Papers

Symmetry adaptation, universality, and gate efficiency are central but often competing requirements in quantum algorithms for electronic structure and many-body physics. For example, fully symmetry-adapted universal operator pools typically generate long and deep quantum circuits, gate-efficient universal operator pools generally break symmetries, and gate-efficient fully symmetry-adapted operator pools may not be universal. In this work, we analyze such symmetry dilemmas both theoretically and numerically. On the theory side, we prove that the popular, gate-efficient operator pool consisting of singlet spin-adapted singles and perfect-pairing doubles is not universal when spatial symmetry is enforced. To demonstrate the strengths and weaknesses of the three types of pools, we perform numerical simulations using an adaptive algorithm paired with operator pools that are (i) fully symmetry-adapted and universal, (ii) fully symmetry-adapted and non-universal, and (iii) breaking a single symmetry and are universal. Our numerical simulations encompass three physically relevant scenarios in which the target state is (i) the global ground state, (ii) the ground state crossed by a state differing in multiple symmetry properties, and (iii) the ground state crossed by a state differing in a single symmetry property. Our results show when symmetry-breaking but universal pools can be used safely, when enforcing at least one distinguishing symmetry suffices, and when a particular symmetry must be rigorously preserved to avoid variational collapse. Together, the formal and numerical analysis provides a practical guide for designing and benchmarking symmetry-adapted operator pools that balance universality, resource requirements, and robust state targeting in quantum simulations for chemistry.

We investigate the creation of electron-positron pairs (EPPs) in a sequence of alternating-sign, time-dependent electric field pulse trains by solving the quantum Vlasov equations. Specifically, we focus on Sauter-like pulse trains with random time delays between successive pulses, drawn from a Gaussian distribution wherein the extent of fluctuations is controlled by the standard deviation $\sigma_T$ of the distribution. We find that increasing $\sigma_T$ leads to a dramatic transformation in the longitudinal momentum spectrum. The well-known fringe pattern, akin to that in the multi-slit interference, gets significantly modified. The averaged spectra exhibit a robust Gaussian-like envelope with residual oscillations, which are much more prominent in the central momentum region. Notably, we find that in certain cases, stochastic time delays lead to a pronounced enhancement in the central peak of the distribution function for pulse train containing $N$ pulses. For example, for $N=20$ pulses, $\sigma_T \approx 31$ $[m^{-1}]$(about $17\%$ of the mean time delay) yields nearly a tenfold increase in the central peak, which for $\sigma_T \approx 50$ $[m^{-1}]$ (about $27\%$ of the mean time delay), scales up to $10^3.$ This may open up new possibilities for optimizing multi-pulse field configurations and guide future experimental designs aimed at maximizing EPPs creation.

We introduce a symmetry-adapted framework for simulating quantum dynamics based on Pauli propagation. When a quantum circuit possesses a symmetry, many Pauli strings evolve redundantly under actions of the symmetry group. We exploit this by merging Pauli strings related through symmetry transformations. This procedure, formalized as the symmetry-merging Pauli propagation algorithm, propagates only a minimal set of orbit representatives. Analytically, we show that symmetry merging reduces space complexity by a factor set by orbit sizes, with explicit gains for translation and permutation symmetries. Numerical benchmarks of all-to-all Heisenberg dynamics confirm improved stability, particularly under truncation and noise. Our results establish a group-theoretic framework for enhancing Pauli propagation, supported by open-source code demonstrating its practical relevance for classical quantum-dynamics simulations.

Despite decades of research, the universal nature of fluctuations in disordered quantum systems remains poorly understood. Here, we present extensive numerical evidence that fluctuations in two-dimensional (2D) Anderson localization belongs to the (1+1)-dimensional Kardar-Parisi-Zhang (KPZ) universality class. In turn, by adopting the KPZ framework, we gain fresh insight into the structure and phenomenology of Anderson localization itself. We analyze both localized eigenstates and time-evolved wave packets, demonstrating that the fluctuation of their logarithmic density follows the KPZ scaling. Moreover, we reveal that the internal structure of these eigenstates exhibits glassy features characteristic of the directed polymer problem, including the emergence of dominant paths together with pinning and avalanche behavior. Localization is not isotropic but organized along preferential branches of weaker confinement, corresponding to these dominant paths. For localized wave packets, we further demonstrate that their spatial profiles obey a stretched-exponential form consistent with the KPZ scaling, while remaining fully compatible with the single-parameter scaling (SPS) hypothesis, a cornerstone of Anderson localization theory. Altogether, our results establish a unified KPZ framework for describing fluctuations and microscopic organization in 2D Anderson localization, revealing the glassy nature of localized states and providing new understanding into the universal structure of disordered quantum systems.

Efficient arithmetic operations are a prerequisite for practical quantum computing. Optimization efforts focus on two primary metrics: Quantum Cost (QC), determined by the number of non-linear gates, and Logical Depth, which defines the execution speed. Existing literature identifies the HNG gate as the standard for Input-Preserving Reversible Full Adders. HNG gate typically requires a QC of 12 and a logical depth of 5, in the area of classical reversible circuits. This paper proposes the PPKN Gate, a novel design that achieves the same inputpreserving functionality using only one Toffoli gate and five CNOT gates. With a Quantum Cost of 10 and a reduced logical depth of 4, the PPKN gate outperforms the standard HNG gate in both complexity and speed. Furthermore, we present a modular architecture for constructing an n-bit Ripple Carry Adder by cascading PPKN modules.

A nonrelativistic proof of the spin-statistics theorem is given in terms of the field operators satisfying commutation and anticommutation relations, which are introduced here in the coordinate space as a means to build the permutation symmetry into the brackets of identical particles. An eigenvalue problem of a $\pi$-rotation for a product of two annihilation operators is combined with an analysis on its rotational property to prove the connection that the field operators for integral-spin and half-integral-spin particles obey the commutation and anticommutation relations, respectively.

Variational Quantum Algorithms (VQAs) are promising for near- and intermediate-term quantum computing, but their execution cost is substantial. Each task requires many iterations and numerous circuits per iteration, and real-world applications often involve multiple tasks, scaling with the precision needed to explore the application's energy landscape. This demands an enormous number of execution shots, making practical use prohibitively expensive. We observe that VQA costs can be significantly reduced by exploiting execution similarities across an application's tasks. Based on this insight, we propose TreeVQA, a tree-based execution framework that begins by executing tasks jointly and progressively branches only as their quantum executions diverge. Implemented as a VQA wrapper, TreeVQA integrates with typical VQA applications. Evaluations on scientific and combinatorial benchmarks show shot count reductions of $25.9\times$ on average and over $100\times$ for large-scale problems at the same target accuracy. The benefits grow further with increasing problem size and precision requirements.

Rapid detection of bacterial growth is crucial in clinical, food safety, and environmental contexts, yet conventional optical methods are limited by noise and require hours of incubation. Here, we present the first experimental demonstration of a quantum-enhanced photometric measurement for early bacterial detection using squeezed light. By monitoring the optical absorbance of an Escherichia coli culture with a quantum probe, we achieve a sensitivity beyond the shot-noise limit, enabling identification of growth onset up to 30 minutes earlier than with a classical sensor. The noise reduction is validated through statistical modeling with a truncated Gaussian distribution and hypothesis testing, confirming earlier detection with low false-alarm rates. This work illustrates how quantum resources can improve real-time, non-invasive diagnostics. Our results pave the way for quantum-enhanced biosensors that accelerate detection of microbial growth and other biological processes without increasing photodamage.

A variety of photon-mediated operations are critical to the realization of scalable quantum information processing platforms and their accurate characterization is essential for the identification of optimal regimes and their experimental realizations. Such light-matter interactions are often studied with a broad variety of analytical and computational methods that are constrained by approximation techniques or by computational scaling. Quantum processors present a new avenue to address these challenges. We consider the case of cavity mediated two-qubit gates. To investigate quantum state transfer between the qubits, we implement simulations with quantum circuits that are able to reliably track the dynamics of the system. Our quantum algorithm, compatible with NISQ (Noisy Intermediate Scale Quantum) era systems, allows us to map out the fidelity of the state transfer operation between qubits as a function of a broad range of system parameters including the respective detunings between the qubits and the cavity, the damping factor of the cavity, and the respective couplings between the qubits and the cavity. The algorithm provides a robust and intuitive solution, alongside a satisfactory agreement with analytical solutions or classical simulation algorithms in their respective regimes of validity. It allows us to identify under-explored regimes of optimal performance, relevant for heterogeneous quantum platforms, where the two-qubit gate can be rather effective between far-detuned qubits that are neither resonant with each other nor with the cavity. Besides its present application, the method introduced in the current paper can be efficiently used in otherwise untractable variations of the model and in various efforts to simulate and optimize photon-mediated two-qubit gates and other relevant operations in quantum information processing.

We propose a randomized algorithm to compute the log-partition function of weakly interacting fermions with polynomial runtime in both the system size and precision. Although weakly interacting fermionic systems are considered tractable for many computational methods such as the diagrammatic quantum Monte Carlo, a mathematically rigorous proof of polynomial runtime has been lacking. In this work we first extend the proof techniques developed in previous works for proving the convergence of the cumulant expansion in periodic systems to the non-periodic case. A key equation used to analyze the sum of connected Feynman diagrams, which we call the tree-determinant expansion, reveals an underlying tree structure in the summation. This enables us to design a new randomized algorithm to compute the log-partition function through importance sampling augmented by belief propagation. This approach differs from the traditional method based on Markov chain Monte Carlo, whose efficiency is hard to guarantee, and enables us to obtain a algorithm with provable polynomial runtime.

Canonical forms are central to the analytical understanding of tensor network states, underpinning key results such as the complete classification of one-dimensional symmetry-protected topological phases within the matrix product state (MPS) framework. Yet, the established theory applies only to uniform MPS with periodic boundary conditions, leaving many physically relevant states beyond its reach. Here we introduce a generalized canonical form for uniform MPS with a boundary matrix, thus extending the analytical MPS framework to a more general setting of wider physical significance. This canonical form reveals that any such MPS can be represented as a block-invertible matrix product operator acting on a structured class of algebraic regular language states that capture its essential long-range and scale-invariant features. Our construction builds on new algebraic results of independent interest that characterize the span and algebra generated by non-semisimple sets of matrices, including a generalized quantum Wielandt's inequality that gives an explicit upper bound on the blocking length at which the fixed-length span stabilizes to an algebra. Together, these results establish a unified theoretical foundation for uniform MPS with boundaries, bridging the gap between periodic and arbitrary-boundary settings, and providing the basis for extending key analytical and classification results of matrix product states to a much broader class of states and operators.

Tensor network methods, most prominently matrix product states (MPS), have become fundamental tools in modern quantum many-body physics. While MPS and extensions like the multiscale entanglement renormalization ansatz (MERA) and tree tensor networks (TTN) efficiently capture area-law entanglement and its logarithmic violations, they inherently struggle to represent highly entangled wavefunctions. Specifically, reaching the volume-law regime typically demands exponential resources within these conventional frameworks. Motivated by this challenge, we propose holographic isometric tensor network states (holographic isoTNS) that simulate quantum lattice models in $D$ spatial dimensions via $(D+1)$-dimensional networks of tensors. The additional dimension substantially enlarges the representational manifold, while isometric constraints on each tensor ensure efficient contractibility. Using one-dimensional systems as testbeds, we analyze the properties of holographic isoTNS. First, we show that randomly initialized holographic isoTNS typically display volume-law entanglement at fixed bond dimension. Second, through analytic constructions and variational optimization, we demonstrate that holographic isoTNS can faithfully describe a broad class of highly entangled yet low-complexity states. In particular, the ansatz can represent arbitrary fermionic Gaussian states, Clifford states, extensions of rainbow states, and certain short-time-evolved states under local evolution. Third, to exploit this expressivity in broader contexts, we implement a time-evolving block decimation (TEBD) algorithm on holographic isoTNS. While the method remains efficient and scalable, error accumulation over TEBD sweeps suggests the need for further algorithmic improvement. Overall, holographic isoTNS broaden the scope of tensor-network methods, opening new avenues to study physics in the volume-law regime.

We find an unexpected phenomenon of coherently synchronized oscillations in a mirror-symmetric many-body localized system. A synchronization transition of the spin oscillations is found by changing the spin-spin interactions. To understand this phenomenon, an effective Ising model based on local integrals of motion is proposed. We find that the synchronization transition can be understood as a paramagnetic-to-ferromagnetic Ising transition. Based on the Ising model, we theoretically estimate the synchronized frequencies and the synchronization transition points, which agree well with numerical results.

Two different algorithms are presented for generating a quantum circuit realization of a matrix representing a permutation on $2^n$ letters. All circuits involve $n$ qubits and only use multi–controlled Toffoli gates. The first algorithm constructs a circuit from any decomposition of the permutation into a product of transpositions, but uses one ancilla line. The second, which uses no ancillae, constructs a circuit from a decomposition into a product of transpositions that have a Hamming distance of one. We show that any permutation admits such a decomposition, and we give a strategy for reducing the number of transpositions involved.

In this paper, Thermofield Dynamics (TFD) is applied to map a quantum optics nonlinear master equation into a Schrodinger-like equation for any arbitrary initial condition. This formalism provides a more efficient way for solving open quantum system problems. Then we use the Hartree-Fock approximation to solve the master equations of two separate noisy quantum systems analytically, which allows us to analyze the entanglement and quantum mutual information in each case using the eigenvalues of a covariance matrix, followed by two-mode and single-mode squeezed states.

We present a room-temperature Extreme High Vacuum (XHV) system engineered to support the long-duration operation of a trapped-ion quantum processor. Background-gas collisions impose limitations on trapped-ion performance and scalability by interrupting algorithmic execution and, in some cases, ejecting ions from the trap. Using molecular-flow simulations, we optimize the chamber geometry, conductance pathways, and pumping configuration to maximize the effective pumping speed at the ion location. We perform high-temperature heat treatment of stainless steel vacuum components to achieve the desired outgassing rate, guided by quantitative relations of bulk diffusive processes, allowing us to reduce the $\mathrm{H_2}$ outgassing load to the $10^{-15}\,\mathrm{mbar\,l\,s^{-1}\,cm^{-2}}$ level. The final pressure in our chamber, measured by a hot cathode gauge, is $1.5\times10^{-12}\,\mathrm{mbar}$, corresponding to the gauge's measurement limit. We measure the local pressure at the ion location by observing collision-induced reordering events in a long ion chain of mixed-isotope Yb$^+$. From the observed reordering frequency, we extract the average interval between collisions to be $(1.9 \pm 0.1)\,\mathrm{hrs/ion}$. This corresponds to a local pressure of $(3.9 \pm 0.3)\times10^{-12}\,\mathrm{mbar}$ at the ion location, assuming that all collisions arise from background H$_2$ molecules at room temperature. Our demonstration extends the continuous operation time of a quantum processor while maintaining the simplicity of a room-temperature system that does not require cryogenic apparatus.

Quantum Krylov subspace methods can extract ground and excited states by diagonalizing the Hamiltonian in a compact variational space. In practice, these spaces are almost always generated by real or imaginary time evolution, forcing a timestep trade-off between dynamical accuracy and basis collapse and often producing ill-conditioned overlap matrices that stall convergence. Here we introduce Quantum Krylov using Unitary Decomposition (QKUD), a time-evolution-free construction that maps Hamiltonian powers to implementable unitaries via the Hermitian transform $\sin(\epsilon H)/\epsilon$. QKUD reduces to the exact Hamiltonian-power Krylov recursion as $\epsilon\rightarrow0$, while finite $\epsilon$ provides a controllable deformation that tunes subspace geometry and improves conditioning. Across molecular active-space benchmarks and a frustrated 2D J1-J2 Heisenberg model, QKUD reproduces exact-Krylov convergence in well-conditioned regimes and systematically restores variational improvement when both exact Krylov and time-evolution Krylov stagnate. These results identify overlap conditioning, instead of time-evolution fidelity, is the key resource for robust quantum Krylov simulation and provide a resilient way forward for accurate quantum simulation of challenging quantum many-body problems.

Quantum mechanics is the most successful theory to describe microscopic phenomena. It was derived in different ways over the past 100 years by Heisenberg, Schrödinger, and Feynman. At the same time, other interpretations have been suggested, including the Bohm-De Broglie interpretation and the so-called Bohmian mechanics. Here, we show that Bohmian mechanics, which utilizes the concept of the Bohm quantum potential, can also serve as a starting point for quantizing classical non-relativistic systems. By incorporating the Bohm quantum potential into the Vlasov framework, we obtain a mean-field theory that captures the corpuscular nature of matter, in agreement with quantum mechanics within the Random Phase Approximation (RPA).

We introduce an unsupervised machine-learning framework that discovers optimally compressed representations of quantum many-body ground states. Using an autoencoder neural network architecture on data from $L$-site Fermi-Hubbard models, we identify minimal latent spaces with a sharp reconstruction quality threshold at $L-1$ latent dimensions, matching the system's intrinsic degrees of freedom. We demonstrate the use of the trained decoder as a differentiable variational ansatz to minimize energy directly within the latent space. Crucially, this approach circumvents the $N$-representability problem, as the learned manifold implicitly restricts the optimization to physically valid quantum states.

Calculating the molecular ground-state energy is a central challenge in computational chemistry. Conventional methods such as the Complete Active Space Configuration Interaction scale exponentially with molecular size, limiting their applicability to large molecules. Quantum computing offers a promising alternative by mapping molecular Hamiltonians by qubits, enabling cheaper computational scaling. Previous studies have shown that it is possible to formulate molecular ground state calculations as discrete optimization problems, addressable by quantum annealing. However, these efforts have been limited by previous generations of hardware and suboptimal annealing techniques. Here, the $H_{2}O$ ground-state problem is mapped to an Ising Hamiltonian using the Xian-Bias-Kas (XBK) method. By taking advantage of enhanced qubit connectivity and shorter embedding chains, it is solved with a more than doubled probability of achieving Hartree-Fock-level solutions with respect to the most advanced predecessor. Advanced annealing strategies extend Hartree-Fock-level accuracy to significantly larger problem instances, enabling solutions that use nearly 2.5 times more physically embedded qubits than the largest cases previously reported and allowing to improve annealing results by two orders of magnitude, reaching an energy difference of 0.120~Hartree relative to Hartree-Fock. These results show tangible progress toward practical quantum annealing applications in NISQ era.

High-fidelity two-qubit gates have been demonstrated in systems of two fluxonium qubits; however, the realization of scalable quantum processors requires maintaining low error rates in substantially larger architectures. In this work, we analyze a system of four inductively coupled fluxonium qubits to determine the impact of spectator qubits on the performance of a cnot gate. Our results show that spectator-induced errors are strongly suppressed when the transition frequencies of the spectator qubits are sufficiently detuned from those of the active qubits. We identify favorable frequency configurations for the four-qubit chain that yield cnot gate errors below $10^{-4}$ for gate times shorter than 100 ns. Leveraging the locality of the nearest-neighbor coupling, we extrapolate our findings to longer fluxonium chains, suggesting a viable path toward scalable, low-error quantum information processing.

While variational quantum algorithms are among the most promising approaches for the noisy intermediate-scale quantum (NISQ) era, their scalability is often hindered by the barren plateau problem. Among the proposals that have demonstrated robustness against this issue, the ADAPT-VQE algorithm stands out for ground state estimation, primarily due to its iterative ansatz construction. Although ADAPT-VQE has been extensively benchmarked on molecular Hamiltonians, where the ground states typically exhibit low entanglement, its performance for highly entangled ground states remains largely unexplored. In this work, we explore a variant of this algorithm known as qubit-ADAPT-VQE, assessing its ability to achieve ground states with substantial entanglement in spin models. We focus on four-qubit systems and employ an algebraic entanglement classification to identify distinct entanglement classes among ground states, and consider a representative of each class as an initial state to evaluate the performance of the algorithm. Our findings highlight the versatility of qubit-ADAPT-VQE, demonstrating that it accurately reaches the ground state across all entanglement classes and initial energy values.

Simulating many-body fermionic systems in conventional qubit-based quantum computers poses significant challenges due to the overheads associated with the encoding of fermionic statistics in qubits, leading to the proposal of native fermionic simulators as an alternative. While allowing for fermionic problems to be simulated efficiently, this class of fermionic simulators carries also specific constraints with them and poses other challenges unfamiliar to qubit systems. Here, we propose to pair fermionic modes to form a so-called qubit in second quantisation representation. This allows fermionic gates to be represented as rotations of these second quantised qubits, enabling adaptation of methods for qubit systems. As an application, we use this pairing scheme to represent the measurement of two- and four-point correlators in fermionic simulators with its native gates as a graph problem. Optimising measurement settings is then analysed with various analytical and algorithmic methods.

Polarization instability is a critical challenge for polarization-entangled satellite quantum key distribution (QKD), where atmospheric effects and platform motion continuously distort photon polarization. To maintain entanglement fidelity, these transformations must be accurately identified and compensated prior to detection. In this work, a compact and fast polarization-compensation approach based on liquid-crystal (LC) variable retarders is presented, using a co-propagating classical reference signal (beacon) for real-time polarization tracking. An LC-based polarimeter is implemented, and its performance is evaluated using both direct and Fourier-based Stokes parameter reconstruction. Experimental results indicate that accurate polarization estimation can be achieved with a limited number of measurements, enabling a favorable trade-off between speed and precision. The impact of liquid-crystal switching dynamics is also analyzed, highlighting the importance of selecting appropriate operating conditions for real-time applications. In addition, the effect of polarimetric inaccuracies on QKD performance is assessed through simulations of an entanglement-based protocol. The results show that only a moderate increase in quantum-bit error rate is introduced, while remaining compatible with secure key distribution. These findings demonstrate that LC-based polarization control represents an efficient and practical solution for real-time compensation in satellite QKD systems.

We propose an interaction-free ghost imaging scheme based on a thermal light source. By utilizing the quantum Zeno-like effect, our approach significantly reduces the light dose absorbed by the sample, thereby effectively preventing sample damage induced by light-matter interactions. Combined with the elimination of entangled photon sources and single-photon detectors, our approach enables significantly more photons to be utilized for image reconstruction, thereby markedly enhancing image quality compared to conventional ghost imaging. We further demonstrate active suppression of background noise via controllable photon loss. Our work offers a practical and cost-effective route to non-destructive, high-quality imaging for light-sensitive samples in fields such as life sciences.

In the transmitter of a quantum key distribution (QKD) system, a wavelength-division multiplexer (WDM) is typically used to combine quantum and synchronization signals and is directly connected to the quantum channel. As a result, it becomes the first optical component exposed to laser-injection attacks. Therefore, understanding the behavior of WDMs under such attacks is essential for assessing the practical security of QKD systems. In this work, we systematically investigate the characteristics of WDMs under high-power laser illumination. Our experimental results show that certain WDM samples exhibit pronounced changes in their spectral features once the injected laser power surpasses a specific threshold. Taking the Trojan-horse attack as an illustrative example, we further perform a theoretical analysis of the resulting spectral side channel and show that it can reduce the maximum secure transmission distance to below $66.9\%$ of its original value. By combining experimental observations with theoretical modeling, this study advances the understanding of the influence of WDMs on the practical security of QKD systems.

We investigate the quantum dynamics of a one-dimensional tight-binding lattice driven by a spatially quadratic and time-periodic potential. Both Hermitian ($J_1 = J_2$) and non-Hermitian ($J_1 \neq J_2$) hopping regimes are analyzed. Within the framework of Floquet theory, the time-dependent Hamiltonian is mapped onto an effective static Floquet Hamiltonian, enabling a detailed study of the quasi-energy spectrum as function of the driving frequency $\omega$. By applying a gauge transformation, we find that critical frequencies $\omega_c$ emerge, at which nearly equidistant quasi-energy ladders appear, as revealed by a pronounced minimum in the normalized variance $\Delta(\omega)$ of the level spacings. This spectral regularity leads to robust periodic revivals and Bloch-like oscillations in the time evolution. Numerical simulations confirm that such coherent oscillations persist even in the non-Hermitian regime, where the periodic driving stabilizes an almost real and uniformly spaced quasi-energy ladder.

Designing optimal control for multiparameter quantum sensing is essential for approaching the ultimate precision limits. However, analytical solutions are generally available only for simple systems, while realistic scenarios often involve coupled qubits and time-dependent Hamiltonians. Here we numerically investigate optimal control of a two-qubit sensor-ancilla system coupled via an Ising term using Gradient Ascent Pulse Engineering (GRAPE) to minimize the objective function. By seeding the optimization recursively with solutions obtained for smaller coupling strengths and selecting a suitable initial guess, we achieve robust convergence and high precision across a wide range of interaction strengths and field configurations. The proposed approach offers a practical route toward high-sensitivity, robust multiparameter magnetometry and it is applicable to solid-state quantum sensors such as nitrogen-vacancy (NV) centers in realistic experimental settings.

The kernel trick is a widely applicable technique in machine learning domains that maps datasets that are difficult to classify into a computationally friendly feature space. As the dimension of the dataset scales, these kernel calculations can quickly become computationally intractable or data inefficient. In this work, we extend prior efforts in quantum kernel design for Kerr nonlinear devices by implementing time-dependent simulations of a Kerr-qubit coupled to acoustic resonators. For experimentally feasible parameters, we demonstrate that the Kerr nonlinearity directly induces non-classical behavior in the multimode system, which we use to define and analyze a quantum-enhanced kernel. Finally, we present a brief scaling characterization that demonstrates the computational intractability of classically simulating the kernel as the number of resonators scales.

Quantum sensing is an emerging field with the potential to outperform classical methods in both precision and spatial resolution. However, the sensitivity of the underlying quantum platform also makes the sensors highly susceptible to their environmental noise. To address this issue, techniques from the field of quantum error mitigation use information about the noise to improve measurement results. We present a novel mitigation technique for quantum sensors to efficiently reverse the effects of any noise that can be described by a completely positive trace preserving map. The method leverages the knowledge acquired by a pre-characterization step of the device to automatically adapt to the complexity of the dissipative evolution and to indicate optimal sensing times $\tau$ to achieve the most accurate results. We demonstrate that our method reaches the best achievable sensitivity in noisy single-NV-center magnetometry. This work marks a further step toward more resilient quantum sensors with the smallest scale of resolution.