and Schroer (1962). Since the conjunction of the three causal axioms implies LPC and other important results in QFT that LPC does not imply, and since LPC helps clarify some of the shortcomings of the three axioms, I advocate for a holistic interpretation of how the axioms characterize the causal structure of AQFT against the strategy in the literature to rivalize the axioms and privilege one among them.

In this work we describe how to systematically implement a full graph decomposition to set up a linked-cluster expansion for the topological phase of Kitaev's toric code in a field. This demands to include the non-local effects mediated by the mutual anyonic statistics of elementary charge and flux excitations. Technically, we describe how to consistently integrate such non-local effects into a hypergraph decomposition for single excitations. The approach is demonstrated for the ground-state energy and the elementary excitation energies of charges and fluxes in the perturbed topological phase.

In this work, we present simulations of two Open Quantum System models, Collisional and Markovian Reservoir, with noise simulations, the IBM devices ($\textit{ibm_kyoto}$, $\textit{ibm_osaka}$) and the OQC device Lucy. Extending the results of Garc\'ia-P\'erez, et al. [npj Quantum Information 6.1 (2020): 1]. Using the Mitiq toolkit, we apply Zero-Noise extrapolation (ZNE), an error mitigation technique, and analyze their deviation from the theoretical results for the models under study. For both models, by applying ZNE, we were able to reduce the error and overlap it with the theoretical results. All our simulations and experiments were done in the qBraid environment.

We consider the impact that temporal correlations in the measurement statistics can have on the achievable precision in a sequential metrological protocol. In this setting, and for a single quantum probe, we establish that it is the transitions between the measurement basis states that plays the most significant role in determining the precision, with the resulting conditional Fisher information being interpretable as a rate of information acquisition. Projective measurements are shown to elegantly demonstrate this in two disparate estimation settings. Firstly, in determining the temperature of an environment and, secondly, to ascertain a parameter of the system Hamiltonian. In both settings we show that the sequential estimation approach can provide a useful method to enhance the achievable precision.

Performing nanoscale scanning electron paramagnetic resonance (EPR) requires three essential ingredients. First, a static magnetic field together to field gradients to Zeeman split the electronic energy levels with spatial resolution. Second, a radiofrequency (rf) magnetic field capable of inducing spin transitions. Finally, a sensitive detection method to quantify the energy absorbed by spins. This is usually achieved by combining externally applied magnetic fields with inductive coils or cavities, fluorescent defects or scanning probes. Here, we {\color{black} theoretically propose the realization of a EPR scanning sensor merging all three characteristics into a single device}: the vortex core stabilized in ferromagnetic thin-film discs. On one hand, the vortex ground state generates a significant static magnetic field and field gradients. On the other hand, the precessional motion of the vortex core around its equilibrium position produces a circularly polarized oscillating magnetic field, which is enough to produce spin transitions. Finally, the spin-magnon coupling broadens the vortex gyrotropic frequency, {\color{black} suggesting} a direct measure of the presence of unpaired electrons. Moreover, the vortex core can be displaced by simply using external magnetic fields of a few mT, enabling EPR scanning microscopy with large spatial resolution. Our {\color{black} numerical} simulations show that, by using low damping magnets, it is {\color{black} theoretically} possible to detect single spins located on the disc's surface. Vortex nanocavities could also attain strong coupling to individual spin molecular qubits, with potential applications to mediate qubit-qubit interactions or to implement qubit readout protocols.

We characterise the category of finite-dimensional Hilbert spaces and linear contractions using simple category-theoretic axioms that do not refer to norms, continuity, dimension, or real numbers. Our proof directly relates limits in category theory to limits in analysis, using a new variant of the classical characterisation of the real numbers instead of Sol\`er's theorem.