The Riemann Hypothesis (RH), one of the most profound unsolved problems in mathematics, concerns the nontrivial zeros of the Riemann zeta function. Linking these zeros to physical phenomena offers new perspectives on their origin and verification. Here we establish a direct correspondence between these zeros and dynamical quantum phase transitions in two complementary engineered quantum many-body systems, characterized by the average accumulated phase factor and the Loschmidt amplitude, respectively. This precise correspondence recasts the RH as the occurrence of phase transitions at a unique temperature and identifies it as a previously unknown transition mechanism. We demonstrate this correspondence in a proof-of-principle experiment on a quantum processor. Moreover, we propose a quantum computational framework that implements both systems with polynomial resources, suggesting quantum advantage in probing the hypothesis. Our work bridges nonequilibrium quantum dynamics and number theory, positioning quantum computing as a powerful platform for exploring mathematical conjectures, phase transitions and beyond.

Anomalous topological Bloch oscillations under non-Abelian gauge fields

Quantum computing is emerging as a promising tool for astrophysics and cosmology, with the potential to address computationally intensive problems more efficiently than classical approaches. In this review, we report recent advances from the INAF Spoke-10 initiative within the Italian National Research Center for High Performance Computing, Big Data and Quantum Computing (ICSC), focused on quantum algorithms and machine learning techniques for astronomical data analysis. We concentrate on two application areas: (1) quantum machine learning for high-energy transients, specifically the detection of Gamma-Ray Bursts (GRBs) with quantum deep-learning models; and (2) quantum algorithms for cosmology, including Quantum Markov Chain Monte Carlo and Quantum Genetic Algorithms, together with developments of Quantum Fourier Transform methods. Quantum machine learning models for GRB detection, such as autoencoders, are tested on simulated space telescope data, achieving performance comparable to classical deep learning methods and indicating potential benefits in data-limited or constrained scenarios. For cosmology, hybrid quantum–classical algorithms have been developed to determine best-fit parameters, sample posterior distributions for standard cosmological models, and perform Quantum Fast Fourier transforms for the Cosmic Microwave Background (CMB) radiation. These methods are validated on benchmark problems, providing results consistent with established classical methods. We discuss the implications for astrophysical and cosmological analysis. While the field is still in its early stages and no quantum advantage has yet been demonstrated in the presented problems, the progress summarized here highlights both the current capabilities of Noisy Intermediate-Scale Quantum (NISQ) devices and the open challenges. For quantum machine learning, we demonstrated that these algorithms are more effective when data is scarce or highly complex, which might hint at future quantum advantages. We outline future directions for integrating quantum processors into astronomical pipelines and the steps required to realize practical quantum advantages in data-intensive astrophysics and cosmology.

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The pursuit of nanoscale light manipulation represents a fundamental challenge in nanophotonics, where overcoming the diffraction limit is essential for developing next-generation optoelectronic devices. Polariton boundary engineering has emerged as a transformative approach that enables unprecedented control over light confinement and propagation at subwavelength scales. However, the field currently lacks a systematic framework to integrate the diverse manifestations of boundary effects across different material systems and polariton types. This comprehensive review addresses this critical gap by providing a unified perspective on how engineered interfaces-including edges, heterojunctions, and metallic structures-govern polariton behaviors such as focusing, stealth transmission, and negative refraction. The analysis encompasses seminal work on van der Waals materials (h-BN, α-MoO3) and phase-change compounds, showcasing advanced devices ranging from hyperbolic nanoresonators to reconfigurable waveguides and super-resolution lenses. By examining the synergy between boundary geometry and material properties alongside advanced nanofabrication techniques, this review not only catalogs state-of-the-art achievements but also establishes design principles for dynamic boundaries using stimuli-responsive materials and machine-learning-driven inverse design. This synthesis provides both a foundational framework for researchers and a roadmap toward developing programmable photonic circuits and multifunctional optical platforms for quantum information technology applications.

Owing to the possession of naturally formed quantum wells with strong spatial and dielectric confinements, 2D lead-halide perovskites are attracting intensive research interest in the context of potential applications in classical optoelectronic devices. Here we have synthesized a 2D (PEA)2PbI4 perovskite microplate and observed at ∼3 K that it can emit single photons from the abundant ultranarrow peaks appearing in the photoluminescence spectrum. This signifies the formation of 0D quantum emitters within the otherwise homogeneous 2D energy landscape, which can be attributed to the thickness fluctuations induced by octahedral tiltings across an inorganic sheet. These findings mark the emergence of a hybrid type of quantum emitters with both 0D and 2D confinements, thus extending the fundamental and practical studies of 2D perovskites to the prospective regime of quantum information technologies.

Controlling excited-state relaxation processes is important in a variety of photochemical and photophysical processes, including the generation of ground- and excited-state spin polarization for quantum information science applications. Here, we address how specific static distortions, based on vibrational spin-orbit active modes at C2v symmetry determined by group theory, in a series of low-symmetry ligand-to-ligand charge transfer complexes enable direct spin-orbit coupling contributions to T1 → S0 excited-state decay. These results are used to address spin-vibronic coupling contributions to T1 → S0 decay in a high-symmetry (tBu2bpy)Pt(S,S) (tBu2bpy = 4,4'-di-tert-butyl-2,2'-bipyridine and S,S = benzene-1,2-dithiolate) ligand-to-ligand charge transfer complex with effective C2v symmetry, where T1 relaxation is both spin- and orbitally forbidden due to the direct spin-orbit coupling matrix element being zero by symmetry. Low-frequency vibrations that involve a pyridine-pyridine twisting motion within the bpy ligand generate large ∂⟨S0|HSO|T1⟩/∂Qi values that will contribute significantly to T1 → S0 relaxation. The work advances ligand design strategies for the generation of tailored T1 → S0 relaxation rates, which can be utilized to optimize the generation of electron spin polarization and excited state decay processes in radical-elaborated ligand-to-ligand charge transfer complexes.

Diazirines and diazo compounds are widely employed as photoreactive precursors for generating carbenes, key intermediates in chemical biology and materials science. However, computationally modeling their reaction pathways remains challenging due to the need for large active spaces and the requirement to accurately capture excited-state surfaces along with transition states and conical intersections. In this work, we utilize a hybrid quantum-classical workflow for investigating carbene formation in representative diazirine-diazomethane systems. Our approach leverages Sample-based Quantum Diagonalization (SQD) and its extended variant, Extended Sample-based Quantum Diagonalization (Ext-SQD), for ground- and excited-state analysis, combined with classical tools for geometry optimization, active-space selection, and diagnostic evaluation. Quantum computations were carried out on superconducting quantum processors, and results for both aliphatic and aryl-substituted diazirine-diazomethane pairs were benchmarked against established classical methods, including density functional theory (DFT), coupled cluster with singles and doubles (CCSD), complete active space configuration interaction (CASCI), and selected configuration interaction (SCI). SQD achieves accuracy surpassing the chemical accuracy threshold for nearly all stationary points on the potential energy surface of parent diazirine relative to the CASCI(12,10) reference, and remains close to chemical accuracy for phenyl-substituted diazirine in a (30,30) active space, with an average deviation of 1.1 kcal/mol relative to the SCI benchmark. SQD closely follows CASCI and SCI trends, showing consistent agreement. The findings demonstrate the promise of quantum computing frameworks in modeling photochemical transformations of electronically complex and pharmacologically relevant molecules.

In this study, we introduce a method for deriving exact master equations from the dynamical map for finite open quantum systems coupled to (in)finite reservoirs, using the principle of minimal dissipation. The exact dynamics of the central spin model, which models a finite-bath open quantum system, is developed for two interaction types: Heisenberg and stochastic pure-dephasing interactions. The Heisenberg interaction yields a novel phase-covariant quantum channel in the strong-coupling regime, offering a new platform for studying a range of quantum information protocols. The stochastic pure-dephasing interaction provides the microscopic derivation of the paradigmatic non-Markovian random telegraph noise (RTN) channel, establishing its quantum foundation and offering insight into stochastic couplings. We derive the closed-form master equations for both models. As a demonstration, we explore the thermodynamic performance of these systems as quantum batteries. A direct relationship between quantum heat current and charging power is revealed, and RTN quantum batteries are shown to have advantages in charge storage.

We present an experimentally feasible implementation of a secure multiparty computation application enabled by quantum oblivious transfer (QOT) on an entanglement-based physical layer. The QOT protocol uses polarization-encoded entangled states to share oblivious keys between two parties with quantum key distribution (QKD) providing authentication. Our system integrates the post-processing for QOT and QKD, both sharing a single physical layer, ensuring efficient key generation and authentication, respectively. Authentication involves hashing messages into a cryptographic context, verifying tags, and replenishing keys. This process uses a parallel QKD pipeline specifically for authentication, not for secure key generation. Oblivious keys are generated over a distance up to 25.8 km with a channel loss of 8.47 dB. In a back-to-back setup, a QOT rate of [Formula: see text] OTs/second is achieved, corresponding to 1 minute and 53 seconds per OT, primarily limited by the entanglement source. Using pre-distributed oblivious keys improved the rate to 0.11 OTs/second, or 9.1 seconds per OT. The considered QOT protocol is statistically correct, computationally secure for an honest receiver, and statistically secure for an honest sender, assuming a computationally hiding, statistically binding commitment. An experimentally feasible use case is demonstrated for privacy-preserving fingerprint matching against no-fly lists for border control. The fingerprint is secret-shared across two sites, ensuring security, while the matching is performed using the MASCOT protocol, supported by QOT. The application required 128 1-out-of-2 OTs, each with message length of 128 bits, with the highest security achieved in 20 minutes and 39 seconds. This work demonstrates the feasibility of QOT in secure quantum communication applications.

Strong coupling between molecular excitations and quantized electromagnetic fields in optical cavities provides a powerful means to control the physical and chemical properties of molecular systems. Here, we study electron transfer (ET) dynamics in cavity-coupled molecules using the numerically exact hierarchical equations of motion method, which captures nonperturbative and non-Markovian effects beyond standard perturbative theories. We identify distinct resonance and collective effects associated with polariton formation and show that the ET rate saturates in the strong-coupling regime, a feature not captured by perturbative approaches. We further extend the cavity-modified ET model by incorporating the nuclear-coordinate dependence of molecular electric dipole moments, which gives rise to a three-body interaction involving molecular electronic and vibrational degrees of freedom and cavity photons. This vibronic polariton formation leads to non-monotonic, oscillatory dependencies of the ET rate on the light-matter coupling strength and cavity frequency, which we attribute to quantum interference among multiple transfer pathways. These findings establish cavity-modified electron transfer as a multichannel quantum process governed by the interplay of electronic, vibrational, and photonic degrees of freedom.

High-performance chiral optical devices capable of active all-optical modulation are indispensable for the emerging quantum information processing and spin-encoded photonic logic. However, realizing such devices is constrained by back-scattering noise and the fundamental trade-off between optical chirality and quality (Q) factors inherent in traditional metasurfaces. Here, we overcome these limitations by demonstrating a rationally engineered silicon metasurface that supports high-Q quasi-bound states in the continuum (q-BIC) featuring near-unity transparent chirality. We simultaneously achieve giant transparent chirality (CD co ≈ 1.00 and CD cross ≈ −1.00) and a high Q-factor (Q ≈ 6.7 × 10 5 ) by leveraging an efficient polarization-conversion mechanism. Furthermore, we demonstrate low-threshold (I on ≈ 1.5 kW/cm 2 ) and high-modulation-depth (ΔT ≈ 80%) Kerr optical bistability in the telecommunication C-band (~1551 nm) based on the high-Q chiral q-BIC resonance. These bistable chiroptical responses enable reconfigurable spin-encoded logic gates and an all-optical spin latch exhibiting near-unity modulation contrast (𝛥CD co ≈ 0.97). This work establishes a novel platform for generating high-Q resonances with giant, lossless transparent chirality, offering a new paradigm for low-threshold, high-contrast all-optical quantum photonic devices.

This study examines the dynamics of quantumness in two-flavor neutrino oscillations in the presence of a dephasing channel, using representative oscillation parameters from the KamLAND, MINOS, and Daya Bay experiments. We analyze three complementary quantum-correlation measures-entanglement of formation (EOF), quantum discord (QD), and local quantum uncertainty (LQU)-within an effective two-qubit description. In the unitary case, all three measures display oscillatory behavior controlled by flavor mixing, and the relevant mixing angle strongly shapes their amplitudes. MINOS exhibits the largest correlations because [Formula: see text] is close to maximal, KamLAND shows intermediate values associated with the solar sector, and Daya Bay yields smaller correlations due to the relatively small value of [Formula: see text]. Under dephasing, the off-diagonal coherence terms are suppressed, and the three quantifiers decrease accordingly, while QD remains non-zero in regimes where entanglement is weak. For pure states, LQU satisfies [Formula: see text] and therefore tracks entanglement monotonically, whereas QD provides a broader witness of non-classical correlations. These results provide a compact quantum information description of two-flavor neutrino oscillations in both the coherent and dephased regimes. We also quantify the sensitivity of these observables to oscillation and decoherence parameters, showing that their main added value relative to flavor probabilities is their direct response to off-diagonal coherence loss.

A material system with strong and broadband optical second-order nonlinearity in the near-infrared is theoretically and experimentally demonstrated. Multiple units of TiN-based coupled metallic quantum wells with slightly shifted nonlinear response peaks are uniquely designed and epitaxially grown to form a multilayered stack. By measuring near-infrared to visible second-harmonic generation, second-order susceptibility χ(2) reaches 740 pm V-1 at 900 nm and spreads 200 nm, covering the wavelength range from 800 nm to 1000 nm. Our discoveries open up the possibility to create materials with tailored optical nonlinearity, which can be valuable for building nonlinear optical devices in the fields of bioimaging, ultrafast light source generation, and quantum information technologies.

The electromagnetic response of materials serves as the foundation for a broad range of vital applications, from imaging, to sensing, to classical and quantum communications. Here we demonstrate, theoretically and experimentally, a fundamentally new regime of electromagnetic material response originating from inherent material nonlocality. We show that by structuring materials on the intrinsic scale of this nonlocal response, it becomes possible to alter the electromagnetics of the composite, revealing the inherent nonlocal behavior of the constituent components. These intrinsically nonlocal metamaterials exhibit strong intrinsic (as opposed to effective) nonlocality, easily detectable at room temperatures, in realistic (lossy), macroscopic materials. Intrinsically nonlocal metamaterials open a new design space for electromagnetic composites, beyond photonic crystals, metasurfaces, and effective medium composites. This allows the control of electromagnetic fields at a deep subwavelength scale, revealing a new dimension for control of light-matter interactions.

The scalability of quantum photonic integrated circuits opens the path towards large-scale quantum computing and communication. To date, this scalability has been limited by the stochastic nature of the quantum light sources. Moreover, hybrid integration of different platforms will likely be necessary to combine state-of-the-art devices into a functioning architecture. Here, we demonstrate the active alignment and edge-coupling of arrays of ten site-controlled gallium arsenide quantum dots to an array of ten silicon nitride single-mode waveguides, at cryogenic temperatures. The coupling is facilitated by the fabrication of nanopillars, deterministically self-aligned around each quantum dot, leading to a high-yield and regular array of single-photon sources. An on-chip beamsplitter verifies the triggered emission of single photons into the silicon nitride chip. The low inhomogeneous broadening of the ensemble enables us to observe the spectral overlap of adjacent site-controlled emitters, and we show that it is possible to tune these into sub-picometre alignment using additional laser. Across the array of waveguides, the signal collected from each coupled quantum dot is consistently and reproducibly 0.17 relative to the free-space collection from the very same single-photon source. Comparing measurement with waveguide simulations, we infer that absolute coupling efficiencies of ≈5% are currently obtained between our quantum dots and the waveguides. Paths to improve this coupling value are discussed.

Controlling molecular spin states is essential for organic electronics, yet achieving high-spin (triplet or higher) ground states in Kekulé-type π-conjugated systems remains a challenge. Achieving high-spin ground states in π-conjugated systems has traditionally relied on two established strategies: implementing specific molecular topologies to create nondisjoint frontier orbitals, or taking advantage of high molecular symmetry (Cn, 3 ≤ n) to induce orbital degeneracy. Consequently, Kekulé-type molecules are overwhelmingly singlet species in their ground state. Here, we report the design and synthesis of o-BenD, a 16π-electron Kekulé-type diradical bridged by an ortho-phenylene unit. Despite lacking conventional structural prerequisites, o-BenD exhibits a robust triplet ground state with strong ferromagnetic coupling (J/kB = +320 K). This magnetism originates from pseudodegeneracy of the frontier orbitals, controlled by a simple "frontier-orbital engineering" approach guided by topological charge stabilization. This mechanism bypasses topology-based spin-state prediction, providing a new conceptual framework for stabilizing high-spin states. Furthermore, we demonstrated that o-BenD exhibits ground-state Baird aromaticity, the aromaticity of [4n]π-systems in the lowest triplet state, due to the unique combination of the ground triplet nature and 16π-Kekulé-type conjugation system. While Baird aromaticity is typically restricted to short-lived photoexcited states, this work provides a molecular design to favor the Baird aromatic state over the Hückel antiaromatic singlet state. The realization of such a previously unanticipated electronic state expands the accessible chemical space for the development of organic spintronics and quantum information technologies.

Digital cameras1 and displays2 use picture elements (pixels3) that perform a single function: detecting or emitting light intensity. To exploit the full information content of electromagnetic waves, more advanced elements are required. This has driven the development of multifunctional components that, for example, simultaneously detect and emit intensity4,5 or extract intensity and spectral information6-8. However, no pixel exists that both senses and generates optical wavefronts with full control over amplitude, phase and polarization, limiting bidirectional control and feedback of sophisticated light fields. Here we present a route to such pixels by demonstrating aversatile platform of miniaturized diffractive elements based on Fourier optics9. We use plasmonic surface waves10, which propagate coherently11 and efficiently12-15 across metallic surfaces. When these plasmons are launched towards wavy microstructures16 designed with simple Fourier analysis, arbitrary and background-free optical wavefronts are generated. Conversely, incoming light can be sensed, and its amplitude, phase and polarization can be fully characterized. By combining or superposing several such components, we create multifunctional 'Fourier pixels' that provide compact and accurate control over the optical field. Our approach, which we extend to photonic waveguide modes, establishes a scalable, universal architecture for vectorially programmable pixels with applications in adaptive optics17,18, holographic displays19-21, optical communication22,23 and quantum information processing24.

Solid-state spins are promising as interfaces from stationary qubits to single photons for quantum communication technologies. Semiconductor quantum dots have excellent optical coherence, exhibit near-unity collection efficiencies when coupled to photonic structures, and possess long-lived spins for quantum memory. However, the incompatibility of performing optical spin control and single-shot readout simultaneously has been a challenge faced by almost all solid-state emitters. To overcome this, we leverage light-hole mixing to realize a highly asymmetric lambda system in a negatively charged heavy-hole exciton in Faraday configuration. By compensating GHz-scale differential Stark shifts, induced by unequal coupling to Raman control fields, and by performing nuclear-spin cooling, we achieve quantum control of an electron-spin qubit with a π-pulse contrast of 97.4% while preserving spin-selective optical transitions with a cyclicity of 471 (50). We demonstrate this scheme for both GaAs and InGaAs quantum dots, and show that it is compatible with the operation of a nuclear quantum memory. Our approach thus enables repeated emission of indistinguishable photons together with qubit control, as required for single-shot readout, photonic cluster-state generation, and quantum repeater technologies.

Contextuality, incompatibility, and intra-system entanglement of mental markers: From cognition and decision making to medicine.