QUROPE Quantum Information Processing and Communication in Europe

With the advancement of quantum computing, the security of public key cryptography is under serious threat. To guarantee security in the quantum era, Quantum Key Distribution has become a competitive solution. QKD networks can be classified into measurement-device-dependent network and measurement-device-independent network. In measurement-device-dependent networks, the information is available for all trusted relays. This means that all trusted relays are strongly trusted relays that require strict control, which is difficult to realize. To address this issue, measurement-device-independent networks reduce the proportion of strongly trusted relay nodes by introducing untrusted relays. However, due to the higher key rate of measurement-device-dependent protocols over short distances, the communication capability of measurement-device-independent networks has a degradation compared to measurement-device-dependent networks. Therefore, how to reduce the dependence of QKD networks on strong trusted relays without significantly affecting the communication capability has become a major issue in the practicalization process of QKD networks. To address this issue, a novel Multi-Protocol Collaborative networking cell is proposed in this paper. The QKD network built by the MPC networking cell reduces the dependence on strongly trusted relays by combining the two protocols to introduce weak trusted relays while maintaining the high communication capacity. What's more, to further enhance the overall performance of the QKD network, an optimal topology design method is presented via the proposed flow-based mathematical model and optimization method. The simulation results show that the proposed scheme reduces the dependence on strongly trusted relays without a significant reduction in communication capability, our work holds great significance in promoting the practicalization of QKD networks.

We study three aspects of work statistics in the context of the fluctuation theorem for the quantum spin chains by numerical methods based on matrix-product states. First, we elaborate that the work done on the spin-chain by a sudden quench can be used to characterize the quantum phase transitions (QPT). We further obtain the numerical results to demonstrate its capability of characterizing the QPT of both Landau-Ginzbrug types, such as the Ising chain, or topological types, such as the Haldane chain. Second, we propose to use the fluctuation theorem, such as Jarzynski's equality, which relates the real-time correlator to the ratio of the thermal partition functions, as a benchmark indicator for the numerical real-time evolving methods. Third, we study the passivity of ground and thermal states of quantum spin chains under some cyclic impulse processes. We show that the passivity of thermal states and ground states under the hermitian actions are ensured by the second laws and variational principles, respectively, and also verify it by numerical calculations. Besides, we also consider the passivity of ground states under non-hermitian actions, for which the variational principle cannot be applied. Despite that, we find no violation of passivity from our numerical results for all the cases considered in both Ising-like and Haldane-like chains.

Non-Hermitian effects have emerged as a new paradigm for the manipulation of phases of matter that profoundly changes our understanding of non-equilibrium systems, introducing novel concepts such as exceptional points and spectral topology, as well as exotic phenomena such as non-Hermitian skin effects (NHSEs). Most existing studies, however, focus on non-Hermitian eigenstates, whereas dynamic properties of non-Hermitian systems have been discussed only very recently, predicting unexpected phenomena such as wave self-healing, chiral Zener tunneling, and the dynamic NHSEs that are not yet confirmed in experiments. Here, we report the first experimental observation of rich non-Hermitian skin dynamics using tunable one-dimensional nonreciprocal double-chain mechanical systems with glide-time symmetry. Remarkably, dynamic NHSEs are observed with various dynamic behaviors in different dynamic phases, revealing the intriguing nature of these phases that can be understood via the generalized Brillouin zone and the related concepts. Moreover, the observed tunable non-Hermitian skin dynamics and amplifications, the bulk unidirectional wave propagation, and the boundary wave trapping provide promising ways to guide, trap, and amplify waves in a controllable and robust way. Our findings unveil the fundamental aspects and open a new pathway toward non-Hermitian dynamics, which will fertilize the study of non-equilibrium phases of matter and give rise to novel applications in information processing.

In the era of extensive data growth, robust and efficient mechanisms are needed to store and manage vast amounts of digital information, such as Data Storage Systems (DSSs). Concurrently, privacy concerns have arisen, leading to the development of techniques like Private Information Retrieval (PIR) to enable data access while preserving privacy. A PIR protocol allows users to retrieve information from a database without revealing the specifics of their query or the data they are accessing.

With the advent of quantum computing, researchers have explored the potential of using quantum systems to enhance privacy in information retrieval. In a Quantum Private Information Retrieval (QPIR) protocol, a user can retrieve information from a database by downloading quantum systems from multiple servers, while ensuring that the servers remain oblivious to the specific information being accessed. This scenario offers a unique advantage by leveraging the inherent properties of quantum systems to provide enhanced privacy guarantees and improved communication rates compared to classical PIR protocols.

In this thesis we consider the QPIR setting where the queries and the coded storage systems are classical, while the responses from the servers are quantum. This problem was treated by Song et al. for replicated storage and different collusion patterns. This thesis aims to develop QPIR protocols for coded storage by combining known classical PIR protocols with quantum communication algorithms, achieving enhanced privacy and communication costs. We consider different storage codes and robustness assumptions, and we prove that the achieved communication cost is always lower than the classical counterparts.

We study the Bisognano-Wichmann Hamiltonian for fractional quantum Hall states defined on a sphere and explore its relationship with the entanglement Hamiltonian associated to the state. We present results for several examples, namely the bosonic Laughlin state stabilized by contact two-body interactions and the bosonic Moore-Read state by either three- or two-body interactions. Our findings demonstrate that the Bisognano-Wichmann Hamiltonian provides a reliable approximation of the entanglement Hamiltonian as a fully-local operator that can be written without any prior knowledge of the specific state under consideration.

While von Neumann entropies for subregions in quantum field theory universally contain ultraviolet divergences, differences between von Neumann entropies are finite and well-defined in many physically relevant scenarios. We demonstrate that such a notion of entropy differences can be rigorously defined in quantum field theory in a general curved spacetime by introducing a novel, covariant regulator for the entropy based on the modular crossed product. This regulator associates a type II von Neumann algebra to each spacetime subregion, resulting in well-defined renormalized entropies. This prescription reproduces formulas for entropy differences that coincide with heuristic formulas widely used in the literature, and we prove that it satisfies desirable properties such as unitary invariance and concavity. As an application, we provide proofs of the Bekenstein bound and the quantum null energy condition, formulated directly in terms of vacuum-subtracted von Neumann entropies.

This paper improves and demonstrates the usefulness of the first quantized plane-wave algorithms for the quantum simulation of electronic structure, developed by Babbush et al. and Su et al. We describe the first quantum algorithm for first quantized simulation that accurately includes pseudopotentials. We focus on the Goedecker-Tetter-Hutter (GTH) pseudopotential, which is among the most accurate and widely used norm-conserving pseudopotentials enabling the removal of core electrons from the simulation. The resultant screened nuclear potential regularizes cusps in the electronic wavefunction so that orders of magnitude fewer plane waves are required for a chemically accurate basis. Despite the complicated form of the GTH pseudopotential, we are able to block encode the associated operator without significantly increasing the overall cost of quantum simulation. This is surprising since simulating the nuclear potential is much simpler without pseudopotentials, yet is still the bottleneck. We also generalize prior methods to enable the simulation of materials with non-cubic unit cells, which requires nontrivial modifications. Finally, we combine these techniques to estimate the block-encoding costs for commercially relevant instances of heterogeneous catalysis (e.g. carbon monoxide adsorption on transition metals) and compare to the quantum resources needed to simulate materials in second quantization. We conclude that for computational cells with many particles, first quantization often requires meaningfully less spacetime volume.

Recent experiments demonstrated quantum computational advantage in random circuit sampling and Gaussian boson sampling. However, it is unclear whether these experiments can lead to practical applications even after considerable research effort. On the other hand, simulating the quantum coherent dynamics of interacting spins has been considered as a potential first useful application of quantum computers, providing a possible quantum advantage. Despite evidence that simulating the dynamics of hundreds of interacting spins is challenging for classical computers, concrete proof is yet to emerge. We address this problem by proving that sampling from the output distribution generated by a wide class of quantum spin Hamiltonians is a hard problem for classical computers. Our proof is based on the Taylor series of the output probability, which contains the permanent of a matrix as a coefficient when bipartite spin interactions are considered. We devise a classical algorithm that extracts the coefficient using an oracle estimating the output probability. Since calculating the permanent is #P-hard, such an oracle does not exist unless the polynomial hierarchy collapses. With an anticoncentration conjecture, the hardness of the sampling task is also proven. Based on our proof, we estimate that an instance involving about 200 spins will be challenging for classical devices but feasible for intermediate-scale quantum computers with fault-tolerant qubits.

One dimensional confinement in waveguide Quantum Electrodynamics (QED) plays a crucial role to enhance light-matter interactions and to induce a strong quantum nonlinear optical response. In two or higher dimensional settings, this response is reduced since photons can be emitted within a larger phase space, opening the question whether strong photon-photon interaction can be still achieved. In this study, we positively answer this question for the case of a 2D square array of atoms coupled to the light confined into a two-dimensional waveguide. More specifically, we demonstrate the occurrence of long-lived two-photon repulsive and bound states with genuine 2D features. Furthermore, we observe signatures of these effects also in free-space atomic arrays in the form of weakly-subradiant in-band scattering resonances. Our findings provide a paradigmatic signature of the presence of strong photon-photon interactions in 2D waveguide QED.

Predicting and analyzing global behaviour of complex systems is challenging due to the intricate nature of their component interactions. Recent work has started modelling complex systems using networks endowed with multiway interactions among nodes, known as higher-order networks. In this context, simplicial complexes are a class of higher-order networks that have received significant attention due to their topological structure and connections to Hodge theory. Topological signal processing utilizes these connections to analyze and manipulate signals defined on non-Euclidean domains such as simplicial complexes. In this work, we present a general quantum algorithm for implementing filtering processes in TSP and describe its application to extracting network data based on the Hodge decomposition. We leverage pre-existing tools introduced in recent quantum algorithms for topological data analysis and combine them with spectral filtering techniques using the quantum singular value transformation framework. While this paper serves as a proof-of-concept, we obtain a super-polynomial improvement over the best known classical algorithms for TSP filtering processes, modulo some important caveats about encoding and retrieving the data from a quantum state. The proposed algorithm generalizes the applicability of tools from quantum topological data analysis to novel applications in analyzing high-dimensional complex systems.

Phase estimation plays a central role in communications, sensing, and information processing. Quantum correlated states, such as squeezed states, enable phase estimation beyond the shot-noise limit, and in principle approach the ultimate quantum limit in precision, when paired with optimal quantum measurements. However, physical realizations of optimal quantum measurements for optical phase estimation with quantum correlated states are still unknown. Here we address this problem by introducing an adaptive Gaussian measurement strategy for optical phase estimation with squeezed vacuum states that, by construction, approaches the quantum limit in precision. This strategy builds from a comprehensive set of locally optimal POVMs through rotations and homodyne measurements and uses the Adaptive Quantum State Estimation framework for optimizing the adaptive measurement process, which, under certain regularity conditions, guarantees asymptotic optimality for this quantum parameter estimation problem. As a result, the adaptive phase estimation strategy based on locally-optimal homodyne measurements achieves the quantum limit within the phase interval of $[0, \pi/2)$. Furthermore, we generalize this strategy by including heterodyne measurements, enabling phase estimation across the full range of phases from $[0, \pi)$, where squeezed vacuum allows for unambiguous phase encoding. Remarkably, for this phase interval, which is the maximum range of phases that can be encoded in squeezed vacuum, this estimation strategy maintains an asymptotic quantum-optimal performance, representing a significant advancement in quantum metrology.

The solution of linear systems of equations is the basis of many other quantum algorithms, and recent results provided an algorithm with optimal scaling in both the condition number $\kappa$ and the allowable error $\epsilon$ [PRX Quantum \textbf{3}, 0403003 (2022)]. That work was based on the discrete adiabatic theorem, and worked out an explicit constant factor for an upper bound on the complexity. Here we show via numerical testing on random matrices that the constant factor is in practice about 1,500 times smaller than the upper bound found numerically in the previous results. That means that this approach is far more efficient than might naively be expected from the upper bound. In particular, it is over an order of magnitude more efficient than using a randomised approach from [arXiv:2305.11352] that claimed to be more efficient.

Hybrid quantum-classical approaches offer potential solutions for quantum chemistry problems, but they also introduce challenges such as the barren plateau and the exactness of the ansatze. These challenges often manifest as constrained optimization problems without a guarantee of identifying global minima. In this work, we highlight the interconnection between constrained optimization and generalized eigenvalue problems, using a unique class of non-orthogonal and overcomplete basis sets generated by Givens rotation-type canonical transformations on a reference state. Employing the generator coordinate approach, we represent the wave function in terms of these basis sets. The ensuing generalized eigenvalue problem yields rigorous lower bounds on energy, outperforming the conventional variational quantum eigensolver (VQE) that employs the same canonical transformations in its ansatze. Our approach effectively tackles the barren plateau issue and the heuristic nature of numerical minimizers in the standard VQE, making it ideal for intricate quantum chemical challenges. For real-world applications, we propose an adaptive scheme for selecting these transformations, emphasizing the linear expansion of the non-orthogonal basis sets. This ensures a harmonious balance between accuracy and efficiency in hybrid quantum-classical simulations. Our analysis and suggested methodology further broaden the applications of quantum computing in quantum chemistry. Notably, they pave the way for alternative strategies in excited state computation and Hamiltonian downfolding, laying the groundwork for sophisticated quantum simulations in chemistry.

Attempts to create quantum degenerate gases without evaporative cooling have been pursued since the early days of laser cooling, with the consensus that polarization gradient cooling (PGC, also known as "optical molasses") alone cannot reach condensation. In the present work, we report that simple PGC can generate a small Bose-Einstein condensate (BEC) inside a corrugated micrometer-sized optical dipole trap. The experimental parameters enabling BEC creation were found by machine learning, which increased the atom number by a factor of 5 and decreased the temperature by a factor of 2.5, corresponding to almost two orders of magnitude gain in phase space density. When the trapping light is slightly misaligned through a microscopic objective lens, a BEC of $\sim 250$ $^{87}$Rb atoms is formed inside a local dimple within 40 ms of PGC.

In the QBist approach to quantum mechanics, a measurement is an action an agent takes on the world external to herself. A measurement device is an extension of the agent and both measurement outcomes and their probabilities are personal to the agent. According to QBism, nothing in the quantum formalism implies either that the quantum state assignments of two agents or their respective measurement outcomes need to be mutually consistent. Recently, Khrennikov has claimed that QBism's personalist theory of quantum measurement is invalidated by Ozawa's so-called intersubjectivity theorem. Here, following Stacey, we refute Khrennikov's claim by showing that it is not Ozawa's mathematical theorem but an additional assumption made by Khrennikov that QBism is incompatible with. We then address the question of intersubjective agreement in QBism more generally. Even though there is never a necessity for two agents to agree on their respective measurement outcomes, a QBist agent can strive to create conditions under which she would expect another agent's reported measurement outcome to agree with hers. It turns out that the assumptions of Ozawa's theorem provide an example for just such a condition.

As it is well known, split Cayley hexagons of order two live in the three-qubit symplectic polar space in two non-isomorphic embeddings, called classical and skew. Although neither of the two embeddings yields observable-based contextual configurations of their own, {\it classically}-embedded copies are found to fully rule contextuality properties of the most prominent three-qubit contextual configurations in the following sense: each set of unsatisfiable contexts of such a contextual configuration is isomorphic to the set of lines that certain classically-embedded hexagon shares with this particular configuration. In particular, for a doily this shared set comprises three pairwise disjoint lines belonging to a grid of the doily, for an elliptic quadric the corresponding set features nine mutually disjoint lines forming a (Desarguesian) spread on the quadric, for a hyperbolic quadric the set entails 21 lines that are in bijection with the edges of the Heawood graph and, finally, for the configuration that consists of all the 315 contexts of the space its 63 unsatisfiable ones cover an entire hexagon. A particular illustration of this encoding is provided by the {\it line-complement} of a skew-embedded hexagon; its 24 unsatisfiable contexts correspond exactly to those 24 lines in which a particular classical copy of the hexagon differs from the considered skew-embedded one. In connection with the last-mentioned case we also conducted some experimental tests on a Noisy Intermediate Scale Quantum (NISQ) computer to validate our theoretical findings.

Radio signal classification plays a pivotal role in identifying the modulation scheme used in received radio signals, which is essential for demodulation and proper interpretation of the transmitted information. Researchers have underscored the high susceptibility of ML algorithms for radio signal classification to adversarial attacks. Such vulnerability could result in severe consequences, including misinterpretation of critical messages, interception of classified information, or disruption of communication channels. Recent advancements in quantum computing have revolutionized theories and implementations of computation, bringing the unprecedented development of Quantum Machine Learning (QML). It is shown that quantum variational classifiers (QVCs) provide notably enhanced robustness against classical adversarial attacks in image classification. However, no research has yet explored whether QML can similarly mitigate adversarial threats in the context of radio signal classification. This work applies QVCs to radio signal classification and studies their robustness to various adversarial attacks. We also propose the novel application of the approximate amplitude encoding (AAE) technique to encode radio signal data efficiently. Our extensive simulation results present that attacks generated on QVCs transfer well to CNN models, indicating that these adversarial examples can fool neural networks that they are not explicitly designed to attack. However, the converse is not true. QVCs primarily resist the attacks generated on CNNs. Overall, with comprehensive simulations, our results shed new light on the growing field of QML by bridging knowledge gaps in QAML in radio signal classification and uncovering the advantages of applying QML methods in practical applications.

Thought experiments are where logical reasoning meets storytelling, catalysing progress in quantum science and technology. Schr\"odinger's famous cat brought quantum science to the public consciousness, while Deutsch's thought experiment to test the many-worlds and Copenhagen interpretations involved the first conception of a quantum computer. I will show how presenting thought experiments using quantum circuits can demystify apparent quantum paradoxes, and provide fun, conceptually important activities for learners to implement themselves on near-term quantum devices. Additionally, I will explain how thought experiments can be used as a first introduction to quantum, and outline a workshop based on the "quantum bomb tester" for school students as young as 11. This paper draws upon my experience in developing and delivering quantum computing workshops in Oxford, and in creating a quantum paradoxes content series with IBM Quantum of videos, blogs and code tutorials.

Quantum sensing utilizing unique quantum properties of non-Hermitian systems to realize ultra-precision measurements has been attracting increasing attention. However, the debate on whether non-Hermitian systems are superior to Hermitian counterparts in sensing remains an open question. Here, we investigate the quantum information in PT-symmetric quantum sensing utilizing two experimental schemes based on the trapped-ion platform. It turns out that the existence of advantages of non-Hermitian quantum sensing heavily depends on additional information resources carried by the extra degrees of freedom introduced to construct PT-symmetric quantum sensors. Moreover, the practical application of non-Hermitian quantum sensing with superior performance is primarily restricted by the additional resource consumption accompanied by the post-selection. Our study provides theoretical references for the construction of non-Hermitian quantum sensors with superior performance and has potential applications in research fields of quantum precision measurement and quantum information processing.

We report the quantum computing of reacting flows by simulating the Hamiltonian dynamics. The scalar transport equation for reacting flows is transformed into a Hamiltonian system, mapping the dissipative and non-Hermitian problem in physical space to a Hermitian one in a higher-dimensional space. Using this approach, we develop the quantum spectral and finite difference methods for simulating reacting flows in periodic and general conditions, respectively. The present quantum computing algorithms offer a ``one-shot'' solution for a given time without temporal discretization, avoiding iterative quantum state preparation and measurement. We compare computational complexities of the quantum and classical algorithms. The quantum spectral method exhibits exponential acceleration relative to its classical counterpart, and the quantum finite difference method can achieve exponential speedup in high-dimensional problems. The quantum algorithms are validated on quantum computing simulators with the Qiskit package. The validation cases cover one- and two-dimensional reacting flows with a linear source term and periodic or inlet-outlet boundary conditions. The results obtained from the quantum spectral and finite difference methods agree with analytical and classical simulation results. They accurately capture the convection, diffusion, and reaction processes. This demonstrates the potential of quantum computing as an efficient tool for the simulation of reactive flows in combustion.