Entangled resources enable quantum sensing that achieves Heisenberg scaling, a quadratic improvement on the standard quantum limit, but preparing large $N$ spin entangled states is challenging in the presence of decoherence. We present a quantum control strategy using highly nonlinear geometric phase gates which can be used for generic state or unitary synthesis on the Dicke subspace with $O(N)$ or $O(N^2)$ gates, respectively. The method uses a dispersive coupling of the spins to a common bosonic mode and does not require addressability, special detunings, or interactions between the spins. By using amplitude amplification our control sequence for preparing states ideal for metrology can be significantly simplified to $O(N^{5/4})$ geometric phase gates with action angles $O(1/N)$ that are more robust to mode decay. The geometrically closed path of the control operations ensures the gates are insensitive to the initial state of the mode and the sequence has built-in dynamical decoupling providing resilience to dephasing errors.

We extend to quenched-disordered systems the variational scheme for real-space renormalization group calculations that we recently introduced for homogeneous spin Hamiltonians. When disorder is present our approach gives access to the flow of the renormalized Hamiltonian distribution, from which one can compute the critical exponents if the correlations of the renormalized couplings retain finite range. Key to the variational approach is the bias potential found by minimizing a convex functional in statistical mechanics. This potential reduces dramatically the Monte Carlo relaxation time in large disordered systems. We demonstrate the method with applications to the two-dimensional dilute Ising model, the random transverse field quantum Ising chain, and the random field Ising in two- and three-dimensional lattices.

At low temperature, collective excitations of one-dimensional (1D) interacting fermions exhibit spin-charge separation, a unique feature predicted by the Tomonaga-Luttinger liquid (TLL) theory, but a rigorous understanding remains challenging. Using the thermodynamic Bethe ansatz (TBA) formalism, we analytically derive universal properties of a 1D repulsive spin-$1/2$ Fermi gas with arbitrary interaction strength. We show how spin-charge separation emerges from the exact TBA formalism, and how it is disrupted by the interplay between the two degrees of freedom that brings us beyond the TLL paradigm. Based on the exact low-lying excitation spectra, we further evaluate the spin and charge dynamical structure factors (DSFs). The peaks of the DSFs exhibit distinguishable propagating velocities of spin and charge as functions of interaction strength, which can be observed by Bragg spectroscopy with ultracold atoms.

Quantum cellular automata are unitary maps that preserve locality and respect causality. We identify them, in any dimension, with simple tensor networks (projected entangled pair unitary) whose bond dimension does not grow with the system size. As a result, they satisfy an area law for the entanglement entropy they can create. We define other classes of nonunitary maps, the so-called quantum channels, that either respect causality or preserve locality. We show that, whereas the latter obey an area law for the number of quantum correlations they can create, as measured by the quantum mutual information, the former may violate it. We also show that neither of them can be expressed as tensor networks with a bond dimension that is independent of the system size.

Unlike the entanglement of quantum states, very little is known about the entanglement of bipartite channels, called dynamical entanglement. Here we work with the partial transpose of a superchannel, and use it to define computable measures of dynamical entanglement, such as the negativity. We show that a version of it, the max-logarithmic negativity, represents the exact asymptotic dynamical entanglement cost. We discover a family of dynamical entanglement measures that provide necessary and sufficient conditions for bipartite channel simulation under local operations and classical communication and under operations with positive partial transpose.

We introduce and study a novel class of sensors whose sensitivity grows exponentially with the size of the device. Remarkably, this drastic enhancement does not rely on any fine-tuning, but is found to be a stable phenomenon immune to local perturbations. Specifically, the physical mechanism behind this striking phenomenon is intimately connected to the anomalous sensitivity to boundary conditions observed in non-Hermitian topological systems. We outline concrete platforms for the practical implementation of these non-Hermitian topological sensors ranging from classical metamaterials to synthetic quantum materials.

We explore the relationship between symmetrization and entanglement through measurements on few-particle systems in a multiwell potential. In particular, considering two or three trapped atoms, we measure and distinguish correlations arising from two different physical origins: antisymmetrization of the fermionic wave function and interaction between particles. We quantify this through the entanglement negativity of states, and the introduction of an antisymmetric negativity, which allows us to understand the role that symmetrization plays in the measured entanglement properties. We apply this concept both to pure theoretical states and to experimentally reconstructed density matrices of two or three mobile particles in an array of optical tweezers.

Spectroscopy is an important tool for probing the properties of materials, chemicals, and biological samples. We design a practical transmitter-receiver system that exploits entanglement to achieve a provable quantum advantage over all spectroscopic schemes based on classical sources. To probe the absorption spectra, modeled as a pattern of transmissivities among different frequency modes, we employ broadband signal-idler pairs in two-mode squeezed vacuum states. At the receiver side, we apply photodetection after optical parametric amplification. Finally, we perform a maximum likelihood decision test on the measurement results, achieving an error probability orders of magnitude lower than the optimum classical systems in various examples, including “wine tasting” and “drug testing” where real molecules are considered. In detecting the presence of an absorption line, our quantum scheme achieves the optimum performance allowed by quantum mechanics. The quantum advantage in our system is robust against noise and loss, which makes near-term experimental demonstration possible.

Quantum correlations in observables of multiple systems not only are of fundamental interest, but also play a key role in quantum information processing. As a signature of these correlations, the violation of Bell inequalities has not been demonstrated with multipartite hybrid entanglement involving both continuous and discrete variables. Here we create a five-partite entangled state with three superconducting transmon qubits and two photonic qubits, each encoded in the mesoscopic field of a microwave cavity. We reveal the quantum correlations among these distinct elements by joint Wigner tomography of the two cavity fields conditional on the detection of the qubits and by test of a five-partite Bell inequality. The measured Bell signal is $8.381\pm 0.038$, surpassing the bound of 8 for a four-partite entanglement imposed by quantum correlations by 10 standard deviations, demonstrating the genuine five-partite entanglement in a hybrid quantum system.

The current understanding of aging phenomena is mainly confined to the study of systems with short-ranged interactions. Little is known about the aging of long-ranged systems. Here, the aging in the phase-ordering kinetics of the two-dimensional Ising model with power-law long-range interactions is studied via Monte Carlo simulations. The dynamical scaling of the two-time spin-spin autocorrelator is well described by simple aging for all interaction ranges studied. The autocorrelation exponents are consistent with $\lambda =1.25$ in the effectively short-range regime, while for stronger long-range interactions the data are consistent with $\lambda =d/2=1$. For very long-ranged interactions, strong finite-size effects are observed. We discuss whether such finite-size effects could be misinterpreted phenomenologically as subaging.

We introduce an equation for density matrices that ensures a monotonic decrease of the free energy and reaches a fixed point at the Gibbs thermal. We build a variational approach for many-body systems that can be applied to a broad class of states, including all bosonic and fermionic Gaussian, as well as their generalizations obtained by unitary transformations, such as polaron transformations in electron-phonon systems. We apply it to the Holstein model on $20\times 20$ and $50\times 50$ square lattices, and predict phase separation between the superconducting and charge-density wave phases in the strong interaction regime.

We study how perturbations affect dynamics of integrable many-body quantum systems, causing transition from integrability to chaos. Looking at spin transport in the Heisenberg chain with impurities we find that in the thermodynamic limit transport gets diffusive already at an infinitesimal perturbation. Small extensive perturbations therefore cause an immediate transition from integrability to chaos. Nevertheless, there is a remnant of integrability encoded in the dependence of the diffusion constant on the impurity density, namely, at small densities it is proportional to the square root of the inverse density, instead of to the inverse density as would follow from Matthiessen’s rule. We show that Matthiessen’s rule has to be modified in nonballistic systems. Results also highlight a nontrivial role of interacting scattering on a single impurity, and that there is a regime where adding more impurities can actually increase transport.

We have implemented a Walsh-Hadamard gate, which performs a quantum Fourier transform, in a superconducting qutrit. The qutrit is encoded in the lowest three energy levels of a capacitively shunted flux device, operated at the optimal flux-symmetry point. We use an efficient decomposition of the Walsh-Hadamard gate into two unitaries, generated by off-diagonal and diagonal Hamiltonians, respectively. The gate implementation utilizes simultaneous driving of all three transitions between the three pairs of energy levels of the qutrit, one of which is implemented with a two-photon process. The gate has a duration of 35 ns and an average fidelity over a representative set of states, including preparation and tomography errors, of 99.2%, characterized with quantum-state tomography. Compensation of ac-Stark and Bloch-Siegert shifts is essential for reaching high gate fidelities.

Constraints on work extraction are fundamental to our operational understanding of the thermodynamics of both classical and quantum systems. In the quantum setting, finite-time control operations typically generate coherence in the instantaneous energy eigenbasis of the dynamical system. Thermodynamic cycles can, in principle, be designed to extract work from this nonequilibrium resource. Here, we isolate and study the quantum coherent component to the work yield in such protocols. Specifically, we identify a coherent contribution to the ergotropy (the maximum amount of unitarily extractable work via cyclical variation of Hamiltonian parameters). We show this by dividing the optimal transformation into an incoherent operation and a coherence extraction cycle. We obtain bounds for both the coherent and incoherent parts of the extractable work and discuss their saturation in specific settings. Our results are illustrated with several examples, including finite-dimensional systems and bosonic Gaussian states that describe recent experiments on quantum heat engines with a quantized load.

The eigenstate entanglement entropy is a powerful tool to distinguish integrable from generic quantum-chaotic models. In integrable models, the average eigenstate entanglement entropy (over all Hamiltonian eigenstates) has a volume-law coefficient that generally depends on the subsystem fraction. In contrast, it is maximal (subsystem fraction independent) in quantum-chaotic models. Using random matrix theory for quadratic Hamiltonians, we obtain a closed-form expression for the average eigenstate entanglement entropy as a function of the subsystem fraction. We test it against numerical results for the quadratic Sachdev-Ye-Kitaev model and show that it describes the results for the power-law random banded matrix model (in the delocalized regime). We show that localization in quasimomentum space produces (small) deviations from our analytic predictions.

Shock waves are examples of the far-from-equilibrium behavior of matter; they are ubiquitous in nature, yet the underlying microscopic mechanisms behind their formation are not well understood. Here, we study the dynamics of dispersive quantum shock waves in a one-dimensional Bose gas, and show that the oscillatory train forming from a local density bump expanding into a uniform background is a result of quantum mechanical self-interference. The amplitude of oscillations, i.e., the interference contrast, decreases with the increase of both the temperature of the gas and the interaction strength due to the reduced phase coherence length. Furthermore, we show that vacuum and thermal fluctuations can significantly wash out the interference contrast, seen in the mean-field approaches, due to shot-to-shot fluctuations in the position of interference fringes around the mean.

Adiabatic quantum computing enables the preparation of many-body ground states. Realization poses major experimental challenges: Direct analog implementation requires complex Hamiltonian engineering, while the digitized version needs deep quantum gate circuits. To bypass these obstacles, we suggest an adiabatic variational hybrid algorithm, which employs short quantum circuits and provides a systematic quantum adiabatic optimization of the circuit parameters. The quantum adiabatic theorem promises not only the ground state but also that the excited eigenstates can be found. We report the first experimental demonstration that many-body eigenstates can be efficiently prepared by an adiabatic variational algorithm assisted with a multiqubit superconducting coprocessor. We track the real-time evolution of the ground and excited states of transverse-field Ising spins with a fidelity that can reach about 99%.

Resonance fluorescence has played a major role in quantum optics with predictions and later experimental confirmation of nonclassical features of its emitted light such as antibunching or squeezing. In the Rayleigh regime where most of the light originates from the scattering of photons with subnatural linewidth, antibunching would appear to coexist with sharp spectral lines. Here, we demonstrate that this simultaneous observation of subnatural linewidth and antibunching is not possible with simple resonant excitation. Using an epitaxial quantum dot for the two-level system, we independently confirm the single-photon character and subnatural linewidth by demonstrating antibunching in a Hanbury Brown and Twiss type setup and using high-resolution spectroscopy, respectively. However, when filtering the coherently scattered photons with filter bandwidths on the order of the homogeneous linewidth of the excited state of the two-level system, the antibunching dip vanishes in the correlation measurement. Our observation is explained by antibunching originating from photon-interferences between the coherent scattering and a weak incoherent signal in a skewed squeezed state. This prefigures schemes to achieve simultaneous subnatural linewidth and antibunched emission.

All known examples suggesting an exponential separation between classical simulation algorithms and stoquastic adiabatic quantum computing (StoqAQC) exploit symmetries that constrain adiabatic dynamics to effective, symmetric subspaces. The symmetries produce large effective eigenvalue gaps, which in turn make adiabatic computation efficient. We present a classical algorithm to subexponentially sample from an effective subspace of any $k$-local stoquastic Hamiltonian $H$, without a priori knowledge of its symmetries (or near symmetries). Our algorithm maps any $k$-local Hamiltonian to a graph $G=(V,E)$ with $|V|=O\mathbf{(}\mathrm{poly}(n)\mathbf{)}$, where $n$ is the number of qubits. Given the well-known result of Babai [Graph isomorphism in quasipolynomial time, in Proceedings of the Forty-Eighth Annual ACM Symposium on Theory of Computing (2016), pp. 684–697], we exploit graph isomorphism to study the automorphisms of $G$ and arrive at an algorithm quasipolynomial in $|V|$ for producing samples from effective subspace eigenstates of $H$. Our results rule out exponential separations between StoqAQC and classical computation that arise from hidden symmetries in $k$-local Hamiltonians. Our graph representation of $H$ is not limited to stoquastic Hamiltonians and may rule out corresponding obstructions in nonstoquastic cases, or be useful in studying additional properties of $k$-local Hamiltonians.

We present an algorithm for studying quantum systems at finite temperature using continuous matrix product operator representation. The approach handles both short-range and long-range interactions in the thermodynamic limit without incurring any time discretization error. Moreover, the approach provides direct access to physical observables including the specific heat, local susceptibility, and local spectral functions. After verifying the method using the prototypical quantum XXZ chains, we apply it to quantum Ising models with power-law decaying interactions and on the infinite cylinder, respectively. The approach offers predictions that are relevant to experiments in quantum simulators and the nuclear magnetic resonance spin-lattice relaxation rate.