Papers

While spin squeezing has been traditionally considered in all-to-all interacting models, recent works have shown that it can also occur in systems with power-law interactions, enabling direct tests in Rydberg atoms, trapped ions, ultracold atoms, and nitrogen-vacancy (NV) centers in diamond. For the latter, Wu et al. Nature 646 (2025) demonstrated that spin squeezing is heavily affected by positional disorder, reducing any capacity for a practical squeezing advantage, which requires scalability with the system size. In this Letter we explore the robustness of spin squeezing in two-dimensional lattices with a fraction of unoccupied lattice sites. Using semiclassical modeling, we demonstrate the existence of scalable squeezing in power-law interacting XXZ models up to a disorder threshold, above which squeezing is not scalable. We produce a phase diagram for scalable squeezing, and explain its absence in the aforementioned NV experiment. Our work illustrates the maximum disorder allowed for realizing scalable spin squeezing in a host of quantum simulators, highlights a regime with substantial tolerance to disorder, and identifies controlled defect creation as a promising route for scalable squeezing in solid-state systems.

We exploit the variational and Hamiltonian structures of quantum hydrodynamics with spin to unfold the correlation and torque mechanisms accompanying spin-orbit coupling (SOC) in electronic motion. Using Hamilton's action principle for the Pauli equation, we isolate SOC-induced quantum forces that act on the orbital Madelung–Bohm trajectories and complement the usual force terms known to appear in quantum hydrodynamics with spin. While the latter spin-hydrodynamic forces relate to the quantum geometric tensor (QGT), SOC-induced orbital forces originate from a particular current operator that contributes prominently to the spin current. This distinction between force terms reveals two fundamentally different mechanisms generating quantum spin-orbit correlations. Leveraging the Hamiltonian structure of the hydrodynamic system, we also elucidate spin transport features such as the correlation-induced quantum torques and the current shift in the spin Hall effect. This Hall shift leads to a new definition of the transport spin current thereby addressing an open question in spintronics. Finally, we illustrate the framework via the Madelung–Rashba equations for planar SOC configurations and propose a particle closure for possible numerical implementations.

Dicke states serve as a critical resource in quantum metrology, communication, and computation. However, unitary preparation of Dicke states is limited to logarithmic depth in standard circuit models and existing constant-depth protocols require measurement and feed-forward. In this work, we present the first unitary, constant-depth protocols for exact Dicke state preparation. We overcome the logarithmic-depth barrier by moving beyond the standard circuit model and leveraging global interactions (native to architectures such as neutral atoms and trapped ions). Specifically, utilizing unbounded CZ gates (i.e. within the QAC$^0$ circuit class), we offer circuits for exact computation of constant-weight Dicke states, using polynomial ancillae, and approximation of weight-1 Dicke states (i.e. $W$ states), using only constant ancillae. Granted additional access to the quantum FAN-OUT operation (i.e. upgrading to the QAC$_f^0$ circuit class), we also achieve exact and clean preparation of arbitrary-weight Dicke states, with polynomial ancillae. These protocols distinguish the constant-depth capabilities of quantum architectures based on connectivity and offer a novel path toward resolving a long-standing quantum complexity conjecture.

Coupling mechanical motion to an optical resonator enables displacement measurements approaching the standard quantum limit (SQL). However, increasing the optomechanical coupling strength will inevitably lead to probing of the nonlinear response of the optical resonator. Thermal intermodulation noise (TIN) arising from the nonlinear mixing of thermomechanical motion can further increase the imprecision well above the SQL and has hitherto been canceled up to second order of nonlinearity via operation at the "magic detuning". In this work, we record the output of a membrane-in-the-middle microcavity system operating at room temperature and achieving high cooperativity, $C>n_\text{th}$, and apply a nonlinear transform that removes all orders of TIN, improving the mechanical signal-to-noise ratio by nearly 10 dB. Our results can be applied to experiments affected by third-order TIN, which we expect to be the dominating intrinsic source of noise in high-cooperativity room-temperature cavity optomechanical systems.

Consider quantum channels with input dimension $d_1$, output dimension $d_2$ and Kraus rank at most $r$. Any such channel must satisfy the constraint $rd_2\geq d_1$, and the parameter regime $rd_2=d_1$ is called the boundary regime. In this paper, we show an optimal query lower bound $\Omega(rd_1d_2/\varepsilon^2)$ for quantum channel tomography to within diamond norm error $\varepsilon$ in the away-from-boundary regime $rd_2\geq 2d_1$, matching the existing upper bound $O(rd_1d_2/\varepsilon^2)$. In particular, this lower bound fully settles the query complexity for the commonly studied case of equal input and output dimensions $d_1=d_2=d$ with $r\geq 2$, in sharp contrast to the unitary case $r=1$ where Heisenberg scaling $\Theta(d^2/\varepsilon)$ is achievable.

This work investigates the use of quantum resources in distributed storage systems. Consider an $(n,k,d)$ distributed storage system in which a file is stored across $n$ nodes such that any $k$ nodes suffice to reconstruct the file. When a node fails, any $d$ helper nodes transmit information to a newcomer to rebuild the system. In contrast to the classical repair, where helper nodes transmit classical bits, we allow them to send classical information over quantum channels to the newcomer. The newcomer then generates its storage by performing appropriate measurements on the received quantum states. In this setting, we fully characterize the fundamental tradeoff between storage and repair bandwidth (total communication cost). Compared to classical systems, the optimal storage–bandwidth tradeoff can be significantly improved with the enhancement of quantum entanglement shared only among the surviving nodes, particularly at the minimum-storage regenerating point. Remarkably, we show that when $d \geq 2k-2$, there exists an operating point at which both storage and repair bandwidth are simultaneously minimized. This phenomenon breaks the tradeoff in the classical setting and reveals a fundamentally new regime enabled by quantum communication.

In optimal quantum-mechanical evolutions, motion can take place along paths of minimal length within an optimal time frame. Alternatively, optimal evolutions may occur along established paths without any waste of energy resources and achieving 100% speed efficiency. Unfortunately, realistic physical scenarios often lead to less-than-ideal evolutions that demonstrate suboptimal efficiency, nonzero curvature, and a high level of complexity. In this paper, we provide an exact analytical expression for the curvature of a quantum evolution pertaining to a two-level quantum system subjected to various time-dependent magnetic fields. Specifically, we examine the dynamics produced by a two-parameter nonstationary Hermitian Hamiltonian with unit speed efficiency. To enhance our understanding of the physical implications of the curvature coefficient, we analyze the curvature behavior in relation to geodesic efficiency, speed efficiency, and the complexity of the quantum evolution (as described by the ratio of the difference between accessible and accessed Bloch-sphere volumes for the evolution from initial to final state to the accessible volume for the given quantum evolution). Our findings indicate that, generally, efficient quantum evolutions exhibit lower complexity compared to inefficient ones. However, we also note that complexity transcends mere length. In fact, longer paths that are sufficiently curved can demonstrate a complexity that is less than that of shorter paths with a lower curvature coefficient.

We examine the pertinent geometric characteristics of entanglement that arise from stationary Hamiltonian evolutions transitioning from separable to maximally entangled two-qubit quantum states. From a geometric perspective, each evolution is characterized by means of geodesic efficiency, speed efficiency, and curvature coefficient. Conversely, from the standpoint of entanglement, these evolutions are quantified using various metrics, such as concurrence, entanglement power, and entangling capability. Overall, our findings indicate that time-optimal evolution trajectories are marked by high geodesic efficiency, with no energy resource wastage, no curvature (i.e., zero bending), and an average path entanglement that is less than that observed in time-suboptimal evolutions. Additionally, when analyzing separable-to-maximally entangled evolutions between nonorthogonal states, time-optimal evolutions demonstrate a greater short-time degree of nonlocality compared to time-suboptimal evolutions between the same initial and final states. Interestingly, the reverse is generally true for separable-to-maximally entangled evolutions involving orthogonal states. Our investigation suggests that this phenomenon arises because suboptimal trajectories between orthogonal states are characterized by longer path lengths with smaller curvature, which are traversed with a higher energy resource wastage compared to suboptimal trajectories between nonorthogonal states. Consequently, a higher initial degree of nonlocality in the unitary time propagators appears to be essential for achieving the maximally entangled state from a separable state. Furthermore, when assessing optimal and suboptimal evolutions...

The Landau–Zener (LZ) model describes a two-level quantum system that undergoes an avoided crossing. In the adiabatic limit, the transition probability vanishes. An auxiliary control field $H_\text{CD}$ can be reverse-engineered so that the full Hamiltonian $H_0 + H_\text{CD}$ reproduces adiabaticity for all parameter values. Our aim is to construct a single control field $H_1$ that drives an ensemble of LZ-type Hamiltonians with a distribution of energy gaps. $H_1$ works best statistically, minimizing the average transition probability. We restrict our attention to a special class of $H_1$ controls, motivated by $H_\text{CD}$. We found a systematic trade-off between instantaneous adiabaticity and the final transition probability. Certain limiting cases with a linear sweep can be treated analytically; one of them being the LZ system with Dirac $\delta(t)$ function. Comprehensive and systematic numerical simulations support and extend the analytic results.

It is known that the continuous-time variant of Grover's search algorithm is characterized by quantum search frameworks that are governed by stationary Hamiltonians, which result in search trajectories confined to the two-dimensional subspace of the complete Hilbert space formed by the source and target states. Specifically, the search approach is ineffective when the source and target states are orthogonal. In this paper, we employ normalization, orthogonality, and energy limitations to demonstrate that it is unfeasible to breach time-optimality between orthogonal states with constant Hamiltonians when the evolution is limited to the two-dimensional space spanned by the initial and final states. Deviations from time-optimality for unitary evolutions between orthogonal states can only occur with time-dependent Hamiltonian evolutions or, alternatively, with constant Hamiltonian evolutions in higher-dimensional subspaces of the entire Hilbert space. Ultimately, we employ our quantitative analysis to provide meaningful insights regarding the relationship between time-optimal evolutions and analog quantum search methods. We determine that the challenge of transitioning between orthogonal states with a constant Hamiltonian in a sub-optimal time is closely linked to the shortcomings of analog quantum search when the source and target states are orthogonal and not interconnected by the search Hamiltonian. In both scenarios, the fundamental cause of the failure lies in the existence of an inherent symmetry within the system.

The entanglement distance of evolutionary quantum states of a two-spin system with the XXZ model has been studied. The analysis has been conducted both analytically and using quantum computing. An analytical dependence of the entanglement distance on the values of the model coupling constants and the parameters of the initial states has been obtained. The speed of evolution of a two-spin system has been investigated. The analysis has been performed analytically and using quantum computing. An explicit dependence of the speed of evolution on the coupling constants and on the parameters of the initial state has been obtained. The results of quantum computations are in good agreement with the theoretical predictions.

Quantum embedding methods, such as dynamical mean-field theory (DMFT), provide a powerful framework for investigating strongly correlated materials. A central computational bottleneck in DMFT is in solving the Anderson impurity model (AIM), whose exact solution is classically intractable for large bath sizes. In this work, we develop and benchmark a quantum-classical hybrid solver tailored for DMFT applications, using the variational quantum eigensolver (VQE) to prepare the ground state of the AIM with shallow quantum circuits. The solver uses a unified ansatz framework to prepare the particle and hole excitations of the ground-state from parameter-shifted circuits, enabling the reconstruction of the impurity Green's function through a continued-fraction expansion. We evaluate the performance of this approach across a few bath sizes and interaction strengths under noisy, shot-limited conditions. We compare three optimization routines (COBYLA, Adam, and L-BFGS-B) in terms of convergence and fidelity, assess the benefits of estimating a quantum-computed moment (QCM) correction to the variational energies, and benchmark the approach by comparing the reconstructed density of states (DOS) against that obtained using a classical pipeline. Our results demonstrate the feasibility of Green's function reconstruction on near-term devices and establish practical benchmarks for quantum impurity solvers embedded within self-consistent DMFT loops.

Whether neural information processing is entirely classical or involves quantum-mechanical elements remains an open question. Here we propose a model-agnostic, information-theoretic test of nonclassicality that bypasses microscopic assumptions and instead probes the structure of neural representations themselves. Using autoencoders as a transparent model system, we introduce a Bell-type consistency test in latent space, and ask whether decoding statistics obtained under multiple readout contexts can be jointly explained by a single positive latent-variable distribution. By shifting the search for quantum-like signatures in neural systems from microscopic dynamics to experimentally testable constraints on information processing, this work opens a new route for probing the fundamental physics of neural computation. The proposed test identifies violations of classical latent-variable consistency at the level of statistical representations, without assuming a specific underlying physical mechanism.

We demonstrate a Doppler thermometer based on direct optical frequency comb spectroscopy of an $^{85}$Rb vapor with a chirped electro-optic frequency comb (EOFC). The direct EOFC Doppler thermometer is accurate to within its approximately 1 K statistical uncertainty. We experimentally compare direct EOFC spectroscopy with conventional Doppler spectroscopy using a single-frequency, step-scanned laser probe. Our results show that direct EOFC spectroscopy mitigates transit-induced optical pumping distortion of the atomic lineshape, which is the dominant systematic temperature shift in alkali atom Doppler thermometry. Optical Bloch equation simulations of conventional and direct EOFC Doppler spectroscopy confirm that EOFC spectroscopy can use higher optical power to reduce statistical noise without optical pumping distortion. Our results indicate that EOFC Doppler thermometry is a promising approach to realizing a primary thermometer with size and measurement rate sufficient for applications including pharmaceutical manufacturing and nuclear waste monitoring.

The scalable preparation of large photon-number (Fock) states is a long-standing frontier in quantum science, with direct implications for quantum metrology and bosonic quantum information processing. Despite substantial progress at small photon numbers, extending state generation to large photon numbers while maintaining high fidelity and operating deterministically remains a significant challenge. Here we demonstrate a scalable and experimentally accessible control protocol for generating large photon-number states using only native spin–oscillator operations. The protocol alternates Jaynes–Cummings interactions with phase-space displacements to imprint photon-number–dependent phases and convert them into selective interference in photon-number space. It already achieves high preparation fidelity unconditionally, while an optional final qubit projection removes residual qubit–field correlations and further enhances the fidelity. Conditioned on this final projection, photon-number state preparation with fidelities exceeding $0.95$ is achieved for photon numbers in the few-hundred regime, with a success probability exceeding $0.90$, placing the protocol in a near-deterministic operating regime. The resulting control sequences remain shallow and are robust against detuning, control noise, and experimentally relevant dissipation. Our results establish a practical route to scalable, high-fidelity photon-number state preparation at large photon numbers and provide a versatile interference-engineering toolbox for nonclassical bosonic state synthesis.

We study the computation of the $\alpha$-Rényi capacity of a classical-quantum (c-q) channel for $\alpha\in(0,1)$. We propose an exponentiated-gradient (mirror descent) iteration that generalizes the Blahut-Arimoto algorithm. Our analysis establishes relative smoothness with respect to the entropy geometry, guaranteeing a global sublinear convergence of the objective values. Furthermore, under a natural tangent-space nondegeneracy condition (and a mild spectral lower bound in one regime), we prove local linear (geometric) convergence in Kullback-Leibler divergence on a truncated probability simplex, with an explicit contraction factor once the local curvature constants are bounded.

Neutral atom quantum processors have emerged as a promising platform for scalable quantum information processing, offering high-fidelity operations and exceptional qubit scalability. A key challenge in realizing practical applications is efficiently extracting readout outcomes while maintaining high system throughput, i.e., the rate of quantum task executions. In this work, we develop a theoretical framework to quantify the trade-off between readout fidelity and atomic retention. Moreover, we introduce a metric of quantum circuit iteration rate (qCIR) and employ normalized quantum Fisher information to characterize system overall performance. Further, by carefully balancing fidelity and retention, we demonstrate a readout strategy for optimizing information acquisition efficiency. Considering the experimentally feasible parameters for 87Rb atoms, we demonstrate that qCIRs of 197.2Hz and 154.5Hz are achievable using single photon detectors and cameras, respectively. These results provide practical guidance for constructing scalable and high-throughput neutral atom quantum processors for applications in sensing, simulation, and near-term algorithm implementation.

Variational Quantum Algorithms (VQAs) are critically threatened by the Barren Plateau (BP) phenomenon. In this work, we introduce the H-EFT Variational Ansatz (H-EFT-VA), an architecture inspired by Effective Field Theory (EFT). By enforcing a hierarchical "UV-cutoff" on initialization, we theoretically restrict the circuit's state exploration, preventing the formation of approximate unitary 2-designs. We provide a rigorous proof that this localization guarantees an inverse-polynomial lower bound on the gradient variance: $Var[\partial\theta] \in \Omega(1/poly(N))$. Crucially, unlike approaches that avoid BPs by limiting entanglement, we demonstrate that H-EFT-VA maintains volume-law entanglement and near-Haar purity, ensuring sufficient expressibility for complex quantum states. Extensive benchmarking across 16 experiments on the Transverse Field Ising Model confirms a 109x improvement in energy convergence and a 10.7x increase in ground-state fidelity over standard Hardware-Efficient Ansätze (HEA), with statistical significance of $p < 10^{-88}$. The static framework is most effective for Hamiltonians with moderate reference-state overlap; extension to systems with larger reference-state gaps is addressed through dynamic UV-cutoff relaxation strategies explored in concurrent work.

We address the spatially nonlocal dielectric functions of graphene at any frequency derived starting fromthe first principles of thermal quantum field theory using the formalism of the polarization tensor. After a brief review of this formalism, the longitudinal and transverse dielectric functions are considered at any relationship between the frequency and the wave vector. The analytic properties of their real and imaginary parts are investigated at low and high frequencies. Emphasis is given to the double pole at zero frequency which arises in the transverse dielectric function. The role of this unusual property for solving the problem of disagreement between experiment and theory in the Casimir effect is discussed. We guess that a more complete dielectric response of ordinary metals should also be spatially nonlocal and its transverse part may possess the double pole in the region of evanescent waves.

Quantum Amplitude Amplification (QAA), the generalization of Grover's algorithm, is capable of yielding optimal solutions to combinatorial optimization problems with high probabilities. In this work we extend the conventional 2-dimensional representation of Grover's (orthogonal collective states) to oracles which encode cost functions such as QUBO, and show that linear cost functions are a special case whereby an exact formula exists for determining optimal oracle parameter settings. Using simulations of problem sizes up to 40 qubits we demonstrate QAA's algorithmic performance across all possible solutions, with an emphasis on the closeness in Grover-like performance for solutions near the global optimum. We conclude with experimental demonstrations of generalized QAA on both IBMQ (superconducting) and IonQ (trapped ion) qubits, showing that the observed probabilities of each basis state match our equations as a function of varying the free parameters in the oracle and diffusion operators.

We analyze quantum systems under a broad class of protocols in which the temperature and a Hamiltonian control parameter are ramped simultaneously and, in general, in a nonlinear fashion toward a quantum critical point. Using an open-system version of a Kitaev quantum wire as an example, we show that, unlike finite-temperature protocols at fixed temperature, these protocols allow us to probe, in an out-of-equilibrium situation and at finite temperature, the universality class (characterized by the critical exponents $\nu$ and $z$) of an equilibrium quantum phase transition at zero temperature. Key to this is the identification of ramps in which both coherent and incoherent parts of the open-system dynamics affect the excitation density in a non-negligible way. We also identify the specific ramps for which subleading corrections to the asymptotic scaling laws are suppressed, which serves as a guide to dynamically probing quantum critical exponents in experimentally realistic finite-temperature situations.

Fast and high fidelity shuttling of spin qubits has been demonstrated in semiconductor quantum dot devices. Several architectures based on shuttling have been proposed; it has been suggested that singlet-triplet (dual-spin) qubits could be optimal for the highest shuttling fidelities. Here we present a fault-tolerant framework for quantum error correction based on such dual-spin qubits, establishing them as a natural realisation of erasure qubits within semiconductor architectures. We introduce a hardware-efficient leakage-detection protocol that automatically projects leaked qubits back onto the computational subspace, without the need for measurement feedback or increased classical control overheads. When combined with the XZZX surface code and leakage-aware decoding, we demonstrate a twofold increase in the error correction threshold and achieve orders-of-magnitude reductions in logical error rates. This establishes the singlet-triplet encoding as a practical route toward high-fidelity shuttling and erasure-based, fault-tolerant quantum computation in semiconductor devices.

We propose a generalization of the Filoche–Mayboroda localization landscape that extends the theory well beyond the static, elliptic and Hermitian settings while preserving its geometric interpretability. Using the positive operator $H^\dagger H$, we obtain a landscape that predicts localization across non-Hermitian, Floquet, and topological systems without computing eigenstates. Singular-value collapse reveals spectral instabilities and skin effects, the Sambe formulation captures coherent destruction of tunneling, and topological zero modes emerge directly from the landscape. Applications to Hatano–Nelson chains, driven two-level systems, and driven Aubry–André–Harper models confirm quantitative accuracy, establishing a unified predictor for localization in equilibrium and driven quantum matter.

We present a unified scheme for generating high-fidelity entangling gates in superconducting platforms by continuous dynamical decoupling (CDD) combined with variational minimal-energy optimal control. During the CDD stage, we suppress residual couplings, calibration drifting, and quasistatic noise, resulting in a stable effective Hamiltonian that preserves the designed ZZ interaction intended for producing tunable couplers. In this stable $\mathrm{SU}(4)$ manifold, we calculate smooth low-energy single-quibt control functions using a variational geodesic optimization process that directly minimizes gate infidelity. We illustrate the methodology by applying it to CZ, CX, and generic engangling gates, achieving virtually unit fidelity and robustness under restricted single-qubit action, with experimentally realistic control fields. These results establish CDD-enhanced variational geometric optimal control as a practical and noise-resilient scheme for designing superconducting entangling gates.

We introduce SpinPulse, an open-source python package for simulating spin qubit-based quantum computers at the pulse-level. SpinPulse models the specific physics of spin qubits, particularly through the inclusion of classical non-Markovian noise. This enables realistic simulations of native gates and quantum circuits, in order to support hardware development. In SpinPulse, a quantum circuit is first transpiled into the native gate set of our model and then converted to a pulse sequence. This pulse sequence is subsequently integrated numerically in the presence of a simulated noisy experimental environment. We showcase workflows including transpilation, pulse-level compilation, hardware benchmarking, quantum error mitigation, and large-scale simulations via integration with the tensor-network library quimb. We expect SpinPulse to be a valuable open-source tool for the quantum computing community, fostering efforts to devise high-fidelity quantum circuits and improved strategies for quantum error mitigation and correction.

The thermodynamic uncertainty relation (TUR) imposes a fundamental constraint between current fluctuations and entropy production, providing a refined formulation of the second law for micro- and nanoscale systems. Quantum violations of the classical TUR reveal genuinely quantum thermodynamic effects, which are essential for improving performance and enabling optimization in quantum technologies. In this work, we analyze the TUR in a class of paradigmatic quantum thermal-machine models whose operation is enabled by coherent coupling between two energy levels forming a virtual qubit. Steady-state coherences are confined to this virtual-qubit subspace, while in the absence of coherent coupling the system satisfies detailed balance with the thermal reservoirs and supports no steady-state heat currents. We show that the steady-state currents and entropy production can be fully reproduced by an effective classical Markov process, whereas current fluctuations acquire an additional purely quantum correction originating from coherence. As a result, the thermodynamic uncertainty naturally decomposes into a classical (diagonal) contribution and a coherent contribution. The latter becomes negative under resonant conditions and reaches its minimum at the coupling strength that maximizes steady-state coherence. We further identify the conditions for minimizing the thermodynamic uncertainty, and the criteria for surpassing the classical TUR bound in the vicinity of the reversible limit.

Classical and quantum physics represent two distinct theories; however, quantum physics is regarded as the more fundamental of the two. It is posited that classical mechanics should arise from quantum mechanics under certain limiting conditions. Nevertheless, this remains a challenging objective. In this work, we explore the potential for unifying the dynamics of classical and quantum physics. This discussion does not suggest that classical behavior emerges from quantum mechanics; rather, it demonstrates the exact equivalence between the dynamics of quantum observables and their classical counterparts. It is shown that the Heisenberg equations of motion can be cast in a form that is structurally equivalent to Newton's equations of motion, with $\hbar$ dropping out from the equations. In a generalized analysis, the Heisenberg equations are cast in a form that is identical to the classical Hamilton's equations of motion. This implies that both quantum and classical dynamics are governed by the same form of equations, with the Heisenberg operators substituting the classical observables.

Experiments on Bose-Einstein condensates at finite temperature typically extract the system parameters, such as temperature, atom number, and condensed fraction from time-of-flight images taken after a free expansion time. This paper systematically examines the effect of repulsive interactions between the condensed and thermal atoms in partially condensed clouds on the expansion profile of the thermal cloud. An analytical expression for the expansion can be obtained only if the interactions between the Bose-Einstein condensate and thermal atoms are neglected, resulting in a Bose-enhanced distribution for the thermal component. Here, the deformation of the cloud due to interactions and the effects on estimated parameters are investigated by simulating the expansion using a ballistic approximation. By fitting the simulated expansion profiles with a Bose-enhanced distribution, the errors of using such a fit are estimated, and the results are explained phenomenologically. The simulation was also used as a fitting function for experimental data, showing better agreement of the extracted condensed fraction with the semi-ideal model than results from a Bose-enhanced fit.

The evolution of an isolated quantum system inevitably exhibits recurrence: the state returns to the vicinity of its initial condition after finite time. Despite its fundamental nature, a rigorous quantitative understanding of recurrence has been lacking. We establish upper bounds on the recurrence time, $t_{\mathrm{rec}} \lesssim t_{\mathrm{exit}}(\epsilon)(1/\epsilon)^d$, where $d$ is the Hilbert-space dimension, $\epsilon$ the neighborhood size, and $t_{\mathrm{exit}}(\epsilon)$ the escape time from this neighborhood. For pure states evolving under a Hamiltonian $H$, estimating $t_{\mathrm{exit}}$ is equivalent to an inverse quantum speed limit problem: finding upper bounds on the time a time-evolved state $\psi_t$ needs to depart from the $\epsilon$-vicinity of the initial state $\psi_0$. We provide a partial solution, showing that under mild assumptions $t_{\mathrm{exit}}(\epsilon) \approx \epsilon /\sqrt{ \Delta(H^2)}$, with $\Delta(H^2)$ the Hamiltonian variance in $\psi_0$. We show that our upper bound on $t_{\mathrm{rec}}$ is generically saturated for random Hamiltonians. Finally, we analyze the impact of coherence of the initial state in the eigenbasis of $H$ on recurrence behavior.

Calculating bounds of properties of many-body quantum systems is of paramount importance, since they guide our understanding of emergent quantum phenomena and complement the insights obtained from estimation methods. Recent semidefinite programming approaches enable probabilistic bounds from finite-shot measurements of easily accessible, yet informationally incomplete, observables. Here we render these methods scalable in the number of qubits by instead utilizing moment-matrix relaxations. After introducing the general formalism, we show how the approach can be adapted with specific knowledge of the system, such as it being the ground state of a given Hamiltonian, possessing specific symmetries or being the steady state of a given Lindbladian. Our approach defines a scalable real-world certification scheme leveraging semidefinite programming relaxations and experimental estimations which, unavoidably, contain shot noise.