Publications from 2025

We propose and validate a framework for analog simulation of the Heisenberg spin model using a circuit quantum electrodynamics (circuit-QED) platform. Our method involves the Dyson-Maleev transformation, for which we develop a procedure to circumvent its inherent non-Hermiticity, yielding the extended Bose-Hubbard (EBH) Hamiltonian. We demonstrate the equivalence of this approach to the Holstein-Primakoff encoding for spin-1/2 systems. For the experimental realization of this EBH model, we design a scalable circuit-QED architecture based on an engineered Josephson junction array. Numerical simulations confirm that the microwave photon dynamics in this simulator accurately reproduces the original spin dynamics. Our work establishes an experimentally accessible method for investigating complex quantum spin dynamics in a highly controllable bosonic setting.

Chiral quantum optics is a growing field of research where light-matter interactions become asymmetrically dependent on momentum and spin, offering novel control over photonic and electronic degrees of freedom. Recently, the platforms for investigating chiral light-matter interactions have expanded from laser-cooled atoms and quantum dots to various solid-state systems, such as microcavity polaritons and two-dimensional layered materials, integrated into photonic structures like waveguides, cavities, and ring resonators. In this perspective, we begin by establishing the foundation for understanding and engineering these chiral light-matter regimes. We review the cutting-edge platforms that have enabled their successful realization in recent years, focusing on solid-state platforms, and discuss the most relevant experimental challenges to fully harness their potential. Finally, we explore the vast opportunities these chiral light-matter interfaces present, particularly their ability to reveal exotic quantum many-body phenomena, such as chiral many-body superradiance and fractional quantum Hall physics.

Subwavelength atomic arrays feature strong light-induced dipole-dipole interactions, resulting in subradiant collective resonances characterized by narrowed linewidths. In this work, we present a sideband cooling scheme for atoms trapped in subwavelength arrays that utilizes these narrow collective resonances. Working in the Lamb-Dicke regime, we derive an effective master equation for the atomic motion by adiabatically eliminating the internal degrees of freedom of the atoms, and validate its prediction with numerical simulations of the full system. Our results demonstrate that subradiant resonances enable the cooling of ensembles of atoms to temperatures lower than those achievable without dipole interactions, provided the atoms have different trap frequencies. Remarkably, narrow collective resonances can be sideband-resolved even when the individual atomic transition is not. In such scenarios, ground-state cooling becomes feasible solely due to light-induced dipole-dipole interactions. This approach could be utilized for future quantum technologies based on dense ensembles of emitters, and paves the way towards harnessing many-body cooperative decay for enhanced motional control.

Flat bands (FBs) are energy bands with zero group velocity, which in electronic systems were shown to favor strongly correlated phenomena. Indeed, a FB can be spanned with a basis of strictly localized states, the so called “compact localized states” (CLSs), which are yet generally non-orthogonal. Here, we study emergent dipole-dipole interactions between emitters dispersively coupled to the photonic analogue of a FB, a setup within reach in state-of the-art experimental platforms. We show that the strength of such photon-mediated interactions decays exponentially with distance with a characteristic localization length which, unlike typical behaviours with standard bands, saturates to a finite value as the emitter’s energy approaches the FB. Remarkably, we find that the localization length grows with the overlap between CLSs according to an analytically-derived universal scaling law valid for a large class of FBs both in 1D and 2D. Using giant atoms (non-local atom-field coupling) allows to tailor interaction potentials having the same shape of a CLS or a superposition of a few of these.

Photonic lattices facilitate band structure engineering, supporting both localized and extended modes through their geometric design. However, greater control over these modes can be achieved by taking advantage of the interference effect between external drives with precisely tuned phases and photonic modes within the lattice. In this work, we build on this principle to demonstrate optical switching, directed light propagation and site-specific localization in a one-dimensional photonic lattice of coupled microresonators by resonantly driving the system with a coherent field of controlled phase. Importantly, our experimental results provide direct evidence that increased driving power acts as a tuning parameter enabling nonlinear localization at frequencies previously inaccessible in the linear regime. These findings open new avenues for controlling light propagation and localization in lattices with more elaborate band structures.

For the preparation of high-dimensional functions on quantum computers, we introduce tensor network algorithms that are efficient with regard to dimensionality, optimize circuits composed of hardware-native gates and take gate errors into account during the optimization. To avoid the notorious barren plateau problem of vanishing gradients in the circuit optimization, we smoothly transform the circuit from an easy-to-prepare initial function into the desired target function. We show that paradigmatic multivariate functions can be accurately prepared such as, by numerical simulations, a 17-dimensional Gaussian encoded in the state of 102 qubits and, through experiments, a 9-dimensional Gaussian realized using 54 qubits on Quantinuum’s H2 quantum processor.

Artificial atoms non-locally coupled to waveguides — the so-called giant atoms — offer new opportunities for the control of light and matter. In this work, we show how to use an array of non-locally coupled transmon “molecules” to engineer a passive photonic controlled gate for waveguide photons. In particular, we show that a conditional elastic phase shift between counter-propagating photons arises from the interplay between direction-dependent couplings, engineered through an interplay of non local interactions and molecular binding strength; and the nonlinearity of the transmon array. We analyze the conditions under which a maximal $\pi$-phase shift — and hence a CZ gate — is obtained, and characterize the gate fidelity as a function of key experimental parameters, including finite transmon nonlinearities, emitter spectral inhomogeneities, and limited cooperativity. Our work opens the use of giant atoms as key elements of microwave photonic quantum computing devices.

The phenomenon where a quantum system can be exponentially accelerated to its stationary state has been referred to as the Quantum Mpemba Effect (QMpE). Due to its analogy with the classical Mpemba effect, hot water freezes faster than cold water, this phenomenon has garnered significant attention. Although QMpE has been characterized and experimentally verified in different scenarios, the sufficient and necessary conditions to achieve such a phenomenon are still under investigation. In this paper, we address a sufficient condition for QMpE through a general approach for open quantum system dynamics. With the help of the Mpemba parameter introduced in this work to quantify how strong the QMpE can be, we discuss how our conditions can predict and explain the emergence of weak and strong QMpE in a robust way. As an application, by harnessing the intrinsic non-classical nature of squeezed thermal environments, we show how enhanced QMpE can be effectively induced when our conditions are met. We demonstrate that when the system interacts with thermal reservoirs, a hot qubit freezes faster than a cold qubit in the presence of squeezing. Our results provide tools and new insights, opening a broad avenue for further investigation at the most fundamental levels of this peculiar phenomenon in the quantum realm.

The distribution of entanglement across distant qubits is a central challenge for the operation of scalable quantum computers and large-scale quantum networks. Existing approaches rely on deterministic state transfer schemes or probabilistic protocols that require active control or measurement and postselection. Here we demonstrate an alternative, fully autonomous process, where two remote qubits are entangled through their coupling to a quantum-correlated photonic reservoir. In our experiment, a Josephson parametric converter produces a Gaussian, continuous-variable entangled state of propagating microwave fields that drives two spatially separated superconducting transmon qubits into a stationary, discrete-variable entangled state. Beyond entanglement distribution, we also show that superconducting qubits can be used to directly certify two-mode squeezing, with higher sensitivity and without the need for calibrated noise-subtraction. These results establish networks of qubits interfaced with distributed continuous-variable entangled states as a powerful new platform for both foundational studies and quantum-technology relevant applications.

We introduce a driven-dissipative Floquet model in which a single harmonic oscillator, with both frequency and decay rate modulated, realizes a non-Hermitian synthetic lattice with an effective electric-field gradient in frequency space. Using the Floquet-Green’s function and the doubled Hamiltonian representation of non-Hermitian matrices, we show that the linear response of this system is characterized by a local winding number. Nontrivial values of the winding number induce directional amplification in the synthetic dimension, thereby converting input signals to different frequencies. The underlying mode structure is well described by a Jackiw-Rebbi-like continuum theory with Dirac cones and solitonic topological zero modes in synthetic frequency. Our results establish a simple and experimentally feasible route to non-Hermitian topological amplification, naturally implementable in current quantum technologies such as superconducting circuits.

Long-range quantum systems, in which the interactions decay as $1/r^{\alpha}$, are of increasing interest due to the variety of experimental set-ups in which they naturally appear. Motivated by this, we study fundamental properties of long-range spin systems in thermal equilibrium, focusing on the weak regime of $ \alpha>D$. Our main result is a proof of analiticity of their partition functions at high temperatures, which allows us to construct a classical algorithm with sub-exponential runtime $\exp(\mathcal{O}(\log^2(N/\epsilon)))$ that approximates the log-partition function to small additive error $\epsilon$. As by-products, we establish the equivalence of ensembles and the Gaussianity of the density of states, which we verify numerically in both the weak and strong long-range regimes. This also yields constraints on the appearance of various classes of phase transitions, including thermal, dynamical and excited-state ones. Our main technical contribution is the extension to the quantum long-range regime of the convergence criterion for cluster expansions of Koteck\’y and Preiss.

The field of superconducting qubits is constantly evolving with new circuit designs. However, when it comes to qubit readout, the use of simple transverse linear coupling remains overwhelmingly prevalent. This standard readout scheme has significant drawbacks: in addition to the Purcell effect, it suffers from a limitation on the maximal number of photons in the readout mode, which restricts the signal-to-noise ratio (SNR) and the Quantum Non-Demolition (QND) nature of the readout. Here, we explore the high-power regime by engineering a nonlinear coupling between a transmon qubit and its readout mode. Our approach builds upon previous work by Dassonneville et al. [Physical Review X 10, 011045 (2020)], on qubit readout with a non-perturbative cross-Kerr coupling in a transmon molecule. We demonstrate a readout fidelity of 99.21% with 89 photons utilizing a parametric amplifier. At this elevated photon number, the QND nature remains high at 96.7%. Even with up to 300 photons, the QNDness is only reduced by a few percent. This is qualitatively explained by deriving a critical number of photons associated with the nonlinear coupling, yielding a theoretical value of $\bar{n}_r^\text{crit} = 377$ photons for our sample’s parameters. These results highlight the promising performance of the transmon molecule in the high-power regime, establishing it as a compelling platform for high-fidelity qubit readout.

Photonic quantum metrology enables the measurement of physical parameters with precision surpassing classical limits by using quantum states of light. However, generating states providing a large metrological advantage is hard because standard probabilistic methods suffer from low generation rates. Deterministic protocols using non-linear interactions offer a path to overcome this problem, but they are currently limited by the errors introduced during the interaction time. Thus, finding strategies to minimize the interaction time of these non-linearities is still a relevant question. In this work, we introduce and compare different deterministic strategies based on continuous and programmable Jaynes-Cummings and Kerr-type interactions, aiming to maximize the metrological advantage while minimizing the interaction time. We find that programmable interactions provide a larger metrological advantage than continuous operations at the expense of slightly larger interaction times. We show that while for Jaynes-Cummings non-linearities the interaction time grows with the photon number, for Kerr-type ones it decreases, favoring the scalability to big photon numbers. Finally, we also optimize different measurement strategies for the deterministically generated states based on photon-counting and homodyne detection.

In classical mechanics and electromagnetism, interference occurs when two or more waves overlap at the same point in spacetime. However, the advent of quantum electrodynamics (QED) and its remarkable success in describing light-matter interactions at the microscopic level invites us to reconsider whether interference-like effects could arise even when the waves do not physically overlap. In this work, we extend the notion of wave interference to a novel and unconventional regime. Building upon the fundamental description of interference in terms of the interaction with the observer [Phys. Rev. Lett. 134, 133603 (2025)], we demonstrate that interference-like phenomena can emerge when two independent fields interact with a single detector at different locations in Minkowski space. We begin by developing a theoretical model in which a spatially extended atom simultaneously couples to two distant fields. We then propose an experimentally feasible implementation using superconducting circuits, where a giant artificial atom interacts with two independent resonators. Our findings open new directions for exploring interference in quantum systems and suggest new possibilities for optical quantum technologies, including the realization of atom-transparent devices controlled by spatially separated laser fields.

Quantum Floquet engineering (QFE) seeks to generalize the control of quantum systems with classical external fields, widely known as Semi-Classical Floquet engineering (SCFE), to quantum fields. However, to faithfully capture the physics at arbitrary coupling, a gauge-invariant description of light-matter interaction in cavity-QED materials is required, which makes the Hamiltonian highly non-linear in photonic operators. We provide a non-perturbative truncation scheme of the Hamiltonian, which is valid or arbitrary coupling strength, and use it to investigate the role of light-matter correlations, which are absent in SCFE. We find that even in the high-frequency regime, light-matter correlations can be crucial, in particular for the topological properties of a system. As an example, we show that for a SSH chain coupled to a cavity, light-matter correlations break the original chiral symmetry of the chain, strongly affecting the robustness of its edge states. In addition, we show how light-matter correlations are imprinted in the photonic spectral function and discuss their relation with the topology of the bands.

Long-range interactions are a key resource in many quantum phenomena and technologies. Free-space photons mediate power-law interactions but lack tunability and suffer from decoherence processes due to their omnidirectional emission. Engineered dielectrics can yield tunable and coherent interactions, but typically at the expense of making them both shorter-ranged and sensitive to material disorder and photon loss. Here, we propose a platform that can circumvent all these limitations based on three-dimensional subwavelength atomic arrays subjected to magnetic fields. Our key result is to show how to design the polaritonic bands of these atomic metamaterials to feature a pair of frequency-isolated Weyl points. These Weyl excitations can thus mediate interactions that are simultaneously long-range, due to their gapless nature; robust, due to the topological protection of Weyl points; and decoherence-free, due to their subradiant character. We demonstrate the robustness of these isolated Weyl points for a large regime of interatomic distances and magnetic field values and characterize the emergence of their corresponding Fermi arcs surface states. The latter can as well lead to two-dimensional, non-reciprocal atomic interactions with no analogue in other chiral quantum optical setups.

We show how the Loschmidt echo of a product state after a quench to a conformal invariant critical point and its leading finite time corrections can be predicted by using conformal field theories (CFT). We check such predictions with tensor networks, finding excellent agreement. As a result, we can use the Loschmidt echo to extract the universal information of the underlying CFT including the central charge, the operator content, and its generalized temporal entropies. We are also able to predict and confirm an emerging dual-unitarity of the evolution at late times, since the spatial transfer matrix operator that evolves the system in space becomes unitary in such limit. Our results on the growth of temporal entropies also imply that, using state-of-the art tensor networks algorithms, such calculations only require resources that increase polynomially with the duration of the quench, thus providing an example of numerically efficiently solvable out-of-equilibrium scenario.

We present a flip-chip architecture for an array of coupled superconducting qubits, in which circuit components reside inside individual microwave enclosures. In contrast to other flip-chip approaches, the qubit chips in our architecture are electrically floating, which guarantees a simple, fully modular assembly of capacitively coupled circuit components such as qubit, control, and coupling structures, as well as reduced crosstalk between the components. We validate the concept with a chain of three nearest neighbor coupled generalized flux qubits in which the center qubit acts as a frequency-tunable coupler. Using this coupler, we demonstrate a transverse coupling on/off ratio $\approx$ 50, zz-crosstalk $\approx$ 0.7 kHz between resonant qubits and isolation between the qubit enclosures > 60 dB.

We introduce SA-FDR, a novel algorithm for $\ell_0$-norm feature selection that considers this task as a combinatorial optimisation problem and solves it by using simulated annealing to perform a global search over the space of feature subsets. The optimisation is guided by the Fisher discriminant ratio, which we use as a computationally efficient proxy for model quality in classification tasks. Our experiments, conducted on datasets with up to hundreds of thousands of samples and hundreds of features, demonstrate that SA-FDR consistently selects more compact feature subsets while achieving a high predictive accuracy. This ability to recover informative yet minimal sets of features stems from its capacity to capture inter-feature dependencies often missed by greedy optimisation approaches. As a result, SA-FDR provides a flexible and effective solution for designing interpretable models in high-dimensional settings, particularly when model sparsity, interpretability, and performance are crucial.

Increasing the number of particles in a system often leads to qualitative changes in its properties, such as breaking of symmetries and the appearance of phase transitions. This renders a macroscopic system fundamentally different from its individual microscopic constituents. Lying between these extremes, mesoscopic systems exhibit microscopic fluctuations that influence behavior on longer length scales, leading to critical phenomena and dynamics. Therefore, tracing the properties of well-controlled mesoscopic systems can help bridge the gap between an exact description of few-body microscopic systems and the emergent description of many-body systems. Here, we explore mesoscopic signatures of an optomechanical self-organization phase transition using arrays of cold atoms inside an optical cavity. By precisely engineering atom-cavity interactions, we reveal how critical behavior depends on atom number, identify characteristic dynamical behaviors in the self-organized regime, and observe a finite optomechanical susceptibility at the critical point. These findings advance our understanding of particle-number- and time-resolved properties of phase transitions in mesoscopic systems.

Engineering deterministic photonic gates with simple resources is one of the long-standing challenges in photonic quantum computing. Here, we design a passive conditional gate between co-propagating photons using an array of only two-level emitters. The key resource is to harness the effective photon-photon interaction induced by the chiral coupling of the emitter array to two waveguide modes with different resonant momenta at the emitter’s transition frequency. By studying the system’s multi-photon scattering response, we demonstrate that, in certain limits, this configuration induces a non-linear $\pi$-phase shift between the polariton eigenstates of the system without distorting spectrally the wavepackets. Then, we show how to harness this non-linear phase shift to engineer a conditional, deterministic photonic gate in different qubit encodings, with a fidelity arbitrarily close to 1 in the limit of large number of emitters and coupling efficiency. Our configuration can be implemented in topological photonic platforms with multiple chiral edge modes, opening their use for quantum information processing, or in other setups where such chiral multi-mode waveguide scenario can be obtained, e.g., in spin-orbit coupled optical fibers or photonic crystal waveguides.

The complexity of simulating the out-of-equilibrium evolution of local operators in the Heisenberg picture is governed by the operator entanglement, which grows linearly in time for generic non-integrable systems, leading to an exponential increase in computational resources. A promising approach to simplify this challenge involves discarding parts of the operator and focusing on a subspace formed by “light” Pauli strings – strings with few Pauli matrices – as proposed by Rakovszki et al. [PRB 105, 075131 (2022)]. In this work, we investigate whether this strategy can be applied to quenches starting from homogeneous product states. For ergodic dynamics, these initial states grant access to a wide range of equilibration temperatures. By concentrating on the desired matrix elements and retaining only the portion of the operator that contains Pauli strings parallel to the initial state, we uncover a complex scenario. In some cases, the light Pauli strings suffice to describe the dynamics, enabling efficient simulation with current algorithms. However, in other cases, heavier strings become necessary, pushing computational demands beyond our current capabilities. We analyze this behavior using a newly introduced measure of complexity, the Operator Weight Entropy, which we compute for different operators across most points on the Bloch sphere.

Sum-frequency generation (SFG) allows for coherent upconversion of an electromagnetic signal and has applications in mid-infrared vibrational spectroscopy of molecules. Recent experimental and theoretical studies have shown that plasmonic nanocavities, with their deep sub-wavelength mode volumes, may allow to obtain vibrational SFG signals from a single molecule. In this article, we compute the degree of second order coherence ($g^{(2)}(0)$) of the upconverted mid-infrared field under realistic parameters and accounting for the anharmonic potential that characterizes vibrational modes of individual molecules. On the one hand, we delineate the regime in which the device should operate in order to preserve the second-order coherence of the mid-infrared source, as required in quantum applications. On the other hand, we show that an anharmonic molecular potential can lead to antibunching of the upconverted photons under coherent, Poisson-distributed mid-infrared and visible drives. Our results therefore open a path toward a new kind of bright and tunable source of indistinguishable single photons by leveraging “vibrational blockade” in a resonantly and parametrically driven molecule, without the need for strong light-matter coupling.

In recent years, Born-Markov master equations based on tracing out the electromagnetic degrees of freedom have been extensively employed in the description of quantum optical phenomena originating from photon-mediated interactions in quantum emitter ensembles. The breakdown of these effective models, built on assumptions such as ensemble spectral homogeneity, an unstructured photonic density of states, and weak light-matter coupling, has also recently attracted considerable attention. Here, we investigate the accuracy of this well-established framework beyond the most conventional, and extensively explored, spontaneous emission configuration. Specifically, we consider a system comprising two coherently driven and detuned quantum emitters, embedded within a hybrid photonic-plasmonic cavity, formed by a metallic nanorod integrated into a high-refractive-index dielectric microresonator. The local density of photonic states in this structure exhibits a complex frequency dependence, making it a compelling platform for exploring photon-mediated interactions beyond the assumptions above. We benchmark this modeling approach for the quantum dynamics of the emitter pair against exact calculations based on a macroscopic field quantization formalism, providing an illustrative assessment of its validity in significantly structured and dispersive photonic environments. Our analysis reveals four distinct regimes of laser driving and frequency splitting that lead to markedly different levels of accuracy in the effective model.

Fermionic atoms in optical lattices provide a native implementation of Fermi-Hubbard (FH) models that can be used as analog quantum simulators of many-body fermionic systems. Recent experimental advances include the time-dependent local control of chemical potentials and tunnelings, and thus enable to operate this platform digitally as a programmable quantum simulator. Here, we explore these opportunities and develop ground-state preparation algorithms for different fermionic models, based on the ability to implement both single-particle and many-body, high-fidelity fermionic gates, as provided by the native FH Hamiltonian. In particular, we first design variational, pre-compiled quantum circuits to prepare the ground state of the natively implemented FH model, with significant speedups relative to competing adiabatic protocols. Besides, the versatility of this variational approach enables to target extended FH models, i.e., including terms that are not natively realized on the platform. As an illustration, we include next-nearest-neighbor tunnelings at finite dopings, relevant in the context of $d$-wave superconductivity. Furthermore, we discuss how to approximate the imaginary-time evolution using variational fermionic circuits, both as an alternative state-preparation strategy, and as a subroutine for the Quantum Lanczos algorithm to further improve the energy estimation. We benchmark our protocols for ladder geometries, though they can be readily applied to 2D experimental setups to address regimes beyond the capabilities of current classical methods. These results pave the way for more efficient and comprehensive explorations of relevant many-body phases with existing programmable fermionic quantum simulators.

This research focuses on solving time-dependent partial differential equations (PDEs), in particular the time-dependent Schr\”odinger equation, using matrix product states (MPS). We propose an extension of Hermite Distributed Approximating Functionals (HDAF) to MPS, a highly accurate pseudospectral method for approximating functions of derivatives. Integrating HDAF into an MPS finite precision algebra, we test four types of quantum-inspired algorithms for time evolution: explicit Runge-Kutta methods, Crank-Nicolson method, explicitly restarted Arnoli iteration and split-step. The benchmark problem is the expansion of a particle in a quantum quench, characterized by a rapid increase in space requirements, where HDAF surpasses traditional finite difference methods in accuracy with a comparable cost. Moreover, the efficient HDAF approximation to the free propagator avoids the need for Fourier transforms in split-step methods, significantly enhancing their performance with an improved balance in cost and accuracy. Both approaches exhibit similar error scaling and run times compared to FFT vector methods; however, MPS offer an exponential advantage in memory, overcoming vector limitations to enable larger discretizations and expansions. Finally, the MPS HDAF split-step method successfully reproduces the physical behavior of a particle expansion in a double-well potential, demonstrating viability for actual research scenarios.

We present a quantum-inspired solver for the one-dimensional Gross-Pitaevskii equation in the Quantics Tensor-Train (QTT) representation. By evolving the system entirely within a low-rank tensor manifold, the method sidesteps the memory and runtime barriers that limit conventional finite-difference and spectral schemes. Two complementary algorithms are developed: an imaginary-time projector that drives the condensate toward its variational ground state and a rank-adapted fourth-order Runge-Kutta integrator for real-time dynamics. The framework captures a broad range of physical scenarios – including barrier-confined condensates, quasi-random potentials, long-range dipolar interactions, and multicomponent spinor dynamics – without leaving the compressed representation. Relative to standard discretizations, the QTT approach achieves an exponential reduction in computational resources while retaining quantitative accuracy, thereby extending the practicable regime of Gross-Pitaevskii simulations on classical hardware. These results position tensor networks as a practical bridge between high-performance classical computing and prospective quantum hardware for the numerical treatment of nonlinear Schrodinger-type partial differential equations.

Continuously monitored quantum systems are emerging as promising platforms for quantum metrology, where a central challenge is to identify measurement strategies that optimally extract information about unknown parameters encoded in the complex quantum state of emitted radiation. Different measurement strategies effectively access distinct temporal modes of the emitted field, and the resulting choice of mode can strongly impact the information available for parameter estimation. While a ubiquitous approach in quantum optics is to select frequency modes through spectral filtering, the metrological potential of this technique has not yet been systematically quantified. We develop a theoretical framework to assess this potential by modeling spectral detection as a cascaded quantum system, allowing us to reconstruct the full density matrix of frequency-filtered photonic modes and to compute their associated Fisher information. This framework provides a minimal yet general method to benchmark the performance of spectral measurements in quantum optics, allowing to identify optimal filtering strategies in terms of frequency selection, detector linewidth, and metrological gain accessible through higher-order frequency-resolved correlations and mean-field engineering. These results lay the groundwork for identifying and designing optimal sensing strategies in practical quantum-optical platforms.

The last two decades has seen quantum thermodynamics become a well established field of research in its own right. In that time, it has demonstrated a remarkably broad applicability, ranging from providing foundational advances in the understanding of how thermodynamic principles apply at the nano-scale and in the presence of quantum coherence, to providing a guiding framework for the development of efficient quantum devices. Exquisite levels of control have allowed state-of-the-art experimental platforms to explore energetics and thermodynamics at the smallest scales which has in turn helped to drive theoretical advances. This Roadmap provides an overview of the recent developments across many of the field’s sub-disciplines, assessing the key challenges and future prospects, providing a guide for its near term progress.

A fast and scalable scheme for multi-qubit resetting in superconducting quantum processors is proposed by exploiting the feasibility of frequency-tunable transmon qubits and transmon-like couplers to engineer a full programmable superconducting erasing head. The scalability of the device is verified by simultaneously resetting two qubits, where we show that collectivity effects may emerge as an fundamental ingredient to speed up the erasing process. Conversely, we also describe the appearance of decoherence-free subspace in multi-qubit chips, causing it to damage the device performance. To overcome this problem, a special set of parameters for the tunable frequency coupler is proposed, which allows us to erase even states within such subspace. To end, we offer a proposal to buildup integrated superconducting processors that can be efficiently connected to erasure heads in a scalable way.

We set up an effective field theory formulation for the renormalization flow of matrix product states (MPS) with finite bond dimension, focusing on systems exhibiting finite-entanglement scaling close to a conformally invariant critical fixed point. We show that the finite MPS bond dimension $\chi$ is equivalent to introducing a perturbation by a relevant operator to the fixed-point Hamiltonian. The fingerprint of this mechanism is encoded in the $\chi$-independent universal transfer matrix’s gap ratios, which are distinct from those predicted by the unperturbed Conformal Field Theory. This phenomenon defines a renormalization group self-congruent point, where the relevant coupling constant ceases to flow due to a balance of two effects; When increasing $\chi$, the infrared scale, set by the correlation length $\xi(\chi)$, increases, while the strength of the perturbation at the lattice scale decreases. The presence of a self-congruent point does not alter the validity of the finite-entanglement scaling hypothesis, since the self-congruent point is located at a finite distance from the critical fixed point, well inside the scaling regime of the CFT. We corroborate this framework with numerical evidences from the exact solution of the Ising model and density matrix renormalization group (DMRG) simulations of an effective lattice model.

The study of many-body quantum systems out of equilibrium remains a significant challenge with complexity barriers arising in both state and operator-based representations. In this work, we review recent approaches based on finding better contraction strategies for the full spatio-temporal tensor networks that encode the path integral of the dynamics, as well as the conceptual integration of influence functionals, process tensors, and transfer matrices within the tensor network formalism. We discuss recent algorithmic developments, highlight the complexity of influence functionals in various dynamical regimes and present consistent results of different communities, showing how ergodic dynamics render these functionals exponentially difficult to compress. Finally, we provide an outlook on strategies to encode complementary influence functional overlaps, paving the way for accurate descriptions of open and closed quantum systems with tensor networks.

We revisit the U(1) quantum link model in a ladder geometry, finding, by finite-size scaling, that the critical exponent $\nu=1$ and the central charge $c=1/2$ are consistent with the Ising universality class for all phase transitions observed. A blind application of the Harris criterion would suggest that this criticality is lost in the presence of the disorder. It turns out not to be the case. For the disorder affecting ladder’s rung hoppings only, we have found that the transitions survive disappearing only for quite strong disorder. The disorder in the ladder’s legs destroys the nonzero mass phase criticality, while the symmetry-protected topological phase for zero mass survives a small disorder. The observed robustness against disorder is explained qualitatively using field-theoretic arguments.

This work introduces a theoretical framework to model the collective dynamics of quantum emitters in highly non-Markovian environments, interacting through the exchange of photons with significant retardations. The formalism consists on a set of coupled delay differential equations for the emitter’s polarizations $\sigma^\pm_i$, supplemented by input-output relations that describe the field mediating the interactions. These equations capture the dynamics of both linear (bosonic) and nonlinear (two-level) emitter arrays. It is exact in some limits$-$e.g., bosonic emitters or generic systems with up to one collective excitation$-$and can be integrated to provide accurate results for larger numbers of photons. These equations support a study of collective spontaneous emission of emitter arrays in open waveguide-QED environments. This study uncovers an effect we term cascaded super- and sub-radiance, characterized by light-cone-limited propagation and increasingly correlated photon emission across distant emitters. The collective nature of this dynamics for two-level systems is evident both in the enhancement of collective emission rates, as well as in a superradiant burst with a faster than linear growth. While these effects should be observable in existing circuit QED devices or slight generalizations thereof, the formalism put forward in this work can be extended to model other systems such as network of quantum emitters or the generation of correlated photon states.

Non-reciprocal couplings or drivings are known to induce steady-state, directional, amplification in driven-dissipative bosonic lattices. This amplification phenomenon has been recently linked to the existence of a non-zero topological invariant defined with the system’s dynamical matrix, and thus, it depends critically on the couplings’ structure. In this work, we demonstrate the emergence of unconventional, non-reciprocal, long-range dissipative couplings induced by the interaction of the bosonic chain with a chiral, multimode channel, and then study their impact on topological amplification phenomena. We show that these couplings can lead to topological invariant values greater than one which induce topological, multimode amplification and metastability behaviour. Besides, we also show how these couplings can also display topological amplifying phases that are dynamically stable in the presence of local parametric drivings. Finally, we conclude by showing how such phenomena can be naturally obtained in two-dimensional topological insulators hosting multiple edge modes.

Digitizing an adiabatic evolution is a strategy able to combine the good performance of gate-based quantum processors with the advantages of adiabatic algorithms, providing then a hybrid model for efficient quantum information processing. In this work we develop validity conditions for high fidelity digital adiabatic tasks. To this end, we assume a digitizing process based on the Suzuki-Trotter decomposition, which allows us to introduce a Digitized Adiabatic Theorem. As consequence of this theorem, we show that the performance of such a hybrid model is limited by the fundamental constraints on the adiabatic theorem validity, even in ideal quantum processors. We argue how our approach predicts the existence of intrinsic non-adiabatic errors reported by R. Barends et al., Nature 534, 222 (2016) through an empirical study of digital annealing. In addition, our approach allows us to explain the existence of a scaling of the number of Suzuki-Trotter blocks for the optimal digital circuit with respect to the optimal adiabatic total evolution time, as reported by G. B. Mbeng et al., Phys. Rev. B 100, 224201 (2019) through robust numerical analysis of digital annealing. We illustrate our results through two examples of digitized adiabatic algorithms, namely, the two-qubits exact-cover problem and the three-qubits adiabatic factorization of the number 21.

We consider a linear array of trapped ions subjected to local parametric modulation of the trapping potential and continuous laser cooling. In our model, the phase of the parametric modulation varies linearly along the array, breaking time-reversal symmetry and inducing non-trivial topological effects. The linear response to an external force is investigated with the Green’s function formalism. We predict the appearance of topological amplification regimes in which the trapped ion array behaves as a directional amplifier of vibrational excitations. The emergence of topological phases is determined by a winding number related to non-Hermitian point-gap topology. Beyond its fundamental interests as a topological driven-dissipative system, our setup can be used for quantum sensing of ultra-weak forces and electric fields. We consider a scheme in which a trapped ion at one edge of the array acts as a sensor of an ultra-weak force, and the vibrational signal gets amplified towards the last trapped ion, which acts as a detector. We consider arrays of 2-30 $^{25}$Mg$^+$ ions, assuming that the detector ion’s displacement is measured via fluorescence with a spatial resolution of 200-500 nm, and predict sensitivities as small as 1 yN $\cdot$ Hz$^{-1/2}$. Our system has the advantage that the detected force frequency can be tuned by adjusting the frequency of the periodic drive.