Papers

We compute the capacity of entanglement in two dimensional dilaton gravity in a setting where Hawking radiation, backreaction, and islands can be treated analytically. Our focus is the eternal black hole of the Russo Susskind Thorlacius model coupled to N conformal matter fields. Unlike previous gravitational computations, which were mostly carried out in JT gravity, the RST model forces one to deal with a genuinely dynamical conformal factor and with the global constraints of the replica construction. The main technical step is therefore to solve the replica deformation on the orbifold globally at first order near n=1, including the homogeneous sector fixed by single valuedness and by the requirement of a fixed microcanonical state. For a single interval we obtain a time independent generalized capacity, parallel to the generalized entropy. For two intervals, even in the late time factorization regime, the global solution generates an interaction term between replica fixed points; after Lorentzian continuation this produces a time dependent capacity on the two QES saddle, despite the corresponding entropy plateau. We discuss the regime of validity of the resulting expressions and explain how the large size of the two QES capacity implies a highly non uniform saddle competition near n=1, providing a concrete mechanism for sharp features of the capacity at the Page transition.

Excitation energy transfer in light-harvesting aggregates is highly efficient, yet whether quantum coherence plays an operational role in transport remains debated. A central challenge is that coherence is usually inferred from spectroscopic signatures, whereas transport performance is assessed through specific observables and depends on both the open system dynamics and the initial state preparation. Here we develop a resource theoretic approach that quantifies the maximum change that initial site-basis coherence can induce in a chosen readout under fixed reduced dynamics. The central quantity is the resource impact functional, which yields state independent, readout specific bounds on coherence-induced changes in signals and transport figures of merit. We apply the framework to two models. For a donor-acceptor dimer, we analyse coherence sensitivity across coupling and bath-timescale regimes and bound trapping efficiency and average transfer time in terms of the impact functional. For a multi-site chain with terminal trapping, we derive rigorous criteria that distinguish population placement from sensitivity to initial state site-basis coherence. These include upper bounds on the largest advantage over incoherent preparations, necessary delocalization requirements for achieving a prescribed improvement, and a simple pairwise sufficient condition that can be checked from local information. For quasi-local reduced dynamics, we further obtain a Lieb-Robinson-type bound that constrains when coherence prepared in a distant region can influence a localized readout at finite times. Together, these results provide operational diagnostics and rigorous bounds for benchmarking coherence effects and for identifying regimes in which they are necessarily negligible or potentially relevant in excitonic transport models.

Achieving decoherence-free quantum state manipulation is a paramount goal in modern quantum technologies. To this end, we demonstrate its implementation in a two-dimensional dissipative photonic graphene featuring exceptional rings. Employing the resolvent method, we analytically explore the quantum dynamics of emitters coupled to photonic graphene. In the thermodynamic limit, our analysis predicts a dissipation-dependent logarithmic relaxation for a single quantum emitter, alongside a pronounced quantum Zeno effect that slows the decay with increased dissipation. Notably, within a finite lattice, the excitation of single quantum emitter stabilizes in a decoherence-protected quantum state, which is identified as a dissipation-robust quasilocalized state. Interestingly, this state, together with a dark state, facilitates decoherence-free interactions between quantum emitters. This capability can be extended to topological graphenic platforms, where edge states mediate analogous protected interactions among giant atoms. Our findings highlight a promising path toward protecting quantum coherence in practical, high-dimensional photonic environment through dissipation engineering.

Non-Gaussian quantum states and operations are essential tools for multiple quantum information protocols exploiting light as information career. In this context, a key role is played by schemes operating with continuous wave light, in which non-Gaussian states are obtained by photon subtraction/addition and eventually reconstructed by quantum state tomography. In these configurations, the temporal resolution of the homodyne detection and the digital data processing critically affect our ability to faithfully reconstruct the produced non-Gaussian states. In this work, we apply digital data processing to experimental data to study how the temporal performances of the detection chain affect the acquisition and treatment of tomographic data. This allows understanding how these features impact the quality of quantum states observed by non-ideal detection chains. By doing so, we discuss the actual constraints on the acquisition and reconstruction of non-Gaussian states by taking into account the limitations of realistic experimental resources.

We present a fiber-based source of narrowband heralded single photons in the telecoms C-band. Photon pairs were generated by spontaneous four-wave mixing in photonic crystal fiber (PCF) with a germanium-doped region incorporated into its core for enhanced photosensitivity. A fiber Bragg grating (FBG) with a bandwidth of 0.2 nm and contrast of 17.5 dB was UV-written into the PCF to reflect a sub-nanometre slice of the photon-pair spectrum. This allowed narrowband photons to be heralded at the proximal end of the fiber by detection events after the distal end. We present photon counting data with a coincidence-to-accidental ratio of up to 70. Our source demonstrates a viable route to fiber-integrated narrowband heralded single photon sources suitable for coupling to quantum memories and interfacing heterogeneous qubit types.

Photonic Quantum Machine Learning (PQML) is an emerging method to implement scalable, energy-efficient quantum information processing by combining photonic quantum computing technologies with machine learning techniques. The features of photonic technologies offer several benefits: room-temperature operation; fast (low delay) processing of signals; and the possibility of representing computations in high-dimensional (Hilbert) spaces. This makes photonic technologies a good candidate for the near-term development of quantum devices. However, noise is still a major limiting factor for the performance, reliability, and scalability of PQML implementations. This review provides a detailed and systematic analysis of the sources of noise that will affect PQML implementations. We will present an overview of the principal photonic quantum computer designs and summarize the many different types of quantum machine learning algorithms that have been successfully implemented using photonic quantum computer architectures such as variational quantum circuits, quantum neural networks, and quantum support vector machines. We identify and categorize the primary sources of noise within photonic quantum systems and how these sources of noise behave algorithm-specifically with respect to degrading the accuracy of learning, unstable training, and slower convergence than expected. Additionally, we review traditional and advanced techniques for characterizing noise and provide an extensive survey of strategies for mitigating the effects of noise on learning performance. Finally, we discuss recent advances that demonstrate PQML's capability to operate in real-world settings with realistic noise conditions and future obstacles that will challenge the use of PQML as an effective quantum processing platform.

We propose an approximate mapping of a molecular Hamiltonian to a Hamiltonian of qubits, which allows for high accuracy quantum chemistry calculations of vertical excitation energies of some molecules. The mapping is based on separating of a very small active space of only two orbitals and on modeling the electronic excitations in the remaining orbitals by a set of qubits or, equivalently, by a set of oscillators. This approach is inspired by the Random Phase Approximation (RPA), in which the excitations of electron gas are described by bosonic degrees of freedom. As a result, the Hamiltonian of the molecule is reduced to that of a system-bath model. The "system" part of the Hamiltonian describes the two molecular orbitals – the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) – which are populated by two electrons. Two qubits are sufficient to encode the Hamiltonian of such a system. The "bath" consists of oscillators or, equivalently, of two level systems with each of them corresponding to an electron excitation from a doubly occupied orbital below the Fermi level to an empty orbital above the Fermi level. We hope that this mapping can inspire new approaches and algorithms aimed at calculating excitation energies of molecules on near term quantum computers.

Flow criteria are used to efficiently extract computations, either in the form of measurement patterns or quantum circuits, from ZX-diagrams. Existing criteria such as causal flow, generalised flow, and Pauli flow, were all originally formulated for graph states, so they require ZX-diagrams to be in a very particular graph-state-like form. This form is easily broken by applying basic ZX rules and makes establishing some desirable properties very complicated. Here, we introduce a new "ZX-native" flow criterion called ZX-flow, formulated using a new type of decoration of a ZX-diagram we call Pauli semiwebs. These are a generalisation of Pauli webs, which have recently been used extensively in reasoning about fault-tolerant computations in the ZX-calculus. We show that ZX-flow is straightforwardly preserved by all Clifford rewrites and furthermore that a ZX-diagram has ZX-flow if and only if it is Clifford-equivalent to a graph-like ZX-diagram with Pauli flow. Finally, we show that any diagram with ZX-flow can be readily interpreted either as a deterministic measurement-based computation or as a Clifford isometry followed by a sequence of Pauli exponentials. The latter can then be efficiently extracted to a quantum circuit.

We investigate nonequilibrium dynamics and weak ergodicity breaking in a harmonically trapped spin-$3/2$ Fermi gas by using the time-dependent Hartree-Fock equation. The Shannon entropy remains bounded and oscillatory throughout the evolution, indicating restricted and nonuniform exploration of Hilbert space rather than immediate thermalization. The fidelity exhibits pronounced, nearly periodic revivals whose period is largely insensitive to particle number and interaction strength, while the revival amplitude gradually decreases with increasing system size and interaction strength. The Fourier spectrum of the fidelity reveals a set of sharp and approximately equally spaced peaks. By projecting the time-evolved state onto the instantaneous eigenbasis of the self-consistent mean-field Hamiltonian, we identify a sparse and spectrally stable manifold that forms a quasi-regular energy ladder, with spacing comparable to the dominant quasienergy interval extracted from the fidelity spectrum. These results indicate that the long-lived coherent oscillations originate from collective phase interference associated with a quasi-regular spectral structure embedded in the many-body continuum, rather than from a conventional eigenstate-dominated scar mechanism.

Recurrent quantum models (RQMs) realize sequential quantum processes through repeated application of a unitary operation on a memory system coupled with a series of output registers. However, such models often rely on unnecessarily large memory spaces, introducing redundancy and limiting scalability. Here, we introduce a variational quantum dimension reduction framework that identifies and removes irrelevant memory degrees of freedom while preserving the recurrent dynamics of the target model. Our approach employs two parameterized quantum circuits: a decoupling unitary $V(\theta_1)$ that isolates the essential memory subspace; and a compressed recurrent unitary $\tilde{U}(\theta_2)$ that reconstructs the dynamics in the reduced space. The optimization is guided by a unified cost function combining decoupling fidelity and dynamical accuracy, evaluated using the Quantum Fidelity Divergence Rate (QFDR), a metric that quantifies long-term fidelity per time step. Applied to a cyclic random walk model, our framework achieves up to three orders of magnitude smaller QFDR compared to variational matrix product state truncation, while requiring only trajectory samples rather than explicit state reconstructions. This establishes a scalable, data-driven paradigm for learning minimal recurrent quantum architectures, enabling variational circuit optimization and quantum process compression for near-term quantum devices.

With the advancement of synchrotron radiation and free-electron laser, X-ray quantum optics has emerged as a novel frontier for exploring light-matter interactions at high photon energies. A significant challenge in this field is achieving well-defined two-level systems through atomic inner-shell transitions, which are often hindered by broad natural linewidths and local electronic structure effects. This study aims to explore the potential of tungsten disilicide (WSi2) as a two-level system for X-ray quantum optics applications. Utilizing high-resolution resonant inelastic X-ray scattering (RIXS) near the W-L3 edge, in this work, the white line of bulk WSi2 is experimentally distinguished, overcoming the spectral broadening caused by short core-hole lifetime. The measurements are conducted by using a von Hamos spectrometer at the GALAXIES beamline of the SOLEIL synchrotron. The results reveal a single resonant emission feature with a fixed energy transfer, confirming the presence of a discrete 2p-5d transition characteristic of a two-level system. Additional high-resolution XAS spectra, obtained via high energy resolution fluorescence detection method and reconstructed from off-resonant emission (free from self-absorption effect for bulk WSi2 sample) method, further support the identification of a sharp white line. These findings demonstrate the feasibility of using WSi2 as a model system in X-ray cavity quantum optics and establish RIXS as a powerful technique to resolve fine inner-shell structures.

According to symmetrization postulate for a system of identical particles, wave function has to be completely symmetric or completely anti-symmetric. In this paper we want to mathematically justify this postulate ignoring the spin part of wave function in three dimension. For a system of N identical particles, if the solution to the governing Schrodinger equation meets these criteria: a) the probability density remains invariant when any two particle positions are exchanged over time, b) the wave function is continuous and has a continuous gradient, and the system exhibits the following characteristics: c) the configuration space, which is 3N dimensional, is connected, and d) the potential term in the Hamiltonian is invariant under the exchange of any two particle positions, then the wave function must be either totally symmetric or totally antisymmetric over time.

We consider a generic model for interacting waveguide QED systems, where photons in a coupled-cavity array localize around atomic impurities while simultaneously interacting through local Kerr nonlinearities. This scenario appears naturally in nanophotonic crystals, circuit QED lattices, and ultracold atomic systems and is governed by the competition between attractive Jaynes-Cummings-mediated binding and intrinsic photon-photon repulsion. We analyze how this interplay affects the formation of localized few-photon bound states and determine the resulting many-body ground states for large periodic arrays of impurities and different filling factors. With the help of large-scale numerical simulations and approximate analytical models, we identify a rich phase diagram featuring Mott-like insulating states as well as superfluid phases with long-range correlations, which are mediated by an unbound, but strongly interacting photonic fluid.

Recently, Rydberg atom has emerged as an attractive choice to realize quantum sensing of low-frequency electric field. The progress so far has mostly utilized the intensity and phase changes in probe laser and the corresponding detection mechanism still remains classical. Nevertheless, external field acting on the Rydberg state can induce the polarization variation of probe laser in the Rydberg electromagnetically induced transparency (EIT) system embedded in realistic multi-state atoms. We experimentally observe this phenomenon and realize signal extraction by appropriately utilizing the polarization degrees of freedom. Based on such a mechanism, we further design and implement a quantum weak measurement scheme, which clearly suppresses the technical noise and leads to considerable improvement of performance. Evaluation of the sensitivities across different post-selection angles demonstrates that the weak measurement results agree well with the theoretical model predictions. The advantages of our method are analyzed from multiple aspects, including characterizing the responses over different frequencies and comparing the responses of the weak measurement scheme and the traditional transmission-based method. After accounting for the screening effect of a measured ratio 17% where the $^\text{87}$Rb atoms experience a substantially reduced field inside the glass cell, the performance reaches 33 $\mu\text{V}~\text{cm}^\text{-1}~\text{Hz}^\text{-1/2}$ in sensitivity and 1.0 $\mu\text{V/cm}$ in minimal detectable field for an integration time of 1000 s, as perceived by the atoms.

Quantum token protocols enable unforgeable quantum tokens promising unconditional security beyond classical cryptographic assumptions. We show here that the three stages of the Quantum token protocols involving the preparation, storage and verification can be made more secure when involving spin-photon interfaces that leverage high fidelity hybrid tripartite (spin-photon-spin) entanglement, Bell state measurements and highly coherent spin quantum memories. Further we describe the physical implementation of various stages of the protocol using the hybrid electron and nuclear spins in diamond interfaced with time-bin photons.

Quantum annealing approximately solves combinatorial optimization problems by leveraging the principles of adiabatic quantum systems. In this approach, the system's Hamiltonian evolves from an initial general state to a problem-specific state. This study introduces multi-tasking quantum annealing (MTQA), a method that enables the parallel processing of multiple optimization problems by embedding them into spatially distinct regions on quantum hardware. MTQA is evaluated using two NP-hard problems: the minimum vertex cover problem (MVCP) and the graph partitioning problem (GPP). This parallel approach optimizes quantum resource utilization by concurrently utilizing idle qubits. The findings demonstrate that MTQA achieves a solution quality comparable to single-problem quantum annealing and classical simulated annealing (SA), while notably reducing the time-to-solution (TTS) metrics. Eigenspectrum analysis further theoretically supports the hypothesis that parallel embedding preserves quantum coherence and does not increase computational complexity by efficiently utilizing available quantum hardware (e.g., qubits and couplers). MTQA enables efficient multitasking in quantum annealing, optimizing hardware utilization and improving throughput for concurrent tasks and demonstrating performance for problems up to 100 nodes in real-world applications.

Quantum networks based on wavelength-multiplexed entanglement enable parallel distribution of quantum correlations, increasing channel capacity for secure communication and distributed quantum information processing. However, broadband integrated sources capable of generating multipartite entanglement beyond photon pairs remain scarce. Here we report on-chip generation of telecom-band four-photon entanglement in a periodically poled thin-film lithium niobate on insulator (LNOI) waveguide. Type-0 spontaneous parametric down-conversion provides a phase-matching bandwidth exceeding 200 nm, enabling spectrally separable generation of multi-photon entanglement across the telecom band. The generated photons are encoded in time bins for robust fiber compatibility, and a coherent interface enabling reversible conversion between time-bin and polarization degrees of freedom allows complete quantum state tomography. We measure two-photon entanglement with a brightness of 6.7 MHz/mW/nm and a fidelity of $0.874 \pm 0.002$. At a pump power of 0.08 mW, the four-photon state exhibits a fourfold coincidence rate of 1 Hz and a fidelity of $0.74 \pm 0.01$, representing a threefold improvement over previous integrated platforms. Our results establish LNOI as a scalable platform for broadband multi-photon entanglement and provide a practical route toward dense wavelength-multiplexed quantum networks.

Predictive optical modelling of van der Waals (vdW) heterostructures is critical for meta-optics, near-field photonics and quantum technologies. At their buried interfaces, charge transfer and spatially extended screening challenge local descriptions based on layer-by-layer stacking of fixed permittivity tensors. However, such nonlocal corrections have been established mainly for plasmonic systems at ångström-nanometre scales and are often assumed negligible on optical-wavelength scales. Here we challenge this view by uncovering a mesoscopic nonlocal screening regime, extending up to ~140 nm, at buried charge-transfer interfaces in transition-metal dichalcogenide/{\alpha}-molybdenum trioxide (TMDC/{\alpha}-MoO3) phonon-polaritonic heterostructures. Using phonon polaritons as an ultrasensitive probe, we quantify charge transfer from polariton-wavelength shifts and find a thickness-independent saturated response as {\alpha}-MoO3 is thinned. Rather than merely complicating optical modelling, this nonlocal saturation turns a design-level correction into an opportunity by yielding a transferable cross-material metric. Across more than 120 devices, this metric scales linearly with the work-function difference between the TMDC and {\alpha}-MoO3. We further identify a lattice-mismatch-set energy threshold for charge transfer, revising Anderson-type band alignment for vdW interfaces.

Delegated quantum computation enables a client with limited quantum capabilities to outsource computations to a more powerful quantum server while preserving correctness and privacy. Verification is crucial in this setting to ensure that the untrusted quantum server performs the computation honestly and returns correct results. A common verification method is the quantum cut-and-choose technique. Inspired by classical verification methods for two-party computation, the client uses the majority of the delegated rounds to test the server's honesty, while keeping the remaining ones for the actual computation. Combining this technique with other methods, such as quantum error correction, could help achieve negligible cheating probabilities for the server; however, such methods can impose significant overheads making implementations unfeasible for the near-term future. In this work, we investigate whether cut-and-choose can yield efficient and secure verifiable quantum computation without additional costly techniques. We find that verifiable delegated quantum computation protocols relying solely on cut-and-choose techniques cannot be secure and efficient at the same time.

We study a two-dimensional Dunkl–Pauli oscillator in the presence of an Aharonov–Bohm (AB) flux. The combination of reflection symmetry (via Dunkl operators) and a topological gauge field imposes a nontrivial constraint on the admissible quantum states: the regularity condition on radial wave functions, together with the matching conditions at the flux tube, leads to a compatibility relation $\nu_1+\varepsilon\nu_2=0$ and forces the emergence of a lowest angular quantum number~$\ell_0$. As a result, the admissible angular sectors are restricted rather than the spectrum being merely shifted in energy. Using the exact spectrum, we construct the canonical partition function and derive closed-form expressions for the internal energy, entropy, and heat capacity. The thermodynamic quantities directly reflect this spectral constraint: the low-temperature behaviour is governed by~$\ell_0$, and the heat capacity exhibits a flux-controlled Schottky-like peak. The Dunkl parameter~$\nu$ plays a dual role: within a fixed sector it shifts the energy scale, while globally it controls the flux threshold that determines which sectors are admissible. At high temperatures the classical two-dimensional oscillator limit is recovered. Our results demonstrate that the interplay between Dunkl symmetry and AB flux qualitatively modifies the set of admissible states, with observable thermodynamic signatures.

We investigate the influence of phonon degrees of freedom on the qubit dynamics in Jaynes-Cummings (JC) model. A strong qubit-phonon coupling is considered giving rise to Jaynes-Cummings-Holstein (JCH) model. Under anti-adiabatic conditions, we perform a unitary transformation to make the underlying problem tractable through Redfield-type non-Markovian master equation. Analytical expression for the time-dependent coherence is obtained, incorporating both cavity-induced dissipation and phonon-induced dressing effects. The dynamics of JC model is highly non-Markovian for a narrow spectral width and finite detuning. However, a non-zero phonon coupling suppresses these non-Markovian features by effectively reducing the qubit-cavity interaction strength. {It is observed that polaronic dressing effectively supresses the detuning effects. Furthermore, the coherence-based non-Markovianity measure shows an order-of-magnitude suppression in the JCH model, indicating a new dynamical regime, while memory effects extend over a wider range of spectral densities than in the JC model.

We present an asymptotic approach towards the standard Landau-Zener problem based on two linearly independent elementary waves of constant amplitude but time-dependent phase. The two contributions to this phase are quadratic and logarithmic in time and result from the linear chirp of the energies and the lowest order correction in the coupling between the two levels in the long-time limit. Indeed, our solutions subjected to initial conditions at a large but finite time in the past, are valid for large negative and large positive times. Due to their asymptotic nature they are not valid in the neighborhood of the moment when the levels cross. However, as the starting point of the dynamics moves further into the past, the time interval of the break-down of our asymptotic solutions shrinks and vanishes in the limit of the infinite past which corresponds to the standard Landau-Zener situation. Our approach explains not only every feature of the exact solution but yields deeper insights into the origin of the effects. In particular, it (i) brings to light the subtleties involved in the asymptotic limit leading to the standard expressions for the Landau-Zener transition amplitudes, (ii) identifies the logarithmic phase as the origin of the exponential transition probability amplitude, and (iii) reveals the structure of the lowest order corrections to the Landau-Zener result when the starting point is not in the infinite past.

Sample-based quantum diagonalization (SQD) is a hybrid quantum-classical algorithm for estimating ground-state energies in electronic-structure calculations. It uses a quantum processor as a sampler to construct a variational subspace, with Hamiltonian projection and diagonalization performed classically. A critical step in SQD is self-consistent particle-number recovery guided by a global reference occupancy vector. In strongly correlated systems, however, dominant determinants can be distributed across regions of determinant space, causing this reference to become mixture-averaged and biasing recovery toward mean occupations. Here, we introduce cluster-adaptive SQD (CSQD), which clusters pooled single-spin strings and performs particle-number recovery using cluster-specific reference occupancy vectors. Under a matched variational budget, CSQD lowers ground-state energies relative to SQD by up to 15.95 mHa for stretched N2 in a (10e,26o) active space and 57.82 mHa for [2Fe-2S] in a (30e,20o) active space. These results suggest that CSQD better captures dispersed occupation structure in strongly correlated systems.

Errors are arguably the most pressing challenge impeding practical applications of quantum computers, which has instigated vigorous research on the development of quantum error mitigation (QEM) techniques. Existing QEM methods suppress errors with a varying degree of efficacy but importantly demand significant additional quantum and classical computational resources. In this work, we present Fictitious Copy Quantum Error Mitigation (FCQEM) method which corrects quantum errors without requiring any additional quantum resources and purely relies on using classical postprocessing of a joint probability distribution to correct expectation values. The joint probability distribution can be measured “fictitiously” by sampling one copy of noisy quantum circuit twice, or classically squaring probabilities from simply one copy. We show that FCQEM can recover eigenvalues even if exact eigenstates are not prepared. Furthermore, our technique can benefit other noise mitigation techniques with no additional quantum resources, which is demonstrated by combining FCQEM with the Quantum Computed Moments (QCM) method. FCQEM can compensate for noise that is pathological to QCM, and QCM allows for FCQEM to recover the ground state energy with a larger variety of trial states. We show that our technique can find the exact ground state energy of molecular and spin models under simulated noise models as well as experiments on a Rigetti 84-qubit superconducting quantum processor. The reported FCQEM method is general purpose for the current generation of quantum devices and is applicable to any problem that measures eigenvalues of operators on sharply peaked distributions.

We show that incoherent operations (IOs) can achieve the state transformations that are forbidden under dephasing-covariant incoherent operations (DIOs), thereby resolving the open problem posed by Chitambar and Gour [Phys. Rev. Lett. 117, 030401 (2016)]. We further demonstrate that no set of IO monotones suffices to characterize state convertibility under strictly incoherent operations (SIOs), and that monotones common to IOs and DIOs are insufficient to characterize convertibility under DIOs.

We introduce a framework for simulating hybrid oscillator-qubit quantum processors on qubit-only systems through position encoding. By encoding continuous-variable position and momentum wave functions into qubit amplitudes, our method efficiently simulates all Gaussian and conditional Gaussian operations – encompassing the phase-space instruction set (beam splitter, single-qubit rotation, conditional displacement) and extending to squeezing, conditional squeezing, conditional rotation, and conditional beam splitter – using $O\!\left(\log^2\!\left(\Gamma + \log(1/\epsilon)\right)\right)$ qubit gates per hybrid gate, where $\Gamma$ is the Fock-level bound and $\epsilon$ is the target precision. This polylogarithmic per-gate complexity represents an exponential improvement over Fock basis encoding approaches, which require exponential quantum or classical resources in the number of qubits per mode. We provide rigorous numerical characterization of quantum Fourier transform errors for Fock-bounded states, enabling precise resource estimation for practical implementations. This work establishes that hybrid oscillator-qubit algorithms can be implemented on qubit processors with polynomial overhead, providing new insights into the computational power trade-offs between discrete-variable and hybrid continuous-discrete-variable quantum computing.

We explore optical quantum engineering of phase-parameterized continuous-variable (CV) probe states to exploit nonclassical light to solve the problem of precise phase estimation. The optical interferometer consists of a single beam splitter (BS) with tunable transmittance and reflectance, and two single-mode squeezed vacuum states (SMSVs). The reference SMSV state is mixed with a weakly squeezed state carrying an unknown phase at the beam splitter to form an output hybrid entangled state. Then, in the measurement mode, the number of photons is measured to generate the target CV state parameterized by the unknown phase. Using the CV states, we propose a sub-Heisenberg metrology protocol in which the quantum Cramer-Rao (QCR) boundary is saturated by intensity measurement. The advantage of quantum engineering of CV probe states for ultra-precise phase estimation of unknown phase is due solely to the nonclassical photonic properties of the measurement induced CV states of definite parity and is independent of the mode entanglement.

High harmonics have emerged as a powerful ultrafast probe of phonon dynamics and electron-phonon interactions in solids, with most studies focusing on odd harmonics. Here, in a pump-probe setup with variable delay, we theoretically investigate how even harmonics reveal coherent phonon dynamics. If pump and probe pulses overlap temporally, the spatial interference effect resulting from a non-coaxial pump-probe setup suppresses harmonic yields. At longer delays, odd-harmonic yields oscillate in phase at the optical phonon frequency, whereas even harmonics exhibit order-dependent phase-shifted oscillations. We identify a responsive range of even harmonic orders, in which the delay of yield oscillations is highly sensitive to subtle features of phonon dynamics and electron-electron interactions. Our findings highlight the potential of even harmonics to elucidate microscopic effects in systems with dynamically broken inversion symmetry.

We conjecture analytic expressions for the non-local magic of bipartite pure qudit states of prime local dimension. Our construction relies on the Schmidt-aligned state attaining the minimum over local unitaries, a hypothesis that we support with numerical evidence for pairs of qutrits and ququints. For composite local dimensions, we find that the analogous expressions do not in general reproduce the global minimum, but can still provide computationally cheap approximations to the non-local magic. We also find that relations between non-local magic and entanglement diagnostics that hold for two qubits generally do not extend to qutrit and higher-dimensional systems. As a few-body application, we evaluate the qutrit non-local magic generated by elastic pion scattering, treating hadronic isospin as the qutrit. We find that $p$-wave charged pion scattering realises the maximum non-local magic allowed in the system just below the $\rho$-meson resonance.

The fast and efficient preparation of quantum critical states is a challenging yet crucial task for various quantum technologies. This difficulty is most particularly for systems near a quantum phase transition, where the closure of the energy gap fundamentally limits the timescale of adiabatic processes and thus precludes rapid state preparation. We propose a framework using deep reinforcement learning (DRL) to rapidly prepare quantum critical states, with broad extendibility to light-matter interaction systems. Specifically, a DRL agent optimizes a set of time-dependent control Hamiltonians to drive the system from an initial noncritical state to a target critical state within a finite time and over experimentally accessible parameter ranges. As a concrete application, we focus on the quantum Rabi model. The DRL-optimized time-dependent control Hamiltonian yield a final state with high-fidelity ($>0.999$) to the target critical state. The protocol can be readily extended to other quantum critical systems described by light-matter interaction models, such as quantum Dicke model. This investigation provides a powerful new framework for preparing and manipulating quantum critical states.