QUROPE Quantum Information Processing and Communication in Europe

Recent experimental results have validated a prediction made almost four decades ago, affirming the existence of quantized current steps in ultrasmall Josephson junctions and superconducting nanowires. These so-called dual Shapiro steps hold promise for a new current standard and thus could close the quantum metrological triangle. This is because the steps mark quantized current levels $I=\pm n \times 2ef$, where the elementary charge $e$ is a fixed constant in the new SI and the frequency $f$ is the physical quantity measured with the highest precision. To realize dual Shapiro steps, we embed an Al/AlO$_\mathrm{x}$/Al dc-SQUID in a high impedance environment made from granular aluminium and oxidized titanium. We successfully demonstrate quantized current steps in the IV-curves by applying sinusoidal driving signals of frequencies up to $6\:\mathrm{GHz}$ resulting in quantized current levels up to $I \approx \pm 2\:\mathrm{nA}$. Remarkably, if changing to a pulsed drive, the first dual Shapiro step has a larger voltage amplitude, while the opposite step vanishes, depending on the sign of the pulse. By using the peak values of the differential resistance as a measure of flatness, we demonstrate improvement due to the pulsed driving signals by a factor of $\sim 2$ compared to sinusoidal driving.

The growing interest in quantum information has enabled the manipulation and readout of microwave photon states with high fidelities. The presently available microwave photon counters, based on superconducting circuits, are limited to non-continuous pulsed mode operation, requiring additional steps for qubit state preparation before an actual measurement. Here, we present a continuous microwave photon counter based on superconducting cavity-coupled semiconductor quantum dots. The device utilizes photon-assisted tunneling in a double quantum dot with tunneling events being probed by a third dot. Our device detects both single and multiple-photon absorption events independently, thanks to the energy tunability of a two-level double-dot absorber. We show that the photon-assisted tunnel rates serve as the measure of the cavity photon state in line with the P(E) theory - a theoretical framework delineating the mediation of the cavity photon field via a two-level environment. We further describe the single photon detection using the Jaynes-Cummings input-output theory and show that it agrees with the P(E) theory predictions.

We prove that the natural isomorphism between GF(2^h) and GF(2)^h induces a bijection between stabiliser codes on n quqits with local dimension q=2^h and binary stabiliser codes on hn qubits. This allows us to describe these codes geometrically: a stabiliser code over a field of even order corresponds to a so-called quantum set of symplectic polar spaces. Moreover, equivalent stabiliser codes have a similar geometry, which can be used to prove the uniqueness of a [[4,0,3]]_4 stabiliser code and the nonexistence of both a [[7,1,4]]_4 and an [[8,0,5]]_4 stabiliser code.

In the development of quantum technologies, a reliable means for characterizing quantum devices, be it a measurement device, a state-preparation device, or a transformation device, is crucial. However, the conventional approach based on, for example, quantum state tomography or process tomography relies on assumptions that are often not necessarily justifiable in a realistic experimental setting. While the device-independent approach to this problem gets around the shortcomings above by making only minimal, justifiable assumptions, most of the theoretical proposals to date only work in the idealized setting where independent and identically distributed (i.i.d.) trials are assumed. Here, we provide a versatile solution for rigorous device-independent certification that does not rely on the i.i.d. assumption. Specifically, we describe how the prediction-based-ratio (PBR) protocol and martingale-based protocol developed for hypothesis testing can be applied in the present context to achieve a device-independent certification of desirable properties with confidence interval. To illustrate the versatility of these methods, we demonstrate how we can use them to certify -- with finite data -- the underlying negativity, Hilbert space dimension, entanglement depth, and fidelity to some target pure state. In particular, we give examples showing how the amount of certifiable negativity and fidelity scales with the number of trials. Our results also show that, while the martingale-based protocol is more straightforward to implement, its performance depends strongly on the choice of the Bell function. Intriguingly, a Bell function useful for self-testing does not necessarily give the optimal confidence-gain rate for certifying the fidelity to the corresponding target state.

The quantum approximate optimization algorithm (QAOA) is one of the most promising candidates for achieving quantum advantage through quantum-enhanced combinatorial optimization. Optimal QAOA parameter concentration effects for special MaxCut problem instances have been observed, but a rigorous study of the subject is still lacking. Due to clustering of optimal QAOA parameters for MaxCut, successful parameter transferability between different MaxCut instances can be explained and predicted based on local properties of the graphs, including the type of subgraphs (lightcones) from which graphs are composed as well as the overall degree of nodes in the graph (parity). In this work, we apply five different graph embedding techniques to determine good donor candidates for parameter transferability, including parameter transferability between different classes of MaxCut instances. Using this technique, we effectively reduce the number of iterations required for parameter optimization, obtaining an approximate solution to the target problem with an order of magnitude speedup. This procedure also effectively removes the problem of encountering barren plateaus during the variational optimization of parameters. Additionally, our findings demonstrate that the transferred parameters maintain effectiveness when subjected to noise, supporting their use in real-world quantum applications. This work presents a framework for identifying classes of combinatorial optimization instances for which optimal donor candidates can be predicted such that QAOA can be substantially accelerated under both ideal and noisy conditions.

Alzheimer's disease (AD) is the most prevalent neurodegenerative brain disorder, which results in significant cognitive impairments, especially in the elderly population. Cognitive impairments can manifest as a decline in various mental faculties, such as concentration, memory, and other higher-order cognitive abilities. These deficits can significantly impact an individual's capacity to comprehend information, acquire new knowledge, and communicate effectively. One of the affected activities due to cognitive impairments is handwriting. By analyzing different aspects of handwriting, including pressure, velocity, and spatial organization, researchers can detect subtle alterations that might indicate early-stage cognitive impairments, especially AD. Recently, several classical artificial intelligence (AI) approaches have been proposed for detecting AD in elderly individuals through handwriting analysis. However, advanced AI methods require more computational power as the size of the data increases. Additionally, diagnoses can be influenced by factors such as limited relevant classical vector space and correlations between features. Recent studies have shown that using quantum computing technologies in healthcare can not only address these problems but also accelerate complex data analysis and process large datasets more efficiently. In this study, we introduced a variational quantum classifier with fewer circuit elements to facilitate the early diagnosis of AD in elderly individuals based on handwriting data. We employed ZZFeatureMap for encoding features. To classify AD, a parameterized quantum circuit consisting of repeated Ry and Rz rotation gates, as well as CY and CZ two-qubit entangling gates, was designed and implemented. The proposed model achieved an accuracy of 0.75 in classifying AD.

The electron spin of a nitrogen-vacancy center in diamond lends itself to the control of proximal $^{13}$C nuclear spins via dynamical decoupling methods, possibly combined with radio-frequency driving. Long-lived single-qubit states and high-fidelity electron-nuclear gates required for the realization of a multiqubit register have already been demonstrated. Towards the goal of a scalable architecture, linking multiple such registers in a photonic network represents an important step. Multiple pairs of remotely entangled qubits can enable advanced algorithms or error correction protocols. We investigate how a photonic architecture can be extended from the intrinsic nitrogen spin to multiple $^{13}$C spins per node. Applying decoherence-protected gates sequentially, we simulate the fidelity of creating multiple pairs of remotely entangled qubits. Even though the currently achieved degree of control of $^{13}$C spins might not be sufficient for large-scale devices, the two schemes are compatible in principle. One requirement is the correction of unconditional phases acquired by unaddressed nuclear spins during a decoupling sequence.

Product states, unentangled tensor products of single qubits, are a ubiquitous ansatz in quantum computation, including for state-of-the-art Hamiltonian approximation algorithms. A natural question is whether we should expect to efficiently solve product state problems on any interesting families of Hamiltonians.

We completely classify the complexity of finding minimum-energy product states for Hamiltonians defined by any fixed set of allowed 2-qubit interactions. Our results follow a line of work classifying the complexity of solving Hamiltonian problems and classical constraint satisfaction problems based on the allowed constraints. We prove that estimating the minimum energy of a product state is in P if and only if all allowed interactions are 1-local, and NP-complete otherwise. Equivalently, any family of non-trivial two-body interactions generates Hamiltonians with NP-complete product-state problems. Our hardness constructions only require coupling strengths of constant magnitude.

A crucial component of our proofs is a collection of hardness results for a new variant of the Vector Max-Cut problem, which should be of independent interest. Our definition involves sums of distances rather than squared distances and allows linear stretches.

A corollary of our classification is a new proof that optimizing product states in the Quantum Max-Cut model (the quantum Heisenberg model) is NP-complete.

Genuine multiparty entangled probes lead to minimum error in estimating the phase corresponding to the generator of a unitary encoder, if the generator comprises of only local terms. We ask if genuine multiparty entanglement remains indispensable in attaining the best metrological precision if we employ higher-order interaction terms in the generator. We identify a dichotomy in the answer. Specifically, we find that generators having odd-body interactions necessarily require genuine multipartite entanglement in probes to attain the best metrological precision, but the situation is opposite in the case of generators with even-body interactions. The optimal probes corresponding to generators that contain even-body interaction terms, may be entangled, but certainly not so in all bipartitions, and particularly, for certain ranges of the number of parties including the large number limit, the optimal state is asymmetric. Asymmetry, which therefore is a resource in this scenario rather than genuine multiparty entanglement, refers to the disparity between states of local parts of the global system. Additionally, we provide an upper bound on the number of parties up to which one can always obtain an asymmetric product state that gives the best metrological precision for even-body interactions. En route, we find the quantum Fisher information in closed form for two- and three-body interactions for an arbitrary number of parties, and prove, in both the cases, that when the number of parties is large, the metrological precision is non-optimal if we consider only symmetric product probes. Further, we identify conditions on the local component of the generator, for which these results hold for arbitrary local dimensions.

The common feature of several experiments, performed and proposed, in which particles provide misleading evidence about where they have been, is identified and discussed. It is argued that the experimental results provide a consistent picture when interference amplification effects are taken into account.

We investigate the impact of quantum vibronic coupling on the electronic properties of solid-state spin defects using stochastic methods and first principles molecular dynamics with a quantum thermostat. Focusing on the negatively charged nitrogen-vacancy center in diamond as an exemplary case, we found a significant dynamic Jahn-Teller splitting of the doubly degenerate single-particle levels within the diamond's band gap, even at 0 K, with a magnitude exceeding 180 meV. This pronounced splitting leads to substantial renormalizations of these levels and subsequently, of the vertical excitation energies of the doubly degenerate singlet and triplet excited states. Our findings underscore the pressing need to incorporate quantum vibronic effects in first-principles calculations, particularly when comparing computed vertical excitation energies with experimental data. Our study also reveals the efficiency of stochastic thermal line sampling for studying phonon renormalizations of solid-state spin defects.

The optical properties of a fixed atom are well-known and investigated. For example, the extraordinarily large cross section of a single atom as seen by a resonant photon is essential for quantum optical applications. Mechanical effects associated with light scattering are also well-studied, forming the basis of laser cooling and trapping, for example. Despite this, there is one fundamental problem that surprisingly has not been extensively studied, yet is relevant to a number of emerging quantum optics experiments. In these experiments, the ground state of the atom experiences a tight optical trap formed by far-off-resonant light, to facilitate efficient interactions with near-resonant light. However, the excited state might experience a different potential, or even be anti-trapped. Here, we systematically analyze the effects of unequal trapping on near-resonant atom-light interactions. In particular, we identify regimes where such trapping can lead to significant excess heating, and a reduction of total and elastic scattering cross sections associated with a decreased atom-photon interaction efficiency. Understanding these effects can be valuable for optimizing quantum optics platforms where efficient atom-light interactions on resonance are desired, but achieving equal trapping is not feasible.

We explore the problem of covertly communicating qubits over the lossy thermal-noise bosonic channel, which is a quantum-mechanical model of many practical channels, including optical. Covert communication ensures that an adversary is unable to detect the presence of transmissions, which are concealed in channel noise. We investigate an achievable lower bound on quantum covert communication using photonic dual-rail qubits. This encoding has practical significance, as it has been proposed for long-range repeater-based quantum communication over optical channels.

Sampling a diverse set of high-quality solutions for hard optimization problems is of great practical relevance in many scientific disciplines and applications, such as artificial intelligence and operations research. One of the main open problems is the lack of ergodicity, or mode collapse, for typical stochastic solvers based on Monte Carlo techniques leading to poor generalization or lack of robustness to uncertainties. Currently, there is no universal metric to quantify such performance deficiencies across various solvers. Here, we introduce a new diversity measure for quantifying the number of independent approximate solutions for NP-hard optimization problems. Among others, it allows benchmarking solver performance by a required time-to-diversity (TTD), a generalization of often used time-to-solution (TTS). We illustrate this metric by comparing the sampling power of various quantum annealing strategies. In particular, we show that the inhomogeneous quantum annealing schedules can redistribute and suppress the emergence of topological defects by controlling space-time separated critical fronts, leading to an advantage over standard quantum annealing schedules with respect to both TTS and TTD for finding rare solutions. Using path-integral Monte Carlo simulations for up to 1600 qubits, we demonstrate that nonequilibrium driving of quantum fluctuations, guided by efficient approximate tensor network contractions, can significantly reduce the fraction of hard instances for random frustrated 2D spin-glasses with local fields. Specifically, we observe that by creating a class of algorithmic quantum phase transitions, the diversity of solutions can be enhanced by up to 40% with the fraction of hard-to-sample instances reducing by more than 25%.

Device-independent quantum key distribution (DIQKD) aims to achieve secure key distribution with only minimal assumptions, by basing its security on the violation of Bell inequalities. While this offers strong security guarantees, it comes at the cost of being challenging to implement experimentally. In this thesis, we present security proofs for several techniques that help to improve the keyrates and noise tolerance of DIQKD, such as noisy preprocessing, random key measurements, and advantage distillation. We also show finite-size security proofs for some protocols based on combining several of these techniques. These results and proof techniques should be useful for further development of DIQKD protocols.

Quantum electronics is significantly involved in the development of the field of quantum information processing. In this domain, the growth of Blind Quantum Source Separation and Blind Quantum Process Tomography has led, within the formalism of the Hilbert space, to the introduction of the concept of a Random-Coefficient Pure State, or RCPS: the coefficients of its development in the chosen basis are random variables. This paper first describes an experimental situation necessitating its introduction. While the von Neumann approach to a statistical mixture considers statistical properties of an observable, in the presence of an RCPS one has to manipulate statistical properties of probabilities of measurement outcomes, these probabilities then being themselves random variables. It is recalled that, in the presence of a von Neumann statistical mixture, the consistency of the density operator \r{ho} formalism is based on a postulate. The interest of the RCPS concept is presented in the simple case of a spin 1/2, through two instances. The most frequent use of the \r{ho} formalism by users of quantum mechanics is a motivation for establishing some links between a given RCPS and the language of the density operator formalism, while keeping in mind that the situation described by an RCPS is different from the one which has led to the introduction of \r{ho}. It is established that the Landau - Feynman use of \r{ho} is mobilized in a situation differing from both the von Neumann statistical mixture and the RCPS. It is shown that the use of the higher-order moments of a well-chosen random variable helps solving a problem already identified by Zeh in 1970.

Whether a given target state can be prepared by starting with a simple product state and acting with a finite-depth quantum circuit is a key question in condensed matter physics and quantum information science. It underpins classifications of topological phases, as well as the understanding of topological quantum codes, and has obvious relevance for device implementations. Traditionally, this question assumes that the quantum circuit is made up of unitary gates that are geometrically local. Inspired by the advent of noisy intermediate-scale quantum devices, we reconsider this question with $k$-local gates, i.e. gates that act on no more than $k$ degrees of freedom, but are not restricted to be geometrically local. First, we construct explicit finite-depth circuits of symmetric $k$-local gates which create symmetry-protected topological (SPT) states from an initial a product state. Our construction applies both to SPT states protected by global symmetries and subsystem symmetries, but not to those with higher-form symmetries, which we conjecture remain nontrivial. Next, we show how to implement arbitrary translationally invariant quantum cellular automata (QCA) in any dimension using finite-depth circuits of $k$-local gates. These results imply that the topological classifications of SPT phases and QCA both collapse to a single trivial phase in the presence of $k$-local interactions. We furthermore argue that SPT phases are fragile to generic $k$-local symmetric perturbations. We conclude by discussing the implications for other phases, such as fracton phases, and surveying future directions. Our analysis opens a new experimentally motivated conceptual direction examining the stability of phases and the feasibility of state preparation without the assumption of geometric locality.

NP-hard problems are not believed to be exactly solvable through general polynomial time algorithms. Hybrid quantum-classical algorithms to address such combinatorial problems have been of great interest in the past few years. Such algorithms are heuristic in nature and aim to obtain an approximate solution. Significant improvements in computational time and/or the ability to treat large problems are some of the principal promises of quantum computing in this regard. The hardware, however, is still in its infancy and the current Noisy Intermediate Scale Quantum (NISQ) computers are not able to optimize industrially relevant problems. Moreover, the storage of qubits and introduction of entanglement require extreme physical conditions. An issue with quantum optimization algorithms such as QAOA is that they scale linearly with problem size. In this paper, we build upon a proprietary methodology which scales logarithmically with problem size - opening an avenue for treating optimization problems of unprecedented scale on gate-based quantum computers. In order to test the performance of the algorithm, we first find a way to apply it to a handful of NP-hard problems: Maximum Cut, Minimum Partition, Maximum Clique, Maximum Weighted Independent Set. Subsequently, these algorithms are tested on a quantum simulator with graph sizes of over a hundred nodes and on a real quantum computer up to graph sizes of 256. To our knowledge, these constitute the largest realistic combinatorial optimization problems ever run on a NISQ device, overcoming previous problem sizes by almost tenfold.

Randomness extraction is a key problem in cryptography and theoretical computer science. With the recent rapid development of quantum cryptography, quantum-proof randomness extraction has also been widely studied, addressing the security issues in the presence of a quantum adversary. In contrast with conventional quantum-proof randomness extractors characterizing the input raw data as min-entropy sources, we find that the input raw data generated by a large class of trusted-device quantum random number generators can be characterized as the so-called reverse block source. This fact enables us to design improved extractors. Specifically, we propose two novel quantum-proof randomness extractors for reverse block sources that realize real-time block-wise extraction. In comparison with the general min-entropy randomness extractors, our designs achieve a significantly higher extraction speed and a longer output data length with the same seed length. In addition, they enjoy the property of online algorithms, which process the raw data on the fly without waiting for the entire input raw data to be available. These features make our design an adequate choice for the real-time post-processing of practical quantum random number generators. Applying our extractors to the raw data generated by a widely used quantum random number generator, we achieve a simulated extraction speed as high as $300$ Gbps.

Pseudo-unitary circuits are recurring in both S-matrix theory and analysis of No-Go theorems. We propose a matrix and diagrammatic representation for the operation that maps S-matrices to T-matrices and, consequently, a unitary group to a pseudo-unitary one. We call this operation ``partial inversion'' and show its diagrammatic representation in terms of permutations. We find the expressions for the deformed metrics and deformed dot products that preserve physical constraints after partial inversion. Subsequently, we define a special set that allows for the simplification of expressions containing infinities in matrix inversion. Finally, we propose a renormalized-growth algorithm for the T-matrix as a possible application. The outcomes of our study expand the methodological toolbox needed to build a family of pseudo-unitary and inter-pseudo-unitary circuits with full diagrammatic representation in three dimensions, so that they can be used to exploit pseudo-unitary flexibilization of unitary No-Go Theorems and renormalized circuits of large scattering lattices.