Papers

Accurate and low-latency qubit state measurement is critical for trapped-ion quantum computing. While deep neural networks (DNNs) have been integrated to enhance detection fidelity, their latency performance on specific hardware platforms remains underexplored. This work benchmarks the latency of DNN-based qubit detection on field-programmable gate arrays (FPGAs) and graphics processing units (GPUs). The FPGA solution directly interfaces an electron-multiplying charge-coupled device (EMCCD) with the subsequent data processing logic, eliminating buffering and interface overheads. As a baseline, the GPU-based system employs a high-speed PCIe image grabber for image input and I/O card for state output. We deploy Multilayer Perceptron (MLP) and Vision Transformer (ViT) models on hardware to evaluate measurement performance. Compared to conventional thresholding, DNNs reduce the mean measurement fidelity (MMF) error by factors of 1.8-2.5x (one-qubit case) and 4.2-7.6x (three-qubit case). FPGA-based MLP and ViT achieve nanosecond- and microsecond-scale inference latencies, while the complete single-shot measurement process achieves over 100x speedup compared to the GPU implementation. Additionally, clock-cycle-level signal analysis reveals inefficiencies in EMCCD data transmission via Cameralink, suggesting that optimizing this interface could further leverage the advantages of ultra-low-latency DNN inference, guiding the development of next-generation qubit detection systems.

This thesis focuses on the intersection of mathematical and computational optimization and quantum information. Main contributions are open-source software code: A hybrid approach mixing "traditional" nonconvex and convex methods can make difficult problems more accessible. A demonstration of how to efficiently implement such an algorithm, avoiding interfacial bottlenecks, is provided, finding optimal protocols to establish entanglement through a lossy channel. The central software package developed addresses polynomial optimization problems. Many problems naturally involve only a polynomial objective and constraint polynomials. Such problems can automatically be cast into semidefinite programs that provide a hierarchy of outer approximations. The resulting problems are often so large and scale so unfavorably with respect to the variable number and degree involved that the boundary of the doable is reached quickly. However, technical progress both in hardware and algorithms has pushed this boundary - but software frameworks for polynomial optimization have not followed in the same manner, often now making them the bottleneck that before was the solver. The package PolynomialOptimization.jl developed during this thesis aims to fill the gap and provide a very resource-efficient intermediate layer together with a wide number of algorithms to reduce the problem size, and naturally supporting complex numbers and semidefinite constraints ubiquitous in quantum information problems. Its application on an entanglement distribution problem is demonstrated, showing that even relaxations with semidefinite matrices of three- and four-digit size can be solved conveniently. Finally, a new way to calculate interior-point barriers for the cone of sums-of-squares matrices in a nearly time-optimal way is developed, whose efficient implementation has the potential of further reducing resource consumption.

Spin-charge stripes belong to the most prominent low-temperature orders besides superconductivity in high-temperature superconductors. This phase is particularly challenging to study numerically due to finite-size effects. By investigating the formation of long, isolated stripes, we offer a perspective complementary to typical finite-doping phase diagrams. We use the density-matrix renormalization group algorithm to extract the ground states of an 18-leg cylindrical strip geometry, making the diameter significantly wider than in previous works. This approach allows us to map out the range of possible stripe filling fractions on the electron versus hole-doped side. We find good agreement with established results, suggesting that the spread of filling fractions observed in the literature is governed by the physics of a single stripe. Taking a microscopic look at stripe formation, we reveal two separate regimes - a high-filling regime captured by a simplified squeezed-space model and a low-filling regime characterized by the structure of individual pairs of dopants. Thereby, we trace back the phenomenology of the striped phase to its microscopic constituents and highlight the different challenges for observing the two regimes in quantum simulation experiments.

The optical fiber is a revolutionary technology of the past century. It enables us to manipulate single modes in nonlinear interactions with precision at the quantum level without involved setups. This setting is useful in the field of analogue gravity (AG), where gravitational phenomena are investigated in accessible analogue lab setups. These lecture notes provide an account of this AG framework and applications. Although light in nonlinear dielectrics is discussed in textbooks, the involved modelling often includes many assumptions that are directed at optical communications, some of which are rarely detailed. Here, we provide a self-contained and sufficiently detailed description of the propagation of light in fibers, with a minimal set of assumptions, which is relevant in the context of AG. Starting with the structure of a step-index fiber, we derive linear-optics propagating modes and show that the transverse electric field of the fundamental mode is well approximated as linearly polarized and of a Gaussian profile. We then incorporate a cubic nonlinearity and derive a general wave envelope propagation equation. With further simplifying assumptions, we arrive at the famous nonlinear Schrödinger equation, which governs fundamental effects in nonlinear fibers, such as solitons. As a first application in AG, we show how intense light in the medium creates an effective background spacetime for probe light akin to the propagation of a scalar field in a black hole spacetime. We introduce optical horizons and particle production in this effective spacetime, giving rise to the optical Hawking effect. Furthermore, we discuss two related light emission mechanisms. Finally, we present a second optical analogue model for the oscillations of black holes, the quasinormal modes, which are important in the program of black hole spectroscopy.

The random purification channel maps n copies of any mixed quantum state to n copies of a random purification of the state. We generalize this construction to arbitrary symmetries: for any group G of unitaries, we construct a quantum channel that maps states contained in the algebra generated by G to random purifications obtained by twirling over G. In addition to giving a surprisingly concise proof of the original random purification theorem, our result implies the existence of fermionic and bosonic Gaussian purification channels. As applications, we obtain the first tomography protocol for fermionic Gaussian states that scales optimally with the number of modes and the error, as well as an improved property test for this class of states.

Fault-tolerant quantum computers use decoders to monitor for errors and find a plausible correction. A decoder may provide a decoder confidence score (DCS) to gauge its success. We adopt a swim distance DCS, computed from the shortest path between syndrome clusters. By contracting tensor networks, we compare its performance under phenomenological noise to the well-known complementary gap and find that both reliably estimate the logical error probability (LEP) in a decoding window. We explore ways to use this to mitigate the LEP in entire logical circuits. For shallow circuits, we just abort if any decoding window produces an exceptionally low DCS: for one window of a distance-13 surface code under circuit-level noise, rejecting a mere $0.1\%$ of possible DCS values improves the window's mean LEP by more than 5 orders of magnitude. For larger algorithms comprising up to billions of windows, DCS-based rejection remains effective for enhancing observable estimation. Moreover, one can use the DCS to assign each circuit's output a unique LEP, and use it as a basis for maximum likelihood estimation. This can reduce the effects of noise by an order of magnitude at no quantum cost; we explore the combination of these methods.

Graph-theoretic structures play a central role in the description and analysis of quantum systems. In this work, we introduce a new class of quantum states, called $A_\alpha$-graph states, which are constructed from either unweighted or weighted graphs by taking the normalised convex combination of the degree matrix $D$ and the adjacency matrix $A_G$ of a graph $G$. The constructed states are different from the standard graph states arising from stabiliser formalism. Our approach is also different from the approach used by Braunstein et al. This class of states depend on a tunable mixing parameter $\alpha \in (0,1]$. We first establish the conditions under which the associated operator $\rho_\alpha^{A_G}$ is positive semidefinite and hence represents a valid quantum state. We then derive a positive partial transposition (PPT) condition for $A_{\alpha}$-graph states in terms of graph parameters. This PPT condition involves only the Frobenius norm of the adjacency matrix of the graph, the degrees of the vertices and the total number of vertices. For simple graphs, we obtain the range of the parameter $\alpha$ for which the $A_{\alpha}$-graph states represent a class of entangled states. We then develop a graph-theoretic formulation of a moments-based entanglement detection criterion, focusing on the recently proposed $p_3$-PPT criterion, which relies on the second and third moments of the partial transposition. Since the estimation of these moments is experimentally accessible via randomised measurements, swap operations, and machine-learning-based protocols, our approach provides a physically relevant framework for detecting entanglement in structured quantum states derived from graphs. This work bridges graph theory and moments-based entanglement detection, offering a new perspective on the role of combinatorial structures in quantum correlations.

Demonstrating quantum advantage in machine learning tasks requires navigating a complex landscape of proposed models and algorithms. To bring clarity to this search, we introduce a framework that connects the structure of parametrized quantum circuits to the mathematical nature of the functions they can actually learn. Within this framework, we show how fundamental properties, like circuit depth and non-Clifford gate count, directly determine whether a model's output leads to efficient classical simulation or surrogation. We argue that this analysis uncovers common pathways to dequantization that underlie many existing simulation methods. More importantly, it reveals critical distinctions between models that are fully simulatable, those whose function space is classically tractable, and those that remain robustly quantum. This perspective provides a conceptual map of this landscape, clarifying how different models relate to classical simulability and pointing to where opportunities for quantum advantage may lie.

Entanglement and Bell nonlocality are known to be inequivalent: there exist entangled states that admit a local hidden-variable model for all local measurements. Here we show that this gap disappears in a minimal broadcast extension of the Bell scenario. Assuming only the validity of quantum theory, we prove that for every entangled state $\rho_{AB}$ there exist local broadcasting maps and local measurements such that the resulting four–partite correlations cannot be reproduced by any broadcast network whose source is separable across the $A|B$ cut. Thus, all entangled states are broadcast nonlocal in quantum theory. In addition, we show that all (also mixed) multipartite states can be broadcast-self-tested, according to a natural operational definition.

Non-Gaussian quantum states of light are essential resources for quantum information processing and precision metrology. Among them, generalized coherent states (GCS), which naturally arise from the evolution of a coherent state with a nonlinear medium, exhibit useful quantum features such as Wigner negativity and metrological advantages [Phys. Rev. Res. 5, 013165 (2023)]. Because these states remain coherent to all orders, their nonclassical character cannot be revealed through standard intensity-intensity correlation measurements. Here, we demonstrate that the intensity-field correlation function alone provides a simple and experimentally accessible witness of nonclassicality. For GCSs, any deviation of this normalized correlation from unity signals nonclassical behavior. We derive analytical results for Kerr-generated states and extend the analysis to statistical mixtures of GCSs. The proposed approach enables real-time, low-complexity detection of quantum signatures in non-Gaussian states, offering a practical tool for experiments across a broad range of nonlinear regimes.

Molecular spin qudits based on lanthanide complexes offer a promising platform for quantum technologies, combining chemical tunability with multi-level encoding. However, experimental demonstrations of their envisaged capabilities remain scarce, posing the difficulty of achieving precise control over coherences between qudit states in long pulse sequences. Here, we implement in 173Yb(trensal) qudit the Quantum Fourier Transform (QFT), a core component of numerous quantum algorithms, storing quantum information in the phases of coherences. QFT provides an ideal benchmark for coherence manipulation and an unprecedented challenge for molecular spin qudits. We address this challenge by embedding a full-refocusing protocol for spin qudits in our algorithm, mitigating inhomogeneous broadening and enabling a high-fidelity recovery of the state. Complete state tomography demostrates the performance of the algorithm, while simulations provide insight into the physical mechanisms behind inhomogeneous broadening. This work shows the feasibility of quantum logic on molecular spin qudits and highlights their potential.

We demonstrate a quadratic enhancement of power in a battery consisting of $N$ two-level systems or spins interacting with two photonic cavity modes, where one of the modes is in the dispersive regime. In contrast to Dicke batteries, the power enhancement arises from a $N^2$ scaling of both quantum correlations and speed of evolution, thus highlighting genuine quantum advantage. Moreover, this hybrid setup is experimentally realizable and ensures that power enhancement is not achieved at significant cost to energy efficiency, while allowing for greater tunability and stable operation in the presence of noise.

The dynamics of disordered nuclear spin ensembles are the subject of nuclear magnetic resonance studies. Due to the through-space long-range dipolar interaction generically many spins are involved in the time evolution, so that exact brute force calculations are impossible. The recently established spin dynamic mean-field theory (spinDMFT) represents an efficient and unbiased alternative to overcome this challenge. The approach only requires the dipolar couplings as input and the only prerequisite for its applicability is that each spin interacts with a large number of other spins. In this article, we show that spinDMFT can be used to describe spectral spin diffusion in static samples and to simulate zero-quantum line shapes which eluded an efficient quantitative simulation so far to the best of our knowledge. We perform benchmarks for two test substances that establish an excellent match with published experimental data. As spinDMFT combines low computational effort with high accuracy, we strongly suggest to use it for large-scale simulations of spin diffusion, which are important in various areas of magnetic resonance.

Photonics can offer a hardware-native route for machine learning (ML). However, efficient deployment of photonics-enhanced ML requires hybrid workflows that integrate optical processing with conventional CPU/GPU based neural network architectures. Here, we propose such a workflow that combines photonic positional embeddings (PEs) with advanced graph ML models. We introduce a photonics-based method that augments graph convolutional networks (GCNs) with PEs derived from light propagation on synthetic frequency lattices whose couplings match the input graph. We simulate propagation and readout to obtain internode intensity correlation matrices, which are used as PEs in GCNs to provide global structural information. Evaluated on Long Range Graph Benchmark molecular datasets, the method outperforms baseline GCNs with Laplacian based PEs, achieving $6.3\%$ lower mean absolute error for regression and $2.3\%$ higher average precision for classification tasks using a two-layer GCN as a baseline. When implemented in high repetition rate photonic hardware, correlation measurements can enable fast feature generation by bypassing digital simulation of PEs. Our results show that photonic PEs improve GCN performance and support optical acceleration of graph ML.

We study the nonequilibrium driven dynamics at topologically nontrivial quantum critical points (QCPs), and find that topological edge modes at criticality give rise to anomalous dynamical scaling behavior. By analyzing the driven dynamics of bulk and boundary order parameters at topologically distinct QCPs in quantum spin chains, we demonstrate that, while the bulk dynamics remain indistinguishable and follow standard Kibble Zurek (KZ) scaling, the anomalous boundary dynamics are unique to topological criticality, obeying modified scaling relation beyond the traditional KZ framework. To elucidate the unified origin of this anomaly, we further study the dynamics of defect production at topologically distinct QCPs in free-fermion models and demonstrate similar anomalous scaling exclusive to topological criticality. These findings establish the existence of anomalous dynamical scaling arising from the interplay between topology and driven dynamics, challenging standard paradigms of quantum critical dynamics.

Environmental decoherence occurs when a quantum system interacts with its surroundings, progressively reducing quantum interference and coherence, complicating the preservation of critical quantum features over time, especially during experimental implementation. The quantum features of a state can be represented in phase space via the Wigner function, which manifests across multiple scales, with decoherence potentially influencing each scale differently, as examined in this work. We consider the compass state and its photon-added and photon-subtracted variants (optimized compass states) as our representative examples, each of which exhibits phase-space features with dimensions beyond the Planck scale, making them suitable for quantum sensing applications. We investigate the interaction of these states with a heat reservoir by employing a range of well-established theoretical tools. We observe that compass states with finer-scale phase-space features are more fragile to decoherence, with parameters favoring greater sub-Planckness in phase space concomitantly increasing the fragility of these compass states to decoherence. Our findings are then validated for generic quantum states interacting with the heat reservoir, for which we provide analytical and numerical investigations, exploring the relationship between quantum state robustness to decoherence and the sizes of their phase-space features; that is, phase-space features at smaller scales decay faster under decoherence, and vice versa.

We find the maximum rate achievable in the private communication over a bosonic quantum channel with a fully Gaussian protocol based on optimal single-mode Gaussian measurements. This rate establishes a lower bound on the secret rate capacity of the channel. We focus on the class of phase-insensitive Gaussian channels. For the thermal-loss and thermal amplification channels, our results demonstrate the optimality, within the constraints of our analysis, of previously proposed protocols, while also providing a significantly simplified formula for their performance evaluation. For the added noise channel, our rate provides a better lower bound than any previously known.

Dynamic programming is a cornerstone of graph-based optimization. While effective, it scales unfavorably with problem size. In this work, we present QuantGraph, a two-stage quantum-enhanced framework that casts local and global graph-optimization problems as quantum searches over discrete trajectory spaces. The solver is designed to operate efficiently by first finding a sequence of locally optimal transitions in the graph (local stage), without considering full trajectories. The accumulated cost of these transitions acts as a threshold that prunes the search space (up to 60% reduction for certain examples). The subsequent global stage, based on this threshold, refines the solution. Both stages utilize variants of the Grover-adaptive-search algorithm. To achieve scalability and robustness, we draw on principles from control theory and embed QuantGraph's global stage within a receding-horizon model-predictive-control scheme. This classical layer stabilizes and guides the quantum search, improving precision and reducing computational burden. In practice, the resulting closed-loop system exhibits robust behavior and lower overall complexity. Notably, for a fixed query budget, QuantGraph attains a 2x increase in control-discretization precision while still benefiting from Grover-search's inherent quadratic speedup compared to classical methods.

Cloud-based quantum computers do not provide users with access to hardware-level information such as the underlying Hamiltonians, which obstructs the characterization of their physical properties. We propose a method to infer the energy scales of gate Hamiltonians in such black-box quantum processors using only user-accessible data, by exploiting quantum speed limits. Specifically, we reinterpret the Margolus-Levitin and Mandelstam-Tamm bounds as estimators of the energy expectation value and variance, respectively, and relate them to the shortest time for the processor to orthogonalize a quantum state. This shortest gate time, expected to lie on the nanosecond scale, is inferred from job execution times measured in seconds by employing gate-time amplification. We apply the method to IBM's superconducting quantum processor and estimate the energy scales associated with single-, two-, and three-qubit gates. The order of estimated energy is consistent with typical drive energies in superconducting qubit systems, suggesting that current gate operations approach the quantum speed limit. Our results demonstrate that fundamental energetic properties of black-box quantum computers can be quantitatively accessed through operational time measurements, reflecting the conjugate relationship between time and energy imposed by the uncertainty principle.

The recently available high-intensity quantum light pulses provide novel tools for controlling light-matter interactions. However, the rigor of the theoretical frameworks currently used to describe the interaction of strong quantum light with atoms and molecules remains unverified. Here, we establish a rigorous benchmark by solving the fully quantized time-dependent Schrödinger equation for an atom exposed to bright squeezed vacuum light. Our ab initio simulations reveal a critical limitation of the widely used $Q$-representation: although it accurately reproduces the total photoelectron spectrum after tracing over photon states, it completely fails to capture the electron-photon joint energy spectrum. To overcome this limitation, we develop a general theoretical framework based on the Feynman path integral that properly incorporates the electron-photon quantum entanglement. Our results provide both quantitative benchmarks and fundamental theoretical insights for the emerging field of strong-field quantum optics.

We present a method to calculate the frequency components of a pump waveform driving a parametric oscillator, which realizes a desired frequency mixing or scattering between modes. The method is validated by numerical analysis and we study its sensitivity to added Gaussian noise. A series of experiments apply the method and demonstrate its ability to realize complex scattering processes involving many modes at microwave frequencies, including non-reciprocal mode circulation. We also present an approximate method to dynamically control mode scattering, capable of rapidly routing signals between modes in a prescribed manner. These methods are useful tools for encoding and manipulating continuous variable quantum information with multi-modal Gaussian states.

Informationally complete measurements form the foundation of universal quantum state reconstruction, while quantum parameter estimation is based on the local structure of the manifold of quantum states. Here we establish a general link between these two aspects, in the context of a single informationally complete measurement, by employing a suitably adapted operator frame theory. In particular, we bound the ratio between the classical and quantum Fisher information in terms of the spectral decomposition of the associated frame operator, and connect these bounds to the optimal and least optimal directions for parameter encoding. The geometric and operational characterization of information extraction thus obtained reveals the fundamental tradeoff imposed by informational completeness on local quantum parameter estimation.

Quantum illumination represents one of the most interesting examples of quantum technologies. On the one hand, it can find significant applications; on the other hand, it is one of the few quantum protocols robust against noise and losses. Here we present a short summary of the history of this quantum protocol.

We introduce a framework that unifies quantum measurement dynamics, Hamiltonian dynamics, and double-bracket gradient flows. We do so by providing explicit expressions for stochastic Hamiltonians that produce state dynamics identical to those that happen during continuous quantum measurements. When such dynamical processes are integrated over sufficiently long time intervals, they yield the same results and statistics as during wavefunction collapse. That is, wavefunction collapse can be interpreted as coarse-grained (stochastic) Hamiltonian dynamics. Alternatively, wavefunction collapse can be interpreted as double-bracket gradient flows determined by derivatives of (stochastic) potentials defined in terms of observables with direct physical interpretations. The gradient flows minimize the variance of the monitored observable. Our derivations hold for general monitoring described by non-Hermitian jump processes. We show that such reinterpretations of measurement dynamics facilitate the design of feedback processes. In particular, we introduce feedback processes that yield deterministic double-bracket flow equations that prepare ground states of a target Hamiltonian, and state-agnostic feedback processes for state preparation. We apply the latter for entanglement stabilization of a two-qubit system considering a setup with imperfect measurements and feedback delay. We conclude by re-interpreting feedback processes as gradient flows with tilted fixed points.

Quantum Key Distribution (QKD) offers information-theoretic security by leveraging quantum mechanics, yet the cost and complexity of dedicated hardware and fiber infrastructure have so far limited large-scale deployment and experimentation. In this paper, we introduce Quditto, an automated open-access emulation platform that combines high-fidelity quantum-channel modeling with a standardized key-delivery API, enabling users to interact with the emulated network exactly as they would with real QKD hardware. Quditto modular design supports pluggable protocol implementations, complex key management schemes and detailed channel models, including variable attenuation and decoherence. We validate Quditto by deploying networks of various sizes and demonstrate its flexibility through two proof-of-concept scenarios featuring eavesdropper attacks and heterogeneous channel conditions.

We incorporate non-local gravitational self-energy, motivated by string-inspired T-duality, into the Schrödinger-Newton equation. In this framework spacetime has an intrinsic non-locality, rendering the standard linear superposition principle only an approximation valid in the absence of gravitational effects. We then invert the logic by assuming the validity of linear superposition and demonstrate that such superpositions inevitably become unstable once gravity is included. The resulting wave-function collapse arises from a fundamental tension between the equivalence principle and the quantum superposition principle in a semiclassical spacetime background. We further show that wave functions computed in inertial and freely falling frames differ by a gravitationally induced phase shift containing linear and cubic time contributions along with a constant global term. These corrections produce a global phase change and lead to a spontaneous, model-independent collapse time inversely proportional to the mass of the system.

The study of spectrum statistics, such as the consecutive-gap ratio distribution, has revealed many interesting properties of many-body complex systems. Here we propose a two-parameter surmise expression for such distribution to describe the crossover between the Gaussian orthogonal ensemble (GOE) and Poisson statistics. This crossover is observed in the isotropic Heisenberg spin-$1/2$ chain with disordered local field, exhibiting the Many-Body Localization (MBL) transition. Inspired by the analysis of stability in dynamical systems, this crossover is presented as a flow pattern in the parameter space, with the Poisson statistics being the fixed point of the system, which represents the MBL phase. We also analyze an isotropic Heisenberg spin-$1/2$ chain with disordered local exchange coupling and a zero magnetic field. In this case, the system never achieves the MBL phase because of the spin rotation symmetry. This case is more sensitive to finite-size effects than the previous one, and thus the flow pattern resembles a two-dimensional random walk close to its fixed point. We propose a system of linearized stochastic differential equations to estimate this fixed point. We study the continuous-state Markov process that governs the probability of finding the system close to this fixed point as the disorder strength increases. In addition, we discuss the conditions under which the stationary probability distribution is given by a bivariate normal distribution.

The detection and characterization of quantum coherence is of fundamental importance both in the foundations of quantum theory as well as for the rapidly developing field of quantum technologies, where coherence has been linked to quantum advantage. Typical approaches for detecting coherence employ coherence witnesses – observable quantities whose expectation value can be used to certify the presence of coherence. By design, coherence witnesses are only able to detect coherence for some, but not all, possible states of a quantum system. In this work we construct protocols capable of detecting the presence of coherence in an unknown pure quantum state $|\psi\rangle$. Having access to $m$ copies of an unknown pure state $|\psi\rangle$ we show that the sample complexity of any experimental procedure for detecting coherence with constant probability of success $\ge 2/3$ is $\Theta(c(|\psi\rangle)^{-1})$, where $c(|\psi\rangle)$ is the geometric measure of coherence of $|\psi\rangle$. However, assuming access to the unitary $U_\psi$ which prepares the unknown state $|\psi\rangle$, and its inverse $U_\psi^\dagger$, we devise a coherence detecting protocol that employs amplitude-amplification a la Grover, and uses a quadratically smaller number $O(c(|\psi\rangle)^{-1/2})$ of samples. Furthermore, by augmenting amplitude amplification with phase estimation we obtain an experimental estimation of upper bounds on the geometric measure of coherence within additive error $\varepsilon$ with a sample complexity that scales as $O(1/\varepsilon)$ as compared to the $O(1/\varepsilon^2)$ sample complexity of Monte Carlo estimation methods. The average number of samples needed in our amplitude estimation protocol provides a new operational interpretation for the geometric measure of coherence. Finally, we also derive bounds on the amount of noise our protocols are able to tolerate.

We propose a quantum analogue of Bluestein's algorithm (QBA) that implements an exact $N$-point Quantum Fourier Transform (QFT) for arbitrary $N$. Our construction factors the $N$-dimensional QFT unitary into three diagonal quadratic-phase gates and two standard radix-2 QFT subcircuits of size $M = 2^m$ (with $M \ge 2N - 1$). This achieves asymptotic gate complexity $O((\log N)^2)$ and uses $O(\log N)$ qubits, matching the performance of a power-of-two QFT on $m$ qubits while avoiding the need to embed into a larger Hilbert space. We validate the correctness of the algorithm through a concrete implementation in Qiskit and classical simulation, confirming that QBA produces the exact $N$-point discrete Fourier transform on arbitrary-length inputs.

Scalable photonic quantum information technologies require a platform combining quantum light sources, waveguides, and detectors on a single chip. Here, we introduce a van der Waals platform comprising strain-engineered bilayer WSe$_2$ quantum emitters, integrated on multimode WS$_2$ waveguides with grating couplers, enabling efficient on-chip quantum light sources. The emitters exhibit bright, highly polarised emission that couples efficiently into WS$_2$ waveguides. Under discrete-state excitation, we observe high-purity, waveguide-coupled single-photon emission, measured using both single-port and cross-correlated, multi-port photon streams, yielding $g^{(2)}(0) = 0.003^{+0.030}_{-0.003}$ and $g^{(2)}(0) = 0.076\pm0.023$, respectively. For a single output, the out-coupled single-photon count rate at the first lens reaches approximately 357 kHz under continuous-wave discrete-state excitation, corresponding to an estimated minimum waveguide-coupled rate of 1.68 MHz. These results demonstrate an efficient, integrated single-photon source and establish a pathway toward scalable photonic quantum information processing centred around nanoengineered van der Waals materials.