Papers

In this work, we propose a deep learning-based approach for quantum entanglement and discord classification using convolutional autoencoders. We train models to distinguish entangled from separable bipartite states for $d \times d$ systems with local dimension $d$ ranging from two to seven, which enables identification of bound and free entanglement. Through extensive numerical simulations across various quantum state families, we demonstrate that our model achieves high classification accuracy. Furthermore, we leverage the learned representations to generate samples of bound entangled states, the rarest form of entanglement and notoriously difficult to construct analytically. We separately train the same convolutional autoencoders architecture for detecting the presence of quantum discord and show that the model also exhibits high accuracy while requiring significantly less training time.

We develop a systematic analysis of the metaplectic semigroup $\mathrm{Mp}_+(d,\mathbb{C})$ associated with positive complex symplectic matrices, a notion introduced almost simultaneously and independently by Hörmander, Brunet, Kramer, and Howe, thereby extending the classical metaplectic theory beyond the unitary setting. While the existing literature has largely focused on propagators of quadratic evolution equations, for which results are typically obtained via Mehler formulas, our approach is operator-theoretic and symplectic in spirit and adapts techniques from the standard metaplectic group $\mathrm{Mp}(d,\mathbb{R})$ to a substantially broader framework that is not driven by differential problems or particular propagators. This point of view provides deeper insight into the structure of the metaplectic semigroup, and allows us to investigate its generators, polar decomposition, and intertwining relations with complex conjugation and with the Wigner distribution. We then exploit these structural results to characterize, from a metaplectic perspective, classes of time-frequency representations satisfying prescribed structural properties. Finally, we discuss further implications for parabolic equations with complex quadratic Hamiltonians, we study the boundedness of their propagators on modulation spaces, we obtain estimates in time of their operator norms. Finally, we apply our theory to the study of propagation of Wigner singularities.

Classical thermodynamics treats temperature as a state variable characterizing systems in equilibrium with idealized infinite reservoirs. We argue that this framing, while computationally exact, obscures an essential physical reality: any system at finite characteristic energy $E_c = k_B T$ continuously emits thermal radiation and cools unless energy input compensates these losses. What thermodynamics calls “thermal equilibrium” is, at the microscopic level, a dynamically sustained steady state maintained by continuous photon exchange. We derive that the average photon energy required to sustain a Planck distribution is $\langle h\nu \rangle = \pi^4 E_c/[30\,\zeta(3)] \approx 2.701\,E_c$, quantifying the energetic throughput that any real system must sustain to maintain a given temperature. We resolve the apparent contradiction with the purely mechanical Maxwell velocity distribution: billiard-ball kinetics correctly describe the shape of the distribution at a given $E_c$, but cannot account for how $E_c$ is established or maintained against radiative losses in any real system of charged particles. We further show that every finite thermal reservoir is itself maintained by photon exchange at a larger scale, organizing physical systems into a natural hierarchy from individual samples through cryostats, laboratories, and planetary surfaces to stellar interiors, with the classical infinite reservoir emerging as the large-capacity limit within that hierarchy rather than a fundamental physical entity. We also comment on the relation between thermodynamic entropy $S = k_B \ln W$ and the dimensionless entropy $\mathcal{S} = \ln W$, emphasizing that $k_B$ primarily fixes units (J/K) rather than introducing new statistical content. These results do not modify thermodynamics but provide its mechanistic interpretation in terms of quantum electrodynamics.

We show that Andreev spin qubits can be realized in a Josephson junction based on the helical edge states of a two-dimensional topological insulator (quantum spin Hall system) proximized by superconducting films, in the presence of magnetic doping. We demonstrate that the electric dipole transitions between the Andreev spin states induced by the magnetic doping can be harnessed to manipulate the Andreev spin qubit by microwave radiation pulses, without applying an external Zeeman field or invoking ancillary states. We numerically simulate the realization of NOT and Hadamard quantum logic gates, and discuss implementations in realistic setups.

Quantum many-body systems display an extraordinary degree of complexity, yet many of their features are universal: they depend not on microscopic details, but on a few fundamental physical aspects such as symmetries. A central challenge is to distill these universal characteristics from model-specific ones. Random quantum states sampled from a uniform distribution, the Haar measure, provide a powerful framework for capturing this typicality. Here, we experimentally study the entanglement and symmetries of random many-body quantum states generated by evolving simple product states under ergodic Floquet models. We find excellent agreement with the predictions from the Haar-random state ensemble. First, we measure the Rényi-2 entanglement entropy as a function of the subsystem size, observing the Page curve. Second, we probe the subsystem symmetries using entanglement asymmetry. Finally, we measure the moments of partially transposed reduced density matrices obtained by tracing out part of the system in the generated ensembles, thereby revealing distinct entanglement phases. Our results offer an experimental perspective on the typical entanglement and symmetries of many-body quantum systems.

Ultra-peripheral collisions (UPCs) involving relativistic heavy ions are a unique laboratory to study quantum correlations. The intense electromagnetic fields generate high rates of photonuclear interactions, including events involving multiple photon exchange. Multiple photon exchange can result in the production of multiple vector mesons and/or nuclear excitations. These interactions share a common impact parameter, so the photons have the same linear polarization. The shared polarization entangles the particles, leading to unique quantum correlations. The decays of these vector excitations are sensitive to this polarization, allowing for the study of these correlations. This letter will compare classical and quantum calculations of the correlations between these azimuthal directions. The two approaches predict vert different angular correlations. The differences are akin to those seen with polarized photons in tests of Bells inequality. Uniquely, UPC photoproduction can produce final states containing three or more particles, all entangled with the same polarization. These more complex states exhibit additional unique phenomenology, allowing new tests of multi-particle entanglement.

This paper examines the application of a Quantum Support Vector Machine (QSVM) for radarbased aerial target classification using micro-Doppler signatures. Classical features are extracted and reduced via Principal Component Analysis (PCA) to enable efficient quantum encoding. The reduced feature vectors are embedded into a quantum kernel-induced feature space using a fully entangled ZZFeatureMap and classified using a kernel based QSVM. Performance is first evaluated on a quantum simulator and subsequently validated on NISQ-era superconducting quantum hardware, specifically the IBM Torino (133-qubit) and IBM Fez (156-qubit) processors. Experimental results demonstrate that the QSVM achieves competitive classification performance relative to classical SVM baselines while operating on substantially reduced feature dimensionality. Hardware experiments reveal the impact of noise and decoherence and measurement shot count on quantum kernel estimation, and further show improved stability and fidelity on newer Heron r2 architecture. This study provides a systematic comparison between simulator-based and hardware-based QSVM implementations and highlights both the feasibility and current limitations of deploying quantum kernel methods for practical radar signal classification tasks.

Quantum mechanics provides extraordinarily accurate probabilistic predictions, yet the framework remains silent on what distinguishes quantum systems from definite measurement outcomes. This paper develops a measurement-theoretic framework for projective gating. The central object is the $\beta$-bound, an inequality that controls how much probability assignments can drift when gating and measurement fail to commute. For a density operator $\rho$, projector $F$, and effect $E$, with gate-passage probability $s = {\rm Tr}(\rho F)$ and commutator norm $\varepsilon = \|[F, E]\|$, the symmetric partial-gating drift satisfies $|\Delta p_F(E)| \leq 2 \sqrt{(1 - s)/s} \cdot \varepsilon$. The constant 2 is sharp. We introduce two diagnostic quantities: the coherence witness $W(\rho, F) = \|F \rho (I - F)\|_1$, measuring cross-boundary coherence, and the record fidelity gap $\Delta_T(\rho_F, R)$, measuring expectation-value change under symmetrisation. Three experimental vignettes demonstrate falsifiability: Hong–Ou–Mandel interferometry, atomic energy-basis dephasing, and decoherence-induced classicality. The framework is operational and interpretation-neutral, compatible with Everettian, Bohmian, QBist, and collapse approaches. It provides quantitative structure that any interpretation must accommodate, along with a template for experimental tests.

We construct a quantum Schwinger-Keldysh (SK) effective field theory for the diffusive hydrodynamics of a conserved scalar field. Quantum corrections within the SK framework are guided by fluctuation-dissipation relations, enforced via a dynamical Kubo-Martin-Schwinger (KMS) symmetry. We find that the KMS symmetry necessarily generates fluctuation contributions in the SK effective action at all orders in the noise field, thereby giving rise to intrinsically non-Gaussian noise. We use our results to compute one-loop quantum corrections to the two-point density-density retarded correlation function, leading to a quantum generalization of hydrodynamic long-time tails. Our results apply at arbitrarily high orders in $\hbar$. The one-loop results for retarded correlation functions have been expressed in terms of a family of polynomials. We also provide a closed-form expression for the one-loop results at leading order in the wavevector expansion.

Interacting spin systems in solids underpin a wide range of quantum technologies, from quantum sensors and single-photon sources to spin-defect-based quantum registers and processors. We develop a quantum-computer-aided framework for simulating such devices using a general many-body electron-spin-resonance Hamiltonian that incorporates zero-field splitting, the Zeeman effect, hyperfine interactions, dipole-dipole spin-spin interactions, and electron-phonon decoherence. Within this framework, we combine Gray-encoded qudit-to-qubit mappings, qubit-wise commuting aggregation, and a multi-reference selected quantum Krylov fast-forwarding hybrid algorithm, aiming to access extended-time dynamics within the constraints of NISQ and early fault-tolerant hardware. Numerical simulations demonstrate the computation of operationally useful quantities including autocorrelation functions up to $\sim100$ ns, together with microwave absorption spectra and the $\ell_1$-norm of coherence, achieving 18-30$\%$ reductions in gate counts and circuit depth for Trotterized time-evolution circuits compared to unoptimized implementations. Using the nitrogen vacancy center in diamond as a testbed, we benchmark the framework against classical simulations and identify the reference-state selection in sQKFF as the primary factor governing accuracy at fixed hardware cost. This methodology provides a flexible blueprint for using quantum computers to design, compare, and optimize solid-state spin-qubit technologies under experimentally realistic conditions.

Open quantum systems interact with their environment, leading to nonunitary dynamics. We investigate the thermodynamics of linear Open Quantum Walks (OQWs), a class of quantum walks whose dynamics is entirely driven by the environment. We define an equilibrium temperature, identify a population inversion near a finite critical value of a control parameter, analyze the thermalization process, and develop the statistical mechanics needed to describe the thermodynamical properties of linear OQWs. We also study nonequilibrium thermodynamics by analyzing the time evolution of entropy, energy, and temperature, while providing analytical tools to understand the system's evolution as it converges to the thermalized state. We examine the validity of the second and third laws of thermodynamics in this setting. Finally, we employ these developments to shed light on dissipative quantum computation within the OQW framework.

A growing variety of optically accessible spin qubits have emerged in recent years as key components for quantum sensors, qubits, and quantum memories. However, the scalability of conventional spin-based quantum architectures remains limited by direct microwave delivery, which introduces thermal noise, electromagnetic cross-talk, and design constraints for cryogenic, high-field, and distributed systems. In this work, we present a unified framework for RF-over-fiber (RFoF) control of optically accessible spins through RFoF optically detected magnetic resonance (ODMR) spectroscopy of nitrogen-vacancy (NV) centers in diamond. The RFoF platform relies on an electro-optically modulated telecom-band laser that transmits microwave signals over fiber and a high-speed photodiode that recovers the RF waveform to drive NV center spin transitions. We obtain an RFoF efficiency of 1.81% at 2.90~GHz, corresponding to $P_{\mathrm{RF,out}}=-0.7$~dBm. The RFoF architecture provides a path toward low-noise, thermally isolated, and cryo-compatible ODMR systems bridging conventional spin-based quantum sensing protocols with emerging distributed quantum technologies.

Quantum machine learning (QML) is often listed as a promising candidate for useful applications of quantum computers, in part due to numerous proofs of possible quantum advantages. A central question is how small a role quantum computers can play while still enabling provable learning advantages over classical methods. We study an especially restricted setting in which a quantum computer is used only as a feature extractor: it acts independently on individual data points, without access to labels or global dataset information, is available only to augment the training set, and is not available at deployment. Training and deployment are therefore carried out by fully classical learners on a dataset augmented with quantum-generated features. We formalize this model by adapting the classical framework of Learning Under Privileged Information (LUPI) to the quantum case, which we call Learning Under Quantum Privileged Information (LUQPI). Within this framework, we show that even such minimally involved quantum feature extraction, available only during training, can yield exponential quantum-classical separations for suitable concept classes and data distributions under reasonable computational assumptions. We further situate LUQPI within a taxonomy of related quantum and classical learning settings and show how standard classical machinery, most notably the SVM+ algorithm, can exploit quantum-augmented data. Finally, we present numerical experiments in a physically motivated many-body setting, where privileged quantum features are expectation values of observables on ground states, and observe consistent performance gains for LUQPI-style models over strong classical baselines.

Distance metrics are central to machine learning, yet distances between ensembles of quantum states remain poorly understood due to fundamental quantum measurement constraints. We introduce a hierarchy of integral probability metrics, termed MMD-$k$, which generalizes the maximum mean discrepancy to quantum ensembles and exhibits a strict trade-off between discriminative power and statistical efficiency as the moment order $k$ increases. For pure-state ensembles of size $N$, estimating MMD-$k$ with arbitrary measurement schemes requires $\Theta(N^{1-1/k})$ samples for constant $k$. At the same time, we prove that any stable distance metric with full discriminative power admits an $O(N\log N)$ upper bound and an $\Omega(N)$ instance-gap lower bound. For quantum Wasserstein distance, with sufficiently large fixed state dimension, we establish a nearly linear lower bound in the ensemble size at constant additive accuracy, together with an $O(N\log N)$ upper bound. These results provide principled guidance for the design of loss functions in quantum machine learning, as we illustrate in training quantum denoising diffusion probabilistic models.

Superconducting resonators and qubits are limited by dielectric losses from surface oxides. Surface oxides are mitigated through various strategies such as the addition of a metal capping layer, surface passivation, and acid processing. In this study, we demonstrate the use of X-ray photoelectron spectroscopy (XPS) as a rapid characterization tool to study the effectiveness cap layers for niobium for further device fabrication. We non-destructively evaluate 17 capping layers to characterize their ability to prevent oxygen diffusion, and the effects of standard fabrication processes – annealing, resist stripping, and acid cleaning. We downselect for resilient capping layers and test their microwave resonator performance.

We compare several definitions of entropy production rate introduced in the literature from a large variety of situations and motivations, and then analyze their relations with memory effects. Considering a relevant experimental example of a qubit interacting with a single bosonic mode playing the role of a finite bath, we show that all definitions of entropy production coincide at weak coupling. In a stronger coupling regime, significant discrepancies emerge between the different entropy production rates, although some similarities in the overall behaviour remain. However, surprisingly, two of these definitions –one based on local quantities of the system and the other on non-local quantities– coincide exactly, even in the case of strong coupling. Finally, a high degree of correspondence is observed when memory effects characterized by P-divisibility are compared with the sign of all entropy production rates in the case of weak coupling. Such correspondence degrades at stronger coupling, leading us to extend the concept of entropy production to the dynamical map. We show a perfect equivalence between the sign of this enlarged concept of entropy production and P-divisibility, both numerically and analytically, in the case of phase-covariant master equations.

We propose a method to suppress collisional loss in strongly dipolar, rotationally excited ultracold molecules using a combination of static (dc) and microwave (ac) electric fields. By tuning two excited pair molecular rotational states into a Förster resonance with a dc field, simultaneously driving excited rotational transitions with an ac field removes all long-range bound states, allowing near complete suppression of all two- and three-body collisional loss channels. While permitting tunable dipolar and anti-dipolar interactions, this bound-state-free ac/dc scheme is not subject to photon-changing collisions that are the primary source of two-body loss in shielding with two microwave fields, used to achieve the first molecular Bose-Einstein condensate [Bigagli et al., Nature 631, 289 (2024)]. Using NaCs as a representative example for strongly dipolar molecules, close-coupling calculations are performed to show that bound-state-free shielding can achieve ratios of elastic-to-loss rates $\gtrsim 10^{6}$ at 100 nK, with currently accessible ac and dc field generation technologies. This work opens new opportunities for realizing large, long-lived samples of strongly interacting degenerate molecular gases with tunable long-range interactions.

We investigate a hybrid quantum-classical algorithm for solving the Maximum Independent Set (MIS) problem on regular graphs, combining the Quantum Approximate Optimization Algorithm (QAOA) with a minimal degree classical greedy algorithm. The method leverages pre-computed QAOA angles, derived from depth-$p$ QAOA circuits on regular trees, to compute local expectation values and inform sequential greedy decisions that progressively build an independent set. This hybrid approach maintains shallow quantum circuit and avoids instance-specific parameter training, making it well-suited for implementation on current quantum hardware: we have implemented the algorithm on a 20 qubit IQM superconducting device to find independent sets in graphs with thousands of nodes. We perform tensor network simulations to evaluate the performance of the algorithm beyond the reach of current quantum hardware and compare to established classical heuristics. Our results show that even at low depth ($p=4$), the quantum-enhanced greedy method significantly outperforms purely classical greedy baselines as well as more sophisticated approximation algorithms. The modular structure of the algorithm and relatively low quantum resource requirements make it a compelling candidate for scalable, hybrid optimization in the NISQ era and beyond.

Each cycle of a quantum computation requires a quantum state initialisation. For semiconductor-based quantum platforms, initialisation is typically performed via slow microwave processes and usually requires cooling to temperatures where only the lowest quantum level is occupied. In silicon, boron atoms are the most common impurities. They bind holes in orbitals including an effective spin-3/2 ground state as well as excited states analogous to the Rydberg series for hydrogen. Here we show that initialisation temperature demands may be relaxed and speeds increased over a thousand-fold by importing, from atomic physics, the procedure of optical pumping via excited orbital states to preferentially occupy a target ground state spin. Spin relaxation within the orbital ground state of unstrained silicon is too fast to measure for conventional pulsed microwave technology, except at temperatures below 2 K, implying a need not only for fast state preparation but also fast state readout. Circularly polarised ~10 THz photon pulses from a free electron laser meet both needs at temperatures above 3 K: a 9 ps pulse enhances the population of one spin eigenstate for the "1s"-like ground state orbital, and the second interrogates this imbalance in spin population. Using parameters given by our data, we calculate that it should be possible to initialise 99% of spins for boron in strained silicon within 250 ps at 3 K. The speedup of both state preparation and measurement gained for THz rather than microwave photons should be explored for the many other solid state quantum systems hosting THz excitations potentially useful as intermediate states.

Distinguishability is central to quantum information theory, but a quantitative measure for distinguishing topological defects–realizations of generalized symmetries in quantum field theory (QFT)–has been lacking. We introduce the notion of the defect relative entropy to fill this gap for topological defects in two-dimensional conformal field theories (CFTs). For defects on a circle, we derive a universal formula that reduces defect relative entropy to a Kullback–Leibler divergence determined entirely by the modular $\mathcal{S}$-matrix and defect coefficients. Thus, the algebraic data governing modular transformations also determines defect distinguishability. A striking consequence is that certain distinct defects can have vanishing relative entropy when restricted to one side, implying that an observer confined to that side cannot distinguish them. This gives rise to information-theoretic equivalence classes of defects, which we term defect relative sectors. We further introduce the sandwiched defect Rényi relative entropy and defect fidelity, derive general formulas for these quantities. Explicit calculations in the Ising model, tricritical Ising model, and $\widehat{su}(2)_k$ WZW models illustrate our results.

Differential geometries derived from tensor decompositions have been extensively studied and provided the foundations for a variety of efficient numerical methods. Despite the practical success of the tensor ring (TR) decomposition, its intrinsic geometry remains less understood, primarily due to the underlying ring structure and the resulting nontrivial gauge invariance. We establish the quotient geometry and immersed-submanifold structure of TR decomposition by imposing full-rank conditions on all unfolding matrices of the core tensors and capturing the gauge invariance. The intrinsic ring structure of TR leads to an analysis that is substantially different from other tensor formats. Additionally, for the uniform TR decomposition, where all core tensors are identical and the manifold structure is known, we derive explicit parameterizations for the vertical and horizontal spaces, which enable Riemannian optimization. Numerical experiments validate the developed geometries via tensor ring completion tasks.

We consider the problem of covert communication over the entanglement-assisted (EA) bosonic multiple access channel (MAC). We derive a closed-form achievable rate region for the general EA bosonic MAC using high-order phase-shift keying (PSK) modulation. Specifically, we demonstrate that in the low-photon regime the capacity region collapses into a rectangle, asymptotically matching the point-to-point capacity as multi-user interference vanishes. We also characterize an achievable covert throughput region, showing that entanglement assistance enables an aggregate throughput scaling of \(O(\sqrt{n} \log n)\) covert bits with the block length $n$ for both senders, surpassing the square-root law as in the point-to-point case. Our analysis reveals that the joint covertness constraint imposes a linear trade-off between the senders throughput.

The Bravyi-König (BK) theorem is an important no-go theorem for the dynamics of topological stabiliser quantum error correcting codes. It states that any logical operation on a $D$-dimensional topological stabiliser code that can be implemented by a short-depth circuit acts on the codespace as an element of the $D$-th level of the Clifford hierarchy. In recent years, a new type of quantum error correcting codes based on Pauli stabilisers, dubbed Floquet codes, has been introduced. In Floquet codes, syndrome measurements are arranged such that they dynamically generate a codespace at each time step. Here, we show that the BK theorem holds for a definition of Floquet codes based on locally conjugate stabiliser groups. Moreover, we introduce and define a class of generalised unitaries in Floquet codes that need not preserve the codespace at each time step, but that combined with the measurements constitute a valid logical operation. We derive a canonical form of these generalised unitaries and show that the BK theorem holds for them too.

Protecting quantum information through quantum error correction (QEC) is a cornerstone of future fault-tolerant quantum computation. However, current QEC-protected logical qubits have only achieved coherence times about twice those of their best physical constituents. Here, we show that the primary barrier to higher QEC gains is ancilla-induced operational errors rather than intrinsic cavity coherence. To overcome this bottleneck, we introduce error-detectable universal control of bosonic modes, wherein ancilla relaxation events are detected and the corresponding trajectories discarded, thereby suppressing operational errors on logical qubits. For binomial codes, we demonstrate universal gates with fidelities exceeding $99.6\%$ and QEC gains of $8.33\times$ beyond break-even. Our results establish that gains beyond $10\times$ are achievable with state-of-the-art devices, establishing a path toward fault-tolerant bosonic quantum computing.

We introduce a principle, implicitly contained in Schroedinger's paper (Schr35), which allows a proof of the non-existence of the EPR-locality paradox in the Copenhagen interpretation of quantum mechanics. The paradox is shown to be well-posed already in the simplest example of an entangled state of two spins one-half, independently of the (well-taken) objections by Araki and Yanase that the measurement of spin is not a local measurement. We assume that any measurement results in the collapse of the wave-packet.

Determining when the multiparameter quantum Cramér–Rao bound (QCRB) is saturable with experimentally relevant single-copy measurements is a central open problem in quantum metrology. Here we establish an equivalence between QCRB saturation and the simultaneous hollowization of a set of traceless operators associated with the estimation model, i.e., the existence of complete (generally nonorthogonal) bases in which all corresponding diagonal matrix elements vanish. This formulation yields a geometric characterization: optimal rank-one measurement vectors are confined to a subspace orthogonal to a state-determined Hermitian span. This provides a direct criterion to construct optimal Positive Operator-Valued Measures(POVMs). We then identify conditions under which the partial commutativity condition proposed in [Phys. Rev. A 100, 032104(2019)] becomes necessary and sufficient for the saturation of the QCRB, demonstrate that this condition is not always sufficient, and prove the counter-intuitive uselessness of informationally-complete POVMs.

Hybrid quantum-classical learning models increasingly integrate neural networks with variational quantum circuits (VQCs) to exploit complementary inductive biases. However, many existing approaches rely on tightly coupled architectures or task-specific encoders, limiting conceptual clarity, generality, and transferability across learning settings. In this work, we introduce Quantum LEGO Learning, a modular and architecture-agnostic learning framework that treats classical and quantum components as reusable, composable learning blocks with well-defined roles. Within this framework, a pre-trained classical neural network serves as a frozen feature block, while a VQC acts as a trainable adaptive module that operates on structured representations rather than raw inputs. This separation enables efficient learning under constrained quantum resources and provides a principled abstraction for analyzing hybrid models. We develop a block-wise generalization theory that decomposes learning error into approximation and estimation components, explicitly characterizing how the complexity and training status of each block influence overall performance. Our analysis generalizes prior tensor-network-specific results and identifies conditions under which quantum modules provide representational advantages over comparably sized classical heads. Empirically, we validate the framework through systematic block-swap experiments across frozen feature extractors and both quantum and classical adaptive heads. Experiments on quantum dot classification demonstrate stable optimization, reduced sensitivity to qubit count, and robustness to realistic noise.

Quantum machine learning (QML) models often require deep, parameterized circuits to capture complex frequency components, limiting their scalability and near-term implementation. We introduce Quantum Random Features (QRF) and Quantum Dynamical Random Features (QDRF), lightweight quantum reservoir models inspired by classical random Fourier features (RFF) that generate high-dimensional spectral representations without variational optimization. Using $Z$-rotation encoding combined with random permutations or Hamiltonian dynamics, these models achieve $N_f$-dimensional feature maps at preprocessing cost $O(\log(N_f))$. Spectral analysis shows that QRF and QDRF reproduce the behavior of RFF, while simulations on Fashion-MNIST reach up to 89.3% accuracy-matching or surpassing classical baselines with scalable qubit requirements. By linking spectral theory with experimentally feasible quantum dynamics, this work provides a compact and hardware-compatible route to scalable quantum learning.

Decoders are a critical component of fault-tolerant quantum computing. They must identify errors based on syndrome measurements to correct quantum states. While finding the optimal correction is NP-hard and thus extremely difficult, approximate decoders with faster runtime often rely on uncontrolled heuristics. In this work, we propose a family of hierarchical quantum decoders with a tunable trade-off between speed and accuracy while retaining guarantees of optimality. We use the Lasserre Sum-of-Squares (SOS) hierarchy from optimization theory to relax the decoding problem. This approach creates a sequence of Semidefinite Programs (SDPs). Lower levels of the hierarchy are faster but approximate, while higher levels are slower but more accurate. We demonstrate that even low levels of this hierarchy significantly outperform standard Linear Programming relaxations. Our results on rotated surface codes and honeycomb color codes show that the SOS decoder approaches the performance of exact decoding. We find that Levels 2 and 3 of our hierarchy perform nearly as well as the exact solver. We analyze the convergence using rank-loop criteria and compare the method against other relaxation schemes. This work bridges the gap between fast heuristics and rigorous optimal decoding.

Many quantum software development kits provide a suite of circuit optimisation passes. These passes have been highly optimised and tested in isolation. However, the order in which they are applied is left to the user, or else defined in general-purpose default pass sequences. While general-purpose sequences miss opportunities for optimisation which are particular to individual circuits, designing pass sequences bespoke to particular circuits requires exceptional knowledge about quantum circuit design and optimisation. Here we propose and demonstrate training a reinforcement learning agent to compose optimisation-pass sequences. In particular the agent's action space consists of passes for two-qubit gate count reduction used in default PyTKET pass sequences. For the circuits in our diverse test set, the (mean, median) fraction of two-qubit gates removed by the agent is $(57.7\%, \ 56.7 \%)$, compared to $(41.8 \%, \ 50.0 \%)$ for the next best default pass sequence. In doing so our model demonstrates the ability to forgo reward to improve the final two-qubit gate count. Our approach clearly separates the problem of designing circuit optimisation passes from the problem of using them optimally in practice. We expect this separation of concerns to facilitate innovations in both areas.