Tree tensor network descriptions of critical quantum spin chains are empirically known to reproduce correlation functions matching conformal field theory (CFT) predictions in the continuum limit. It is natural to seek a more complete correspondence, additionally incorporating dynamics. On the CFT side, this is determined by a representation of the diffeomorphism group of the circle. In a remarkable series of papers, Jones outlined a research program where the Thompson group $\mathsf{T}$ takes the role of the latter in the discrete setting, and representations of $\mathsf{T}$ are constructed from certain elements of a subfactor planar algebra. He also showed that, for a particular example of such a construction, this approach only yields—in the continuum limit—a representation which is highly discontinuous and hence unphysical. Here we show that the same issue arises generically when considering tree tensor networks: the set of coarse-graining maps yielding discontinuous representations has full measure in the set of all isometries. This extends Jones’s no-go example to typical elements of the so-called tensor planar algebra. We also identify an easily verified necessary condition for a continuous limit to exist. This singles out a particular class of tree tensor networks. Our considerations apply to recent approaches for introducing dynamics in holographic codes.

The study of thermal operations allows one to investigate the ultimate possibilities of quantum states and of nanoscale thermal machines. Whilst fairly general, these results typically do not apply to continuous variable systems and do not take into account that, in many practically relevant settings, system-environment interactions are effectively bilinear. Here we tackle these issues by focusing on Gaussian quantum states and channels. We provide a complete characterization of the most general Gaussian thermal operation acting on an arbitrary number of bosonic modes, which turn out to be all embeddable in a Markovian dynamics, and derive necessary and sufficient conditions for state transformations under such operations in the single-mode case, encompassing states with nonzero coherence in the energy eigenbasis (i.e., squeezed states). Our analysis leads to a no-go result for the technologically relevant task of algorithmic cooling: We show that it is impossible to reduce the entropy of a system coupled to a Gaussian environment below its own or the environmental temperature, by means of a sequence of Gaussian thermal operations interspersed by arbitrary (even non-Gaussian) unitaries. These findings establish fundamental constraints on the usefulness of Gaussian resources for quantum thermodynamic processes.

Synthetic spaces allow physicists to bypass constraints imposed by certain physical laws in experiments. Here, we show that a synthetic torus, which consists of a ring trap in the real space and internal states of ultracold atoms cyclically coupled by Laguerre-Gaussian Raman beams, could be threaded by a net effective magnetic flux through its surface—an impossible mission in the real space. Such a synthetic Hall torus gives rise to a periodic lattice in real dimensions, in which the periodicity of the density modulation of atoms fractionalizes that of the Hamiltonian. Correspondingly, the energy spectrum is featured by multiple bands grouping into clusters with nonsymmorphic-symmetry-protected band crossings in each cluster, leading to swaps of wave packets in Bloch oscillations. Our scheme allows physicists to glue two synthetic Hall tori such that localization may emerge in a quasicrystalline lattice. If the Laguerre-Gaussian Raman beams and ring traps were replaced by linear Raman beams and ordinary traps, a synthetic Hall cylinder could be realized and deliver many of the aforementioned phenomena.

Arrays of atoms trapped in optical tweezers combine features of programmable analog quantum simulators with atomic quantum sensors. Here we propose variational quantum algorithms, tailored for tweezer arrays as programmable quantum sensors, capable of generating entangled states on demand for precision metrology. The scheme is designed to generate metrological enhancement by optimizing it in a feedback loop on the quantum device itself, thus preparing the best entangled states given the available quantum resources. We apply our ideas to the generation of spin-squeezed states on Sr atom tweezer arrays, where finite-range interactions are generated through Rydberg dressing. The complexity of experimental variational optimization of our quantum circuits is expected to scale favorably with system size. We numerically show our approach to be robust to noise, and surpassing known protocols.

We experimentally realize a highly tunable superfluid oscillator circuit in a quantum gas of ultracold atoms and develop and verify a simple lumped-element description of this circuit. At low oscillator currents, we demonstrate that the circuit is accurately described as a Helmholtz resonator, a fundamental element of acoustic circuits. At larger currents, the breakdown of the Helmholtz regime is heralded by a turbulent shedding of vortices and density waves. Although a simple phase-slip model offers qualitative insights into the circuit’s resistive behavior, our results indicate deviations from the phase-slip model. A full understanding of the dissipation in superfluid circuits will thus require the development of empirical models of the turbulent dynamics in this system, as have been developed for classical acoustic systems.

Macroscopic superposition states enable fundamental tests of quantum mechanics and hold a huge potential in metrology, sensing, and other quantum technologies. We propose to generate macroscopic superposition states of a large number of atoms in the ground state of a spin-1 Bose-Einstein condensate. Measuring the number of particles in one mode prepares with large probability highly entangled macroscopic superposition states in the two remaining modes. The macroscopic superposition states are heralded by the measurement outcome. Our protocol is robust under realistic conditions in current experiments, including finite adiabaticity, particle loss, and measurement uncertainty.

We develop a scheme of quantum reservoir state preparation, based on a quantum neural network framework, which takes classical optical excitation as input and provides desired quantum states as output. We theoretically demonstrate the broad potential of our scheme by explicitly preparing a range of intriguing quantum states, including single-photon states, Schrödinger’s cat states, and two-mode entangled states. This scheme can be used as a compact quantum state preparation device for emerging quantum technologies.

Efficient verification of pure quantum states in the adversarial scenario is crucial to many applications in quantum information processing, such as blind measurement-based quantum computation and quantum networks. However, little is known about this topic so far. Here, we establish a general framework for verifying pure quantum states in the adversarial scenario and clarify the resource cost. Moreover, we propose a simple and general recipe to constructing efficient verification protocols for the adversarial scenario from protocols for the nonadversarial scenario. With this recipe, arbitrary pure states can be verified in the adversarial scenario with almost the same efficiency as in the nonadversarial scenario. Many important quantum states can be verified in the adversarial scenario using local projective measurements with unprecedented high efficiencies.

We construct an effective Hamiltonian of interacting bosons, based on scattered radiation off vibrational modes of designed molecular architectures. Making use of the infinite yet countable set of spatial modes representing the scattering of light, we obtain a variable photon-photon interaction in this basis. The effective Hamiltonian Hermiticity is controlled by a geometric factor set by the overlaps of spatial modes. Using this mapping, we relate intensity measurements of the light to correlation functions of the interacting bosons evolving according to the effective Hamiltonian, rendering local as well as nonlocal observables accessible. This architecture may be used to simulate the dynamics of interacting bosons, as well as a designing tool for multiqubit photonic gates in quantum computing applications. Variable hopping, interaction, and confinement of the active space of the bosons are demonstrated on a model system.

Microwave trapped-ion quantum logic gates avoid spontaneous emission as a fundamental source of decoherence. However, microwave two-qubit gates are still slower than laser-induced gates and hence more sensitive to fluctuations and noise of the motional mode frequency. We propose and implement amplitude-shaped gate drives to obtain resilience to such frequency changes without increasing the pulse energy per gate operation. We demonstrate the resilience by noise injection during a two-qubit entangling gate with ${}^9{\mathrm{Be}}^{+}$ ion qubits. In the absence of injected noise, amplitude modulation gives an operation infidelity in the ${10}^{-3}$ range.

Few equilibrium—even less so nonequilibrium—statistical-mechanical models with continuous degrees of freedom can be solved exactly. Classical hard spheres in infinitely many space dimensions are a notable exception. We show that, even without resorting to a Boltzmann distribution, dimensionality is a powerful organizing device for exploring the stationary properties of active hard spheres evolving far from equilibrium. In infinite dimensions, we exactly compute the stationary state properties that govern and characterize the collective behavior of active hard spheres: the structure factor and the equation of state for the pressure. In turn, this allows us to account for motility-induced phase separation. Finally, we determine the crowding density at which the effective propulsion of a particle vanishes.

Nonstationary longtime dynamics was recently observed in a driven two-component Bose-Einstein condensate coupled to an optical cavity [N. Dogra, M. Landini, K. Kroeger, L. Hruby, T. Donner, and T. Esslinger, arXiv:1901.05974] and analyzed in mean-field theory. We solve the underlying model in the thermodynamic limit and show that this system is always dynamically unstable—even when mean-field theory predicts stability. Instabilities always occur in higher-order correlation functions leading to squeezing and entanglement induced by cavity dissipation. The dynamics may be understood as the formation of a dissipative time crystal. We use perturbation theory for finite system sizes to confirm the nonstationary behavior.

We report on the experimental measurement of the Hilbert-Schmidt distance between two two-qubit states by many-particle interference. We demonstrate that our three-step method for measuring distances in the Hilbert space is far less complex than reconstructing density matrices and that it can be applied in quantum-enhanced machine learning to reduce the complexity of calculating Euclidean distances between multidimensional points, which can be especially interesting for near term quantum technologies and quantum artificial intelligence research. Our results are also a novel example of applying mixed states in quantum information processing. Usually working with mixed states is undesired, but here it gives the possibility of encoding extra information as the degree of coherence between the given two dimensions of the density matrix.

Generic rotationally invariant matrix models satisfy a simple relation: the probability distribution of half the difference between any two diagonal elements and the one of off-diagonal elements are the same. In the spirit of the eigenstate thermalization hypothesis, we test the hypothesis that the same relation holds in quantum systems that are nonlocalized, when one considers small energy differences. The relation provides a stringent test of the eigenstate thermalization hypothesis beyond the Gaussian ensemble. We apply it to a disordered spin chain, the Sachdev-Ye-Kitaev model, and a Floquet system.

Classical dynamical systems close to a critical point are known to act as efficient sensors due to a strongly nonlinear response. We explore such systems in the quantum regime by modeling a quantum version of a driven van der Pol oscillator. We find the classical response survives down to one excitation quantum. At very weak drives, genuine quantum features arise, including diverging and negative susceptibilities. Further, the linear response is greatly enhanced by using a strong incoherent pump. These results are largely generic and can be probed in current experimental platforms suited for quantum sensing.

We study the dynamics of a Bose-Einstein condensate trapped circumferentially on a ring, and which is governed by an interacting gauge theory. We show that the associated density-dependent gauge potential and concomitant current nonlinearity permits a ground state in the form of a rotating chiral bright soliton. This chiral soliton is constrained to move in one direction by virtue of the current nonlinearity, and represents a time crystal in the same vein as Wilczek’s original proposal.

Perfect entanglement swapping, which can be realized without the postselection by using the nonlinear optical technology, provides an important way toward generating the large-scale quantum network. We explore an entanglement-swapping-based dense wavelength division multiplexed network in the experiment. Four users receive single quantum states at different wavelengths, and we perform a time-energy entanglement swapping operation based on the sum-frequency generation to make users fully connected in the network. The results show that the fidelity of the entangled state is larger than 90% and is independent of the number of users. Our Letter demonstrates the feasibility of a proposed multiuser network, and hence paves a route toward a variety of quantum applications, including entanglement-swapping-based quantum direct communication.

In a locally interacting many-body system, two isolated qubits, separated by a large distance $r$, become correlated and entangled with each other at a time $t\ge r/v$. This finite speed $v$ of quantum information scrambling limits quantum information processing, thermalization, and even equilibrium correlations. Yet most experimental systems contain long range power-law interactions—qubits separated by $r$ have potential energy $V(r)\propto r^{-\alpha }$. Examples include the long range Coulomb interactions in plasma ($\alpha =1$) and dipolar interactions between spins ($\alpha =3$). In one spatial dimension, we prove that the speed of quantum scrambling remains finite for sufficiently large $\alpha$. This result parametrically improves previous bounds, compares favorably with recent numerical simulations, and can be realized in quantum simulators with dipolar interactions. Our new mathematical methods lead to improved algorithms for classically simulating quantum systems, and improve bounds on environmental decoherence in experimental quantum information processors.

We address the question of verifying the quantumness of thermal machines. A Szilárd engine is truly quantum if its work output cannot be described by a local hidden state model, i.e., an objective local statistical ensemble. Quantumness in this scenario is revealed by a steering-type inequality which bounds the classically extractable work. A quantum Maxwell demon can violate that inequality by exploiting quantum correlations between the work medium and the thermal environment. While for a classical Szilárd engine an objective description of the medium always exists, any such description can be ruled out by a steering task in a truly quantum case.

We study quantum metrology for unitary dynamics. Analytic solutions are given for both the optimal unitary state preparation starting from an arbitrary mixed state and the corresponding optimal measurement precision. This represents a rigorous generalization of known results for optimal initial states and upper bounds on measurement precision which can only be saturated if pure states are available. In particular, we provide a generalization to mixed states of an upper bound on measurement precision for time-dependent Hamiltonians that can be saturated with optimal Hamiltonian control. These results make precise and reveal the full potential of mixed states for quantum metrology.