Papers

Consensus formation is a central problem in collective behavior. In this work, we develop quantum models of opinion dynamics that can be exactly solved and implemented on current quantum hardware. By exploiting quantum superposition, measurement-induced state collapse, and entanglement, our framework captures key features of opinion evolution and allows a systematic investigation of how network connectivity shapes consensus formation. We demonstrate our approach using practical quantum circuits and validate representative cases on IBM Quantum devices for the open-chain. These findings pave the way for further exploration into quantum-enhanced social modeling, highlighting the potential of near-term quantum computers for simulating collective behavior in complex systems.

Cubic phase states provide the essential non-Gaussian resource for continuous-variable quantum computing. We show that they also offer significant potential for quantum metrology, surpassing the phase-sensing sensitivity of all Gaussian states at equal average photon number. Optimal sensitivity requires only moderate initial squeezing, and the non-Gaussian advantage remains robust against loss and detection noise. We identify optimal measurement strategies and show that several experimentally relevant preparation schemes surpass Gaussian limits, in some cases reaching the sensitivity of cubic phase states. Our results establish cubic phase states as a promising resource for quantum-enhanced precision measurements beyond Gaussian limits.

Computational fluid dynamics (CFD) is a cornerstone of classical scientific computing, and there is growing interest in whether quantum computers can accelerate such simulations. The existing proposals for fault-tolerant quantum algorithms for CFD have almost exclusively been based on the Carleman embedding method, used to encode nonlinearities on a quantum computer. Here, we first identify several key challenges that must be addressed in order to establish quantum advantage using this method, including Carleman convergence, time-stepping requirements, condition-number scaling, and data extraction. Building on this analysis, we develop a novel algorithm for the incompressible lattice Boltzmann equation that addresses them, and provide its detailed analysis, including all potential sources of algorithmic complexity, as well as gate count estimates. We find that for an end-to-end problem, a modest quantum advantage may be preserved for selected observables in the high-error-tolerance regime. We establish a lower bound for the Reynolds number scaling of our quantum algorithm in dimension $D$ at Kolmogorov microscale resolution with $O(\mathrm{Re}^{\frac{3}{4}(1+\frac{D}{2})} \times q_M)$, where $q_M$ is a multiplicative overhead for data extraction with $q_M = O(\mathrm{Re}^{\frac{3}{8}})$ for the drag force. This upper bounds the scaling improvement over classical algorithms by $O(\mathrm{Re}^{\frac{3D}{8}})$. However, our numerical investigations suggest a lower speedup, with a scaling estimate of $O(\mathrm{Re}^{1.936} \times q_M)$ for $D=2$. Our results give robust evidence that small, but nontrivial, quantum advantages can be achieved in the context of CFD, and motivate the need for additional rigorous end-to-end quantum algorithm development.

Many spintronic, magnetic-memory, and neuromorphic devices rely on spatially varying magnetic fields. Quantitatively imaging these fields with full vector information over extended areas remains a major challenge. Existing probes either offer nanoscale resolution at the cost of slow scanning, or widefield imaging with limited vector sensitivity or material constraints. Quantum sensing with nitrogen-vacancy (NV) centers in diamond promises to bridge this gap, but a practical camera-based vector magnetometry implementation on relevant microstructures has not been demonstrated. Here we adapt a commercial widefield microscope to implement a camera-compatible pulsed optically detected magnetic resonance protocol to reconstruct stray-field vectors from microscale devices. By resolving the Zeeman shifts of the four NV orientations, we reconstruct the stray-field vector generated by microfabricated permalloy structures that host multiple stable remanent states. Our implementation achieves a spatial resolution of $\approx 0.52 ~\mu\mathrm{m}$ across an $83~\mu\mathrm{m} \times 83~\mu\mathrm{m}$ field of view and a peak sensitivity of $ (828 \pm 142)~\mathrm{nT\,Hz^{-1}}$, with acquisition times of only a few minutes. These results establish pulsed widefield NV magnetometry on standard microscopes as a practical and scalable tool for routine vector-resolved imaging of complex magnetic devices.

The Quantum Max-$d$-Cut ($d$-QMC) problem is a special instance of a $2$-local Hamiltonian problem, representing the quantum analog of the classical Max-$d$-Cut problem. The $d$-QMC problem seeks the largest eigenvalue of a Hamiltonian defined on a graph with $n$ vertices, where edges correspond to swap operators acting on $(\mathbb{C}^d)^{\otimes n}$. In recent years, progress has been made by investigating the algebraic structure of the $d$-QMC Hamiltonian. Building on this approach, this article solves the $d$-QMC problem for complete tripartite graphs for small local dimensions, $d \le 3$.

The fundamental metrological limits of temperature sensing in open quantum systems remain largely unresolved, particularly regarding the role of non-Gaussian quantum resources. In this letter, we establish analytic bounds on the quantum Fisher information (QFI) for temperature estimation using non-Gaussian states undergoing dissipative bosonic evolution. By focusing on the short-time regime governed by a time-local master equation, we derive precise scaling laws that elucidate when and how non-Gaussian probes decisively outperform Gaussian states under identical energy constraints. Our analysis uncovers a distinct linear-in-time QFI enhancement unique to Fock states, in contrast to the inherently weaker, quadratic scaling of Gaussian probes. These theoretical insights are substantiated through exact numerical simulations and mapped onto experimentally accessible platforms such as circuit QED. Our results not only clarify the quantum thermometric advantage of non-Gaussianity but also chart a realistic pathway toward harnessing it in noisy quantum technologies.

Quantifiers of stationarity, classicality, purity and vorticity are derived from phase-space differential geometrical structures within the Weyl-Wigner framework, after which they are related to the hyperbolic stability of classical and quantum-modified Hamiltonian (non-linear) equations of motion. By examining the equilibrium regime produced by such an autonomous system of ordinary differential equations, a correspondence between Wigner flow properties and hyperbolic stability boundaries in the phase-space is identified. Explicit analytical expressions for equilibrium-stability parameters are obtained for quantum Gaussian ensembles, wherein information quantifiers driven by Wigner currents are identified. Illustrated by an application to a Harper-like system, the results provide a self-contained analysis for identifying the influence of quantum fluctuations associated to the emergence of phase-space vorticity in order to quantify equilibrium and stability properties of Hamiltonian non-linear dynamics.

Optomechanical cooling of levitated nanoparticles has become an essential topic in modern quantum physics, providing a platform for exploring macroscopic quantum phenomena and high-precision sensing. However, conventional cavity-assisted cooling is fundamentally constrained by cavity dissipation and environmental noise, limiting the attainable minimum temperature. In this work, we propose a non-Hermitian optomechanical cooling scheme through nonreciprocal coupling between two levitated nanoparticles, where one particle is directly cooled by an optical cavity and the other is cooled indirectly through a non-Hermitian interaction. Both analytical solutions and numerical simulations reveal that increasing nonreciprocity enhances directional energy transfer, enabling the target particle to reach a lower phonon occupation than is achievable in conventional cavity cooling. This study demonstrates a new cooling mechanism driven by non-Hermitian interactions, offering theoretical guidance for realizing controllable energy flow and deep cooling in levitated optomechanical systems, and paving the way for future developments in quantum control and sensing technologies.

Cold-atom experiments based on alkali-like atoms provide us with a tool to experimentally realize Hubbard models with a large number $N$ of components. The value of $N$ can be seen as a new handle to tune the properties of the system, leading to new physics both in the case of fully SU($N$) symmetric systems, or in the presence of controlled symmetry breaking. We focus on the Mott transition at global half filling and we characterize local correlations between particles through the inter-flavor mutual information, an experimentally accessible quantity that rigorously measures the distance from the closest gaussian state, unveiling features that cannot be accessed by conventional probes of Mottness. We prove that these correlations are fully independent from local entanglement and quantum discord, and, using Dynamical Mean-Field Theory, we show that the SU(4) system has significantly smaller correlations than the SU(2) counterpart. In the atomic limit we prove that increasing $N$ further decreases the strength of the correlations. This suggests that a controlled reduction of the symmetry, reducing the number of effective components, can be used to enhance the degree of correlation. We confirm this scenario solving the model for $N=4$ and gradually breaking the symmetry via a Raman field, revealing an evolution from the SU(4) to the SU(2) Mott transition as the symmetry-breaking term increases, with a sudden recovery of the large correlations of the SU(2) model at weak Raman coupling in the Mott state. By further exploring the interplay between energy repulsion and the Raman field, we obtain a rich phase diagram with three different phases – a metal, a band insulator, and a Mott insulator – all coexisting at a single tricritical point.

Much recent work on distributed quantum computing have focused on the use of entangled pairs and distributed two qubit gates. But there has also been work on efficient schemes for achieving multipartite entanglement between nodes in a single shot, removing the need to generate multipartite entangled states using many entangled pairs. This paper looks at how multipartite entanglement resources (e.g., GHZ states) can be useful for distributed fan-out operations; we also consider the use of qudits of dimension four for distributed quantum circuit compression. In particular, we consider how such fan-out operations and qudits can be used to implement circuits which are challenging for distributed quantum computation, involving pairwise qubit interactions, i.e., what has been called global gates (a.k.a. global Mølmer-Sørensen gates). Such gates have been explored to possibly yield more efficient computations via reduced circuit depth, and can be carried out efficiently in some types of quantum hardware (e.g., trapped-ion quantum computers); we consider this as an exploration of an “extreme” case for distribution given the global qubit-qubit interactions. We also conclude with some implications for future work on quantum circuit compilation and quantum data centre design.

Continuous time quantum walks on exponentially large, sparse graphs form a powerful paradigm for quantum computing: On the one hand, they can be efficiently simulated on a quantum computer. On the other hand, they are themselves BQP-complete, providing an alternative framework for thinking about quantum computing – a perspective which has indeed led to a number of novel algorithms and oracle problems. Recently, simulating the dynamics of a system of harmonic oscillators (that is, masses and springs) was set forth as another BQP-complete problem defined on exponentially large, sparse graphs. In this work, we establish a direct and transparent mapping between these two classes of problems. As compared to linking the two classes of problems via their BQP-completeness, our mapping has several desirable features: It is transparent, in that it respects the structure of the problem, including the geometry of the underlying graph, initialization, read-out, and efficient oracle access, resulting in low overhead in terms of both space and time; it allows to map also between restricted subsets of instances of both problems which are not BQP-complete; it provides a recipe to directly translate any quantum algorithm designed in the quantum walk paradigm to harmonic oscillators (and vice versa); and finally, it provides an alternative, transparent way to prove BQP-completeness of the harmonic oscillator problem by mapping it to BQP-completeness construction for the quantum walk problem (or vice versa).

Quantum communication protocols seek to leverage the unique properties of quantum systems for coordination or communication tasks, usually with guarantees of security or anonymity that exceed what is possible classically. One promising domain of application is elections, where strong such guarantees are essential to ensure legitimacy. We experimentally implement a recently proposed election protocol from Centrone et al. such that no one, including a potential central authority, can know the preferred candidate of any voter other than themself. We conduct a four-party election, generating and distributing four-partite GHZ states with $\approx 89\%$ fidelity and successfully recording voters' intentions $\approx 87\%$ of the time.

Ultracold neutral atoms in optical lattices are a promising platform for simulating the behavior of complex materials and implementing quantum gates. We optimize collision gates for fermionic Lithium atoms confined in a double-well potential, controlling the laser amplitude and keeping its relative phase constant. We obtain high-fidelity gates based on a one-dimensional confinement simulation. Our approach extends beyond earlier Fermi-Hubbard simulations by capturing a momentum dependence in the interaction energy. This leads to a higher interaction strength when atoms begin in separate subwells compared to the same subwell. This momentum dependence might limit the gate fidelity under realistic experimental conditions, but also enables tailored applications in quantum chemistry and quantum simulation by optimizing gates for each of these cases separately.

Recent advances in coherent conveyor-mode spin qubit shuttling are paving the way for large-scale quantum computing platforms with qubit connectivity achieved by spin qubit shuttles. We developed a simulation tool to investigate numerically the impact of device imperfections on the spin-coherence of conveyor-mode shuttling in Si/SiGe. We simulate the quantum evolution of a mobile electron spin-qubit under the influence of sparse and singly charged point defects placed in the Si/SiGe heterostructure in close proximity to the shuttle lane. We consider different locations of a single charge defect with respect to the center of the shuttle lane, multiple orbital states of the electron in the shuttle with $g$-factor differences between the orbital levels, and orbital relaxation induced by electron-phonon interaction. With this simulation framework, we identify the critical defect density of charged point defects in the heterostructure for conveyor-mode spin qubit shuttle devices and quantify the impact of a single defect on the coherence of a qubit.

The performance of Gottesman-Kitaev-Preskill (GKP) codes, an approach to hardware-efficient quantum error correction, is limited by the finite squeezing capabilities of current experimental platforms. To circumvent this hardware demand, we introduce Energy-Scaled Zero-Noise Extrapolation (ES-ZNE), a quantum error mitigation protocol that uses the mean photon number of the GKP code as a tunable effective noise parameter. The protocol measures logical observables at a series of accessible finite energies and extrapolates the results to the ideal, infinite-energy limit using an ansatz based on the code's asymptotic error scaling. Through simulating a GKP qubit under a pure-loss channel, we demonstrate that ES-ZNE successfully mitigates finite-energy errors, recovering the ideal expectation values (within numerical uncertainty) in the shallow-noise regime. Furthermore, by computationally removing artifacts arising from the finite-energy encoding, our method characterizes the intrinsic performance of the ideal GKP code, revealing a sharp error threshold beyond which the code's corrective power diminishes. These results establish ES-ZNE as a practical, software-based strategy for enhancing the performance of near-term bosonic quantum processors, trading sampling overhead for demanding physical resources like high squeezing.

We present Quantum Graph Hash (QGH-256), a novel quantum spectral hashing algorithm that generates high-entropy fingerprints from message-induced graphs. Each input message is mapped to a weighted graph via a discrete random walk on an n X n toroidal grid, where the walk dynamics determine the edge weights. Quantum Phase Estimation (QPE) is then used to extract the phase spectrum of the graph Laplacian. Unlike standard QPE settings, the phase estimation is performed with respect to a superposition state (a uniform superposition over all node basis states) rather than an eigenvector, ensuring that all eigencomponents contribute to the resulting spectrum. This yields spectral features that distinguish even co-spectral but non-isomorphic message-induced graphs. The final spectral fingerprint is converted into a 256-bit digest, producing a compact representation of the input. As the fingerprint encodes both spectral and dynamical properties of the message-induced graph, the resulting hash exhibits strong sensitivity to input perturbations and provides a structurally rich foundation for post-quantum hashing. To demonstrate the feasibility of the approach, we implement QGH-256 on a 4 X 4 toroidal grid, chosen empirically: smaller grids exhibit collisions, whereas larger grids significantly increase execution time. The entire pipeline is implemented in Qiskit, and we use a seeded statevector simulator to obtain stable, noise-free results.

Edge bit in an average symmetry protected topological (ASPT) mixed state is studied. The state is protected by one strong $Z_2$ and one weak (average) $Z_2$ symmetries. As analogous objects of pure symmetry protected topological (SPT) states, the ASPT possesses edge bits. In particular, the analogous operator response exists, that is, symmetry fractionalization. The fractionalization preserves the presence of the ASPT in the bulk, and the fractionalized edge operators acting on the edge bits of the ASPT. %analogous to the ones in the pure SPTs. In this work, based on the cluster model and by employing Choi mapping, we discuss generic features of the edge bits and numerically clarify the behavior of the edge bits and their robustness for varying decoherence and perturbative interactions. By using an operator-space mutual information (OSMI), we track the flow of quantum correlations between the two edges. Remarkably, even in the ASPT regime, a finite portion of the initial edge-to-edge correlation survives.

The success of a quantum annealing algorithm requires a polynomial scaling of the energy gap. Recently it was shown that a two-dimensional transverse-field Ising model on a square lattice with nearest-neighbor $\pm J$ random coupling has a polynomial energy gap in the symmetric subspace of the parity operator [Nature 631, 749-754 (2024)], indicating the efficient preparation of its ground states by quantum annealing. However, it is not clear if this result can be generalized to other spin glass models with continuous or biased randomness. Here we prove that under general independent and identical distributions (i.i.d.) of the exchange energies, the energy gap of a one-dimensional random transverse-field Ising model follows a stretched exponential scaling even in the parity-restricted subspace. We discuss the implication of this result to quantum annealing problems.

We develop a complex-entropy framework for Wigner negativity and apply it to avoided crossings in an oval quantum billiard. For a real Wigner function the Gibbs–Shannon functional becomes complex; its imaginary part, proportional to the Wigner-negative volume, serves as an entropy-like measure of phase-space nonclassicality. A sign-resolved decomposition separates the total negative weight from its phase-space distribution and defines a negative-channel Fisher information that quantifies how sensitively the negative lobe reshapes as a control parameter is varied. This structure yields a Cauchy–Schwarz bound that limits how rapidly the imaginary entropy, and hence the Wigner negativity, can change with the parameter. In the oval billiard, avoided crossings display enhanced negativity and an amplified negative-channel Fisher response, providing a clear phase-space signature of mode hybridization. The construction is generic and extends to other wave-chaotic and mesoscopic systems with phase-space representations.

We establish rigorous guarantees for quantum thermal and ground state preparation via system-bath interactions beyond the Lindblad approximation regime. In contrast to existing analyses, we show that the system-bath coupling strength need not vanish with the target accuracy: even when the coupling strength is chosen independently of the desired precision, the induced quantum channel admits the target thermal and ground states as approximate fixed points with arbitrarily small error. Our analysis develops new techniques to control all orders of the Dyson expansion and the associated multidimensional operator Fourier transforms, thereby going beyond the leading-order Lindbladian description. Building on these estimates, we derive an improved end-to-end complexity analysis and provide rigorous guarantees for thermalization and cooling outside the conventional Lindblad approximation regime. Numerical simulations further demonstrate the robustness of the system-bath interaction framework over a broad range of coupling strengths, including regimes where the Lindblad approximation is no longer accurate.

Encrypted control has been extensively studied to ensure the confidentiality of system states and control inputs for networked control systems. This paper presents a computationally efficient encrypted control framework for networked systems enabled by quantum communication. A quantum channel between sensors and actuators is used to generate identical secret keys, whose security is further enhanced through quantum key distribution. These keys enable lightweight encryption and decryption while preserving confidentiality and control accuracy. We develop a novel encryption-decryption architecture for state-feedback control of linear systems based on quantum keys, and characterize the impact of quantum state errors on closed-loop stability. In particular, we establish the existence of a critical threshold on intrinsic quantum noise below which stability is guaranteed. In contrast to classical encrypted control schemes, which may collapse under a single key-bit error, the proposed quantum encrypted control exhibits strong robustness to key imperfections. We further adopt quantization techniques to address the scenarios with limited communication bits in practical situations, and implement privacy protection for quantum keys based on a stochastic quantizer. These results demonstrate that integrating quantum technologies into control systems in a nontrivial and principled manner, even at their current level of maturity, can yield substantial performance gains in reducing computational complexity and improving resilience to key errors while ensuring security against multiple eavesdropping sources.

Non-trivial dispersion relations engineered in photonic waveguide for the precise control of atomic dynamics has recently attracted considerable attention. Here, we study a system in which atoms are coupled to one-dimensional coupled-resonator waveguides with long-range hoppings. By carefully engineering the jth-order nearest neighbor (JNN) hoppings between resonators, we construct linear dispersion relations with the chiral characteristic. To quantify the degree of linearity, we analyze the propagation fidelities of Gaussian wave packets in these waveguides. Furthermore, we demonstrate that such coupled-resonator waveguides can serve as versatile platforms for enabling directional atomic radiation and absorption. Beyond linear dispersion relations, more general forms, including quadratic and cubic relations, can also be achieved through tailored JNN-hoppings. Our study thus provides a unified framework for simulating atom-environment couplings with arbitrary dispersion relations.

An electronic modulation can retain a substantial local amplitude while its translational coherence is limited by spatial disorder. Its coupling to superconductivity therefore cannot be characterized by a single modulation intensity. We develop a phenomenological formulation of a finite-wave-vector complex electronic envelope coupled to a charged superconducting field. Translation and gauge symmetries constrain the interaction terms, while amplitude, modulation-gradient and condensate-gradient couplings act on distinct responses. The resulting variational equations give uniform coexistence conditions, local stability criteria and phase-gradient coefficients. We define the helicity modulus by a boundary twist, distinguish phase-only from amplitude-weighted correlations, and give an explicit minimal spectral Hamiltonian illustrating how the electronic texture may enter momentum-resolved measurements. The proposed tests use distinct spatial, spectral and stiffness observables; none assumes that a tunnelling gap directly measures condensate amplitude. An explicit kernel expansion yields the leading displacement of the selected wave vector, while the thermodynamic twist response determines phase rigidity independently of charge intensity. The analytical relations and selected numerical responses distinguish amplitude, spatial organization and condensate rigidity within the specified coupled-field model.

Federated learning (FL) deployed over quantum enabled and heterogeneous classical networks faces significant performance degradation due to uneven client quality, stochastic teleportation fidelity, device instability, and geometric mismatch between local and global models. Classical aggregation rules assume euclidean topology and uniform communication reliability, limiting their suitability for emerging quantum federated systems. This paper introduces A2G (Adaptive Aggregation with Two Gains), a dual gain framework that jointly regulates geometric blending through a geometry gain and modulates client importance using a QoS gain derived from teleportation fidelity, latency, and instability.

Parametric amplification is essential for quantum measurement, enabling the amplification of weak microwave signals with minimal added noise. While Josephson-junction-based amplifiers have become standard in superconducting quantum circuits, their magnetic sensitivity, limited saturation power, and sub-kelvin operating requirements motivate the development of alternative nonlinear platforms. Here we demonstrate a two-mode kinetic-inductance parametric amplifier based on a pair of capacitively coupled Kerr-nonlinear resonators fabricated from NbTiN and NbN thin films. The distributed Kerr nonlinearity of these materials enables nondegenerate four-wave-mixing amplification with gains approaching 40 dB, gain-bandwidth products up to 6.9 MHz, and 1-dB compression powers two to three orders of magnitude higher than those of state-of-the-art Josephson amplifiers. A coupled-mode theoretical model accurately captures the pump-induced modification of the hybridized modes and quantitatively reproduces the observed signal and idler responses. The NbN device exhibits a significantly larger Kerr coefficient and superior gain-bandwidth performance, highlighting the advantages of high-kinetic-inductance materials. Our results establish coupled kinetic-inductance resonators as a robust platform for broadband, high-power, and magnetically resilient quantum-limited amplification, offering a scalable route for advanced readout in superconducting qubits, spin ensembles, quantum dots, and other microwave-quantum technologies.

We investigate quench dynamics in the quantum $S=1/2$ XXZ antiferromagnetic chain with staggered and anisotropic interactions in the flat-band limit. We consider global quenches that interchange odd- and even-bond strengths in a fully dimerized chain, yielding a postquench Hamiltonian with couplings only on even links. Due to the vanishing group velocity of excitations, the system fails to relax, providing an ideal setting to study dynamical topological quantum phase transitions. We show that the $z$-component of the interactions, controlled by the anisotropy $\Delta$, acts as a relevant term that generates additional dynamical quantum phase transitions and induces rich structures in the Loschmidt echo. These transitions are symmetry-protected and robust for quenches between distinct dimerization patterns. Using a Bell-basis representation, we derive closed-form results for entanglement entropies, Loschmidt echoes for finite and infinite systems, and identify both $\Delta$-independent and $\Delta$-dependent critical times. Quantum simulations on IBM Quantum processors demonstrate that key observables can be reliably extracted on noisy intermediate-scale devices without error mitigation.

We introduce Sketch Tomography, an efficient procedure for quantum state tomography based on the classical shadow protocol used for quantum observable estimations. The procedure applies to the case where the ground truth quantum state is a matrix product state (MPS). The density matrix of the ground truth state admits a tensor train ansatz as a result of the MPS assumption, and we estimate the tensor components of the ansatz through a series of observable estimations, thus outputting an approximation of the density matrix. The procedure is provably convergent with a sample complexity that scales quadratically in the system size. We conduct extensive numerical experiments to show that the procedure outputs an accurate approximation to the quantum state. For observable estimation tasks involving moderately large subsystems, we show that our procedure gives rise to a more accurate estimation than the classical shadow protocol. We also show that sketch tomography is more accurate in observable estimation than quantum states trained from the maximum likelihood estimation formulation.

A common route to ground-state preparation couples a system to one ancilla qubit, applies a conditional feedback operation, and resets the ancilla. I ask what physical quantity governs the energy such a cycle exchanges. The answer is a commutator, not the correlation the ancilla acquires. The energy change per cycle is exactly $W = \langle\Psi_1| A - U^\dagger A U |\Psi_1\rangle$ with $A = I_A \otimes H$, for every feedback strength and every sensing time, and it vanishes identically whenever the feedback generator commutes with $H$. No function of the system-ancilla correlation can therefore determine the work: on an explicit one-parameter family the mutual information and the logarithmic negativity are invariant to $2\times10^{-15}$ while the work varies continuously and changes sign. At fixed correlation the reachable work is a closed-form interval, and to leading order in the feedback strength it is symmetric about zero, so an unfiltered conditional kick heats as readily as it cools. That symmetry is exactly one orthogonality condition on the two spectra, and the two sufficient conditions I identify are its degenerate solutions, one holding automatically whenever the post-sensing branch is pure. At that order no choice of generator repairs a protocol that starts pure, and no choice of state repairs one with a symmetric generator. Breaking both is necessary but not sufficient: across the grid I searched, a finite kick's second-order bias raises the directional fraction only to $0.015$. Directional cooling instead requires the frequency-filtered jump operators of single-ancilla Lindbladian preparation, which fall outside this Hermitian class. Read in reverse the same commutator is constructive: it identifies, before any circuit runs, variational parameter blocks whose energy gradient is identically zero, removing a fifth of the circuits from an optimisation run.

Many years have passed since the conception of the quintessential method of shortcut to adiabaticity known as counterdiabatic driving (or transitionless quantum driving). Yet, this method appears to be energetically cost-free and thus continually challenges the task of quantifying the amount of energy it demands to be accomplished. This paper proposes that the energy cost of controlling a closed quantum system using the counterdiabatic method can also be assessed using the instantaneous excess work during the process and related quantities, as the time-averaged excess work. Starting from the Mandelstam-Tamm bound for driven dynamics, we have shown that the speed-up of counterdiabatic driving is linked with the spreading of energy between the eigenstates of the total Hamiltonian, which is necessarily accompanied by transitions between these eigenstates. Nonetheless, although excess work can be used to quantify energetically these transitions, it is well known that the excess work is zero throughout the entire process under counterdiabatic driving. To recover the excess work as an energetic cost quantifier for counterdiabatic driving, we will propose a different interpretation of the parameters of the counterdiabatic Hamiltonian, leading to an excess work different from zero. We have illustrated our findings with the Landau-Zener model.

An excitonic approach to the ultrafast optical response of confined semiconductors at elevated densities below the Mott transition is presented. The theory is valid from the coherent regime, where coherent excitonic transitions and biexcitons dominate, to the incoherent regime, where excitonic occupations dominate. Numerical simulations of the $1s$ exciton dynamics during intense circularly polarized pump pulses in two different Coulomb-interaction regimes are performed for two-dimensional semiconductors: Moderate Coulomb interaction is compared with dominating Coulomb interaction with respect to the light-matter interaction strength. The different many-body contributions are disentangled and it is found, that excitonic Rabi oscillations in the Coulomb-dominated regime are considerably less strong. By also comparing circular and linear excitation in a MoSe$_2$ monolayer, it is found, that linear excitation creates a regime, where excitonic Rabi oscillations are almost completely suppressed.