Papers

Re-visiting the problem of the coupled electronic–nuclear motion, we prove that the so called `mean-field' Ehrenfest picture is an exact theory, rather than an approximation, in the classical limit for nuclei. By establishing its full equivalence to the much more involved Exact Factorization approach to the problem (Abedi et al., Europhys. Lett. 106, 33001 (2014)), our conclusion rehabilitates the mean-field Ehrenfest molecular dynamics as a simple, effective, while formally exact scheme, amenable to the use within the framework of the time-dependent density functional theory.

In this paper, we do not try to solve the measurement problem, but rather to properly formulate it. One of the reasons why it still lacks a precise, agreed definition is that the problem may take very different aspects depending on the interpretation of quantum mechanics embraced. Inspired by the methodology of theory-independent results like Bell's theorem, we propose to identify the common root of the puzzle in an interpretation-independent way i.e. as a property of the empirical statistics only, before deriving its philosophical consequences. The key observation is that quantum matter can not be described by a Kolmogorovian probabilistic theory. Arguing that the Kolmogorov axioms of probability theory are the postulates of epistemic uncertainty leads us to reformulate the measurement problem as the impossibility to build an ontology independent of epistemology for quantum matter. Said differently, there exists no God's-eye view on quantum systems. Although it is meaningless to solve the measurement problem as defined in this way, insofar as it is a feature of the universe's statistics, such a formulation may on the other hand bring side benefits. In particular, we argue that it allows to: (i) shed a new light on the variety of interpretations; (ii) propose a fundamental reason why quantum mechanics and general relativity are so incompatible, not relying on purely mathematical or technical arguments; (iii) guide the quest for quantum gravity.

Self-sustained oscillations combine finite-amplitude stabilization with a neutral phase degree of freedom. We develop this bifurcation-based framework for driven-dissipative collective spins and show that the microscopic structure of the U(1)-covariant dissipation selects the background attractor, while the explicit U(1)-breaking channel governs its local bifurcation response. In the thermodynamic-limit mean-field dynamics, a single linear U(1)-covariant jump produces only polar fixed-point backgrounds, whereas nonlinear covariant dissipation provides amplitude-dependent saturation and stabilizes a finite-latitude self-sustained-oscillator manifold through a supercritical Hopf bifurcation. Under coherent U(1) breaking, exact resonance leads to a reversible double-zero degeneracy with vanishing critical frequency rather than a standard Hopf onset. Finite detuning unfolds this singularity into a genuine finite-frequency Hopf boundary, which exists only on the self-sustained-oscillator side and can be either supercritical or subcritical. By contrast, a single linear dissipative U(1)-breaking jump cannot generate a standard Hopf instability: when its phase-pinning invariant vanishes the azimuthal direction remains neutral, whereas otherwise the phase-locked fixed points have a purely real Jacobian spectrum. These results establish a general design principle: nonlinear covariant dissipation selects the selfsustained background, while the structure of the symmetry-breaking channel determines whether the resulting local response is double-zero, genuinely Hopf, or non-Hopf.

QBism understands quantum mechanics to be probability theory supplemented by additional nonclassical coherence conditions. In this dissertation, we develop these nonclassical coherence conditions from first principles, emphasizing the role of a well chosen reference measurement. After treating standard probability on subjective Bayesian lines, we demonstrate an equivalence between the QBist approach and the existing framework of generalized probabilistic theories. We show that the fundamental nonclassical coherence relation may almost always be taken to be a gentle modification of the law of total probability, and give a coherentist account of when an experimental scenario has a classical explanation. Finally, we show that when the reference measurement is chosen to correspond to a complex projective 3-design, the shape of quantum state space is implicit in the probabilities which characterize the reference measurement itself. Thus coherence with this single reference measurement, properly understood, implies coherence with all of finite dimensional quantum mechanics. We then attempt a modest reconstruction of quantum theory along these lines, one practical consequence of which is a method for self-testing complex projective $t$-designs for $t\ge 3$ in a theory-agnostic way.

Let $D=2^n$ and $M=3n+9\binom n2$. We study the right-invariant one-step-cliff metric $d_Q$ on $\operatorname{PU}(D)$, with unit penalty on Pauli weights one and two and penalty $Q$ on all higher weights. If $M/Q_D\to0$ and $MQ_D^{3/4}/D^2\to0$, then, for every fixed $0<x<\pi/\sqrt3$, \[ \mu_D\bigl(B_{Q_D}([I],x\sqrt{Q_D})\bigr)\le e^{-c_xD^2}. \] Here $\mu_D$ is normalized Haar measure. Thus the Haar-typical distance from the identity and the diameter are both asymptotic to $(\pi/\sqrt3)\sqrt{Q_D}$ throughout the window $M\ll Q_D\ll D^{8/3}M^{-4/3}$. Choosing $Q_D=\kappa D^{8/3}M^{-4/3}$ with sufficiently small fixed $\kappa>0$ yields a Haar-typical lower bound of order $D^{4/3}M^{-2/3}$ for the corresponding infinite-cliff Carnot–Carathéodory distance, outside an $e^{-\Omega(D^2)}$ exceptional set. The infinite-cliff diameter therefore has exponential lower rate at least $4/3$, disproving Brown's exponent-one conjecture. The same estimate gives a fixed-error no-ancilla two-qubit circuit lower bound of the same order.

Classically equivalent formulations of an optimization problem need not lead to equivalent quantum algorithms. For MaxCut, fixing the value of a single vertex removes a simple global symmetry without changing the underlying optimization problem, yet it can substantially alter the quantum dynamics generated by the Quantum Approximate Optimization Algorithm (QAOA). These dynamics are captured by the circuit's dynamical Lie algebra (DLA), whose direct construction can become exponentially expensive. Here we show that, for symmetry-reduced QAOA on trees, substantial information about the reduced DLA can instead be obtained efficiently from the graph alone. We introduce a polynomial classical algorithm that recursively distinguishes vertices using shortest path structure and degree parity. When all vertices are resolved individually, the method determines the complete reduced DLA and, under the corresponding graph conditions, certifies maximal expressibility of the reduced QAOA ansatz. Even when full resolution is not achieved, the algorithm identifies embedded subalgebras, provides rigorous lower bounds on DLA dimension, and certifies controllable subsystems. Our theoretical and experimental results show how classical graph structure can be used to diagnose and potentially guide the quantum dynamics of variational algorithms before running them on quantum hardware.

We propose all-optical tests of photon-photon interactions in the matter vacuum using standing-wave laser interferometers, which do not require external magnetic fields and use conventional laser sources. We show that the interferometric detection of photon-photon scattering predicted by quantum electrodynamics is within reach of laboratory-scale experiments with a sensitivity that improves nonlinearly with the circulating power within the cavity. We outline how such an experiment could be adapted to probe properties of quantum fields beyond the Standard Model of particle physics.

In this work, we extend the scattering quantum walk (SQW) framework to a lattice of energy-dependent point interactions. This yields, within the coined quantum walk (CQW) formalism, a coin operator that is directly related to the scattering matrix of zero-range potentials. The model thus provides a discrete-time quantum-walk (DTQW) analog of a periodic array of point interactions of the Kronig-Penney type, where the walker's wavenumber serves as a continuous, physically transparent control parameter for the coin operation. We analyze the spectra and the dynamics of position probability and entanglement, yielding distinct results for specific energies and point interactions. We relate the spectral structure to the spatial probability distribution and explicitly characterize the long-time entanglement behavior for each point interaction. The transmission modulus determines the quasienergy gap, bandwidth, and maximum group velocity, while also controlling the long-time coin-position entanglement for the initial state considered. The four families of one-dimensional point interactions ($\delta$, $\delta'$, crossed and asymmetric) realize qualitatively distinct transmission profiles and span the full range of behavior, including enhanced or strongly suppressed spreading and oscillatory entanglement.

Quantum Schrödinger bridge constructions establish the existence of a conditioned process under a positivity hypothesis on the endpoint data, and three independent ones adopt it. We show that hypothesis fails on a definite locus once the conditioned object is the two-state amplitude $\phi^*\psi$ of a pre- and post-selected pair on configuration space, and that the failure is testable on recorded data. Whenever $\phi^*\psi$ has a moving zero of order $k$ across which probability flows, no diffusion of constant diffusion coefficient can both carry the conditioned density and avoid the nodal curve: the current velocity it would need grows as the inverse $2k$-th power of the distance to that curve and points toward it on one side, placing the curve at finite scale distance, so it is reached and not merely approached. Identifying the weak momentum with a bridge drift fails independently: for a free particle post-selected in position the current velocity is exactly minus the drift of the bridge to the target. The positive Doob $h$-transform and the Bernstein conditioning built on it exist wherever $\phi^*\psi$ is nodeless and fail on the nodal curve. There the osmotic part of the weak momentum diverges as the inverse distance to the zero and changes sign across it with a coefficient set by $k$, while the current part stays bounded; that boundedness rests on the signed factorization of the real-envelope class and hides the obstruction from any picture built on the current velocity alone. A measured fringe visibility fixes a single length, which puts a Lorentzian of order $10^{-3}$ into the current channel reconstructed in the two-slit trajectory experiment if the contrast is limited by an off-axis zero, and nothing there if by incoherence. The results are one-dimensional, covering the separable transverse field of a two-slit geometry, not general two-dimensional vortices.

Quantum computers promise advantages for simulating strongly correlated quantum many-body systems, like atomic nuclei, that are beyond the reach of classical computers. Realizing this potential requires understanding the quantum complexity structure of the target problem. We investigate the time-evolution of two key indicators of quantum complexity, bipartite entanglement entropy and non-local magic (non-stabilizerness), in nuclear reaction dynamics. We analyze two representative dynamical processes: scattering in a one-dimensional model of strongly interacting fermions governed by the Negele potential, and a realistic simulation of $^{240}$Pu fission within time-dependent Hartree-Fock-Bogoliubov (TDHFB) theory. In the former case, we find that interactions dynamically generate both entanglement and non-local magic, leaving persistent signatures of quantum complexity in the outgoing states. In the latter, we observe that substantial quantum complexity survives in the spatial bipartition of daughter fragments well beyond scission. The presence of significant non-local magic and entanglement in both cases strongly indicate that quantum computers would provide substantial advantages for accurately simulating nuclear reaction dynamics.

We introduce a diagnostic framework based on the full probability distribution of quantum coherence to probe single-particle and many-body phases at finite temperature. We first apply this approach to the localization transition in the non-interacting Aubry-André model and then extend the analysis to its interacting counterpart, whose phase diagram is substantially richer. We show that the moments of the coherence distribution provide clear signatures of quantum phase transitions and capture the emergence of many-body phases. More importantly, we find that the entropy of the coherence distribution emerges as an even more powerful indicator, retaining clear signatures of the underlying quantum phases while remaining remarkably robust against increasing thermal fluctuations.

Hamiltonian embeddings can represent dissipative nonreciprocal classical dynamics exactly on invariant manifolds of enlarged reciprocal systems. We show that canonical quantization of such an embedding need not commute with reduction to the target dynamics. For the mirror construction recently introduced for pairwise nonreciprocal interactions, the invariant manifold is Lagrangian. Exact quantum enforcement of the mirror condition therefore removes the dynamical sector rather than producing a quantum analogue of the reduced flow. If the constraint is imposed only semiclassically, contraction of the target dynamics generates inverse-transpose expansion in the conjugate mirror directions. Quantum uncertainty then gives $\ln D\ge\Xi(t)+n\ln[\pi/(\sigma\epsilon)]$, where $\Xi=-\ln|\det M|$ is the accumulated contraction and $D$ the torus Hilbert-space dimension. Exact finite-dimensional Weyl evolution of one- and two-degree-of-freedom nonreciprocal models confirms the resulting logarithmic correspondence time, including its predicted change when the initial localization scales with $\hbar$. Thus the classical embedding is exact, but its direct canonical quantization is a singular semiclassical construction.

A key challenge in practical quantum machine learning (QML), particularly for discriminative tasks such as classification, is the limited capacity of near-term quantum devices to encode high-dimensional classical data into small quantum registers. In optimized basis-encoded (bit-bit) settings, this constraint leads to cross-class collisions, where samples with different labels are mapped to the same discrete bit-string and thus become indistinguishable to any downstream model. In this work, we investigate how data representation affects QML performance under such severe information bottlenecks. We introduce discretization-aware fine-tuning (DAFT), a method that adapts a pre-trained chemical foundation model to produce representations that remain informative after quantization. DAFT reduces collision probability through a differentiable soft collision loss. We evaluate both quantum and classical models under a controlled setting in which they receive identical discretized bit-string inputs, isolating the effect of representation from model architecture. On the blood-brain barrier penetration (BBBP) molecular property prediction benchmark using ChemBERTa-77M, DAFT reduces collision counts by several orders of magnitude and improves quantum classification accuracy by more than 12 percentage points compared to a frozen backbone. Importantly, without DAFT, classical models outperform QML under the same input constraints. With DAFT, however, this comparison reverses at higher qubit counts. At 10 qubits, the quantum model surpasses a matched classical baseline trained on identical bit-strings (0.883 vs. 0.855, $p = 0.026$). These results show that, in information-constrained regimes, achieving a quantum advantage critically depends on aligning continuous representations with discrete quantum encodings.

Quantum error correction (QEC) is beginning to enable logical operations that outperform their unencoded physical counterparts, but useful fault-tolerant computation will require more than low-error quantum memory. An effective architecture must orchestrate efficient logical encoding, low-overhead logical operations, and access to the non-Clifford resources required for universal computation. Here, we introduce and experimentally validate such an architecture based on the $[[20,2,6]]$ $C_4$-Helix code, designed for the early fault-tolerant regime. Using Quantinuum Helios, a 98-qubit trapped-ion quantum processor, we experimentally demonstrate the principal components of this architecture: we perform repeated quantum error correction with an error of $4.6^{+6.2}_{-2.6}\times10^{-5}$ per logical qubit per QEC cycle. We benchmark the complete Clifford group on the two logical qubits of a single codeblock under active error correction, obtaining an error of $2.8^{+1.0}_{-1.6}\times 10^{-4}$ per two-qubit logical Clifford. We further demonstrate a fault-tolerant chain-map interface between $C_4$-Helix and a distance-5 surface code, preparing a heterogeneous three-logical-qubit GHZ state with a fidelity lower bound of $99.925^{+0.068}_{-0.245}\%$. In each case, the encoded implementation outperforms its corresponding unencoded physical baseline without relying on postselection. Circuit-level simulations indicate that improvements in physical fidelity bring the same architecture into the $10^{-6}$-$10^{-8}$ logical-error regime targeted for early fault-tolerant computation. Together, these results establish $C_4$-Helix as a hardware-validated fault-tolerant architecture rather than a bare quantum memory.

Schrödinger bridges and entropic optimal transport are usually formulated as stochastic interpolation problems between initial and final probability distributions. In their computational form, the bridge potentials are obtained by Sinkhorn or iterative proportional fitting, and are often regarded as auxiliary scaling functions. We show that for continuously monitored quantum systems, these potentials acquire a direct measurement-theoretic meaning. The mathematical structure of conditional quantum trajectory theory induces a Fokker–Planck equation on quantum state space. Conditioning this diffusion on a terminal distribution or a terminal measurement effect produces a Doob/Sinkhorn potential whose directional derivative along a unitary control vector field is the imaginary part of a generalized weak value. The same construction connects the Schrödinger-bridge viewpoint to the optimal-path framework for continuously monitored trajectories: the backward bridge potential plays the role of an effect-like costate, and its weak-value directional derivative gives the local control signal. By specifying the desired endpoint distribution, the induced drift produced by the Schrödinger bridge solution is the control solution that minimizes the quadratic cost feedback law, guiding the distribution to its desired endpoint. We quantify the control score of the available control Hamiltonian as a logarithmic directional derivative of the bridge potential, or an imaginary weak value. Three explicit examples identify weak measurement as a natural entropic regularization mechanism for quantum state transport and gives a route from Sinkhorn scaling to quantum feedback and Hamiltonian control synthesis for practical optimal control.

Non-KAM (Kolmogorov-Arnold-Moser) systems, when subjected to weak time-dependent perturbations, exhibit an abrupt transition to classical chaos through the breakdown of invariant phase-space tori. We showcase the utilization of non-KAM systems in the quantum regime as quantum sensors, leveraging their sensitivity at resonances. Quantum Fisher information (QFI) is a central quantity in quantum parameter estimation theory that measures how much information a quantum state contains about an unknown parameter that is encoded into it. In other words, it quantifies the sensitivity of a quantum state to small changes in that parameter. In this work, through numerical analysis in conjunction with analytical results, we study the performance of the non-KAM systems for quantum sensing applications by computing the QFI. We find that the growth of the QFI is remarkably enhanced when the resonance condition is satisfied. For frequency estimation under Floquet unitary encodings, we derive a transport bound: if the mean excitation number grows as $\langle\hat n(t)\rangle\sim t^{\alpha}$, the QFI obeys $I(t)\lesssim t^{2\alpha+2}$. The quantum kicked harmonic oscillator, a paradigmatic non-KAM system, realizes the full hierarchy: localized dynamics ($\alpha=0$) yield quadratic growth, delocalized diffusion along stochastic webs ($\alpha=1$) yields quartic growth, and translationally invariant resonances ($\alpha=2$) saturate the bound with anomalous hexic growth, $I(t)\sim t^{6}$, established analytically at resonance $R=2$ and numerically at $R=4$. The enhancement stems from resonance-induced translational symmetry rather than exponential instability, identifying non-KAM resonances as a metrological resource distinct from chaos-assisted and criticality-based sensing.

Semiconductor quantum dots (QDs) are a leading platform for realising bright, wavelength-tunable sources of single and entangled photon pairs for photonic quantum technologies. Site-selected nanowire quantum dots (NWQDs) are a promising platform for fabricating such photonic devices in a scalable manner. However, implementing additional structures around the photonic nanowire while maintaining its vertical growth geometry has remained a challenge. In this work, we develop a deterministic pick-and-place technique to conduct a vertical-to-vertical transfer of NWQDs from the growth substrate to arbitrary templates. Using this transfer technique, we enhance the photon extraction efficiency to 75% by implementing a bottom gold mirror and tune the emission wavelength by 3.6 GHz via implementing electrostatic gates around the QD. Importantly, we measure low-multiphoton probability (g^(2)(0) = 0.002) and high indistinguishability (>80% for +/-100 ps) of the QD emission after the transfer process, yielding high-quality devices. These results demonstrate the repeatability and versatility of the developed transfer technique, which is an enabling step towards scalable single and entangled photon sources.

Simulating quantum error correction (QEC) circuits including non-Clifford gates at scale is important to accelerate progress toward fault-tolerant quantum computing. Here we demonstrate that matrix product state (MPS) techniques can handle many QEC circuits exactly and without restriction on gate types. Crucially, we find that MPS efficiency depends sensitively on implementation choices, and we introduce a series of targeted optimizations that reduce bond dimensions and simulation time by several orders of magnitude compared to naive approaches. We illustrate this with examples including: (a) a rotated surface code quantum memory up to distance 11, (b) logical Bell-state preparation up to distance 9, (c) a 15-to-1 magic-state distillation circuit including hundreds of QEC rounds that we optimize to be simulated with only 11 logical qubits (187 physical qubits) and a maximal bond dimension of 64 in under 40 seconds, and (d) a narrow, deep random circuit that scales linearly with the number of T gates. These results demonstrate the importance of circuit-level optimizations and position MPS as a valuable complement to near-Clifford simulators for QEC circuits.

Pseudorandomness is increasingly recognized as a key property of ensembles in quantum information theory, statistical mechanics, and quantum many-body physics. Yet it appears in two conceptually different forms: statistical pseudorandomness, embodied by unitary designs, and computational pseudorandomness captured by pseudorandom unitaries (PRUs). The relationship between these two forms of pseudorandomness remains surprisingly poorly understood. Existing PRU constructions reveal this interplay where a statistically randomizing ingredient, a unitary design, is combined with classical cryptographic primitives to produce computational pseudorandomness. We show that statistical pseudorandomness is not necessary for computationally pseudorandom unitaries. We do this by replacing the unitary $2$-design layer in the existing constructions with ensembles that are not even state $1$-designs, yet are sufficiently distinct, a property we identify to be necessary for any PRU. This yields new non-adaptively secure PRU ensembles whose computational pseudorandomness is obtained without an underlying statistically pseudorandom quantum ensemble, such as a $2$-design. We characterize distinctness via an entangled analogue of anticoncentration and use it to show that distinctness already captures constraints on coherence and imaginarity of PRUs, while identifying broad classes of inputs for which the latter obstruction disappears, enabling real-valued PRUs even for certain (maximally) entangled states. As an application, we use lack of distinctness to constrain the conjectured pseudorandomness of the random phase-Hadamard ensemble to form a PRU.

Unlike standard quantum teleportation, many-body teleportation uses scrambling to transmit quantum information. In this protocol, initially localized information spreads over many degrees of freedom and is later refocused at the receiver by a simple coupling between the systems, followed by further many-body evolution. The protocol was developed from models of traversable wormholes in holography and has become a useful probe of scrambling. In particular, it can distinguish genuine scrambling from decoherence or noise when out-of-time-order correlators fail, and can reveal signatures of different scrambling mechanisms, including the distinctive behavior expected in holographic systems. Holography predicts that related protocols can transmit information between selected boundaries of multi-boundary wormhole geometries. Motivated by this setting, we study single-qubit many-body teleportation among three systems of qubits. The initial state consists of EPR pairs distributed among them, providing a simple analogue of an infinite-temperature three-boundary holographic state. We analyze the protocol with one-dimensional and all-to-all dynamics, both analytically and numerically using random circuits. We find that the third system suppresses teleportation once the spreading message reaches the region of qubits that are entangled with it. In one dimension, both the minimum coupling required for successful teleportation and the fidelity depend on the distance from the injection site to this region, a feature reminiscent of holographic causal shadows. For all-to-all dynamics, successful teleportation is instead restricted to early times and to sufficiently few qubits entangled with the third system. A third system therefore provides spatial, or subsystem, resolution of information spreading that is absent from the two-sided protocol. Our results offer a step toward many-body teleportation networks.

Distributed architectures have been proposed as a pathway to large-scale quantum computers. Combined with the need for fault-tolerance, such architectures require distributed quantum error correction (DQEC) and distributed logical gates. An important challenge is how to realize DQEC primitives in the setting where interaction between modules is restricted to shared Bell pairs that are significantly noisier than on-chip operations. We extend the framework known as fault tolerance by construction to this setting, deriving different strategies for handling the additional noise. Through fault-improvement we recover conventional entanglement distillation, and also find more dynamical protocols that enable space-time trade-offs. We show that integrated decoding halves the required distillation code distance compared to entanglement distillation implemented using separate decoding, thus requiring significantly fewer Bell pairs. As a main focus of the work, we synthesize efficient circuits for an important primitive in distributed fault tolerance: distributed stabilizer measurements. These circuits can be adapted to resource constraints, e.g. on the Bell pair generation rate or the space available for on-chip auxiliary qubits. Noting that full local fault-tolerance is not always needed to preserve the correct scaling of logical error rates, we further optimize the circuits depending on the surrounding context. We consider in particular the surface code and the color code, both as distributed memories and in the case of lattice surgery across separate modules. Here, robustness to certain hook and readout errors reduces the number of required Bell pairs even further, compared to the context-free setting. We numerically benchmark the resulting implementations under circuit level noise with additional interconnect noise.

We present a robust protocol to reshape interactions in a spin ensemble based on global control pulse sequences applied to multiple subensembles in parallel. This setting arises naturally from ensembles of solid-state defects or multi-species atomic arrays. We show that it is provably computationally hard to find pulse sequences that simultaneously engineer interactions both within and between subensembles. Despite its formal hardness, we identify a set of necessary or sufficient conditions under which one can synthesize a target Hamiltonian from the native one. Moreover, we introduce efficient numerical strategies for designing pulse sequences that engineer target Hamiltonians robust against common control imperfections. As a specific application, we discuss the robust generation of two-mode spin squeezing in dual-species atomic ensembles, which is a challenging task without subensemble control. Our results provide a practical toolbox to design novel quantum simulation and sensing experiments with minimal control overhead.

The radiative properties of quantum emitters are profoundly influenced by their electromagnetic environment. When coupled to a waveguide terminated at one end by a mirror, distant emitters interact strongly via virtual photon exchange, leading to collective superradiant and subradiant states with enhanced or suppressed decay rates. We demonstrate that applying optimal frequency shifts to each emitter enables the formation of perfect single-excitation dark states (i.e. states with zero decay rate) and near-perfect multi-excitation dark states in small ensembles. These collective states can be deterministically prepared with high fidelity using classical driving fields or few-photon pulses propagating along the waveguide. These results, readily implementable in superconducting qubit platforms, open new avenues for quantum information storage, networking and control of light.

Many-body dynamics constitutes a promising approach for creating correlations between quantum particles which can be used for applications in sensing and metrology. However, utilizing this potential for substantial gains in practical settings is a challenging task with only a very few applications realized to date. Here, we demonstrate an approach to nanoscale magnetic sensing enabled by strongly interacting electronic spins in a room temperature solid. By coherently controlling collective many-body dynamics of a dipolar ensemble of $\sim 10^4$ nitrogen-vacancy (NV) centres in diamond with pulsed magnetic field gradients, we demonstrate practical metrological gain up to $7.9(2)\,\mathrm{dB}$ for magnetic signal detection and $8.8(3)\,\mathrm{dB}$ for magnetic noise sensing, fully accounting for experimental overheads. Finally, we combine these methods to demonstrate a momentum-space-resolved sensing modality that enables detection of spatially correlated magnetic noise at continuously tunable length scales down to 50 nanometers. These observations open the door toward practical applications of interaction-enhanced quantum sensors for nanoscale biological imaging and material characterization.

Universal quantum computation with continuous variables cannot be attained solely with a set of Gaussian operations, it requires the addition of a non-Gaussian element, at least of third order in the quadrature operators, such as the cubic phase state. In this work, we present a method to generate a quantum state in the vibrational mode of a trapped ion that exhibits characteristics compatible with the cubic phase state, such as the distinctive oscillating pattern in its Wigner function. This state emerges from the nonlinear Jaynes-Cummings interaction native to the trapped-ion model, and under the assumption of an initial coherent vibrational state with a large occupation number. Consequently, the evolved vibrational state approximates the cubic phase state with high fidelity, and we use the variance of a nonlinear combination of the quadratures to characterize it. Finally, we provide an analytical expression for its cubicity that shows the high performance of the approximate vibrational cubic phase state.

Gottesman-Kitaev-Preskill (GKP) codes provide a family of promising schemes for encoding discrete quantum information (qudits) into infinite-dimensional bosonic modes based on mathematical lattices. While such codes, when concatenated with discrete-variable codes, are relatively well studied, the construction and decoding of native GKP codes has largely remained open due to the computationally hard problems encountered. To address this challenge, we advocate a strategy of co-designing the decoder and the quantum error-correcting code itself by constructing lattices for which decoding is feasible: The requirement of efficient decoding effectively determines the quantum error-correcting code. This construction is built on classical low-density lattice codes (LDLCs), a lattice analogue of low-density parity-check codes, here lifted to families of GKP codes. Concretely, we introduce quantum versions of classical, randomly constructed LDLCs. We show that after suitable dimensionality reduction these codes have code properties comparable to or better than concatenated GKP-surface codes of equal number of modes. However, the GKP-LDLCs constructed here do not have a strictly sparse parity check matrix, which motivates our study of the performance of natively analog message-passing decoders originally developed for LDLCs when applied to concatenated GKP-LDPC codes. We show that the fully analog, linear-time decoder achieves performances close to state-of-the-art hybrid qubit-analog decoders. To facilitate future research on the structure and performance of general GKP codes, the relevant source code will be released in open-source Julia packages LatticeDecoder.jl and SymplecticGKP.jl.

We derive an exact transport equation for the quantum Calogero model, i.e. inverse-square interacting bosons on a line, from microscopic first principles.

Dynamical decoupling (DD) helps maintain high-fidelity quantum computations by suppressing dephasing noise through carefully timed refocusing pulses. In quantum charge-coupled device (QCCD) architectures, however, where ions are shuttled throughout the device, transport constrains when pulses can be applied and affects the phase accumulated by an ion. Conventional DD methods do not account for shuttling and may therefore schedule pulses that must be omitted or shifted after transport scheduling, weakening the protection from dephasing. We therefore introduce shuttling-aware dynamical decoupling (SADD), an offline compiler pass that jointly selects refocusing pulses and local ion rerouting while preserving logical-gate timings and the total schedule length. In benchmark simulations, SADD improves average final-state fidelity over both the original schedules and a simple nearest-feasible Hahn-echo baseline when dephasing dominates control and transport errors and varies slowly enough for DD. Rerouting enables otherwise infeasible pulse timings, while spatial information about the noise can provide further gains. These benefits disappear, however, when the added transport introduces too much error. Overall, our results show that coordinating DD with ion transport is an effective compiler strategy for reducing dephasing in QCCD processors.

We develop a framework for logical computation with qLDPC codes that places logical Pauli, Clifford, and non-Clifford operations on the same footing. This brings the simple homological description of Pauli logicals to the patchwork landscape of logical Clifford and non-Clifford operations, providing a tool for the discovery of new logical gates. In particular, we define the chain map hierarchy: a family of chain complexes whose homology classes encode logical unitary and code surgery operations at any level of the Clifford hierarchy, precisely analogous to the chain complex description of Pauli logicals. Consequently, intuition for Pauli logicals can be leveraged to discover new logical operations on qLDPC codes. For instance, the familiar ability to deform Pauli logicals with stabilizers—i.e. boundaries of the chain complex—becomes a way to search for constant-depth unitary implementations of (non-)Clifford logical gates. Using this strategy, we discover constant-depth unitary implementations of the full logical Clifford group on any number of blocks of the 2D toric code, including within a single block, and addressable logical CCZ gates on any triple of logical qubits on any number of blocks of the 3D toric code. Beyond manifold codes, we find addressable non-Clifford gates on codes with many encoded qubits. The chain map hierarchy naturally encompasses and extends other constructions of logical gadgets, for instance providing a universal parameterization of cup products. As such, our work provides a unified, useful, and intuitive language for computing with qLDPC codes.

We investigate even-denominator fractional quantum Hall (EDFQH) states in monolayer graphene, focusing on the experimentally observed filling fractions $\nu = 1/2$ and $\nu = 1/4$. Owing to the approximate SU(4) symmetry arising from spin and valley degrees of freedom, graphene hosts a rich variety of multi-component fractional quantum Hall states with different polarization configurations. Using the Chern-Simons composite fermion framework for SU(4) systems, we construct candidate variational wave functions corresponding to distinct spin, valley, and mixed polarization states. The ground-state energies of these states are evaluated numerically using the Coulomb interaction in spherical geometry. By comparing energies across different polarization sectors, we identify the energetically favored configurations at $\nu = 1/2$ and $\nu = 1/4$. Our variational energy comparison suggests that the energetically favored candidate states correspond to multi-component correlated quantum Hall liquids. Within the restricted family of trial states considered here, these states differ from a simple composite-fermion Fermi-sea description. These findings provide insight into the role of valley polarization and SU(4) symmetry in stabilizing even-denominator fractional quantum Hall states in graphene.