A two-dimensional (2D) harmonically trapped interacting Fermi gas is anticipated to exhibit a quantum anomaly and possesses a breathing mode at frequencies different from a classical scale-invariant value ${\omega }_B=2{\omega }_{\perp }$, where ${\omega }_{\perp }$ is the trapping frequency. The predicted maximum quantum anomaly ($\sim 10\%$) has not been confirmed in experiments. Here, we theoretically investigate the zero-temperature density equation of state and the breathing mode frequency of an interacting Fermi superfluid at the dimensional crossover from three to two dimensions. We find that the simple model of a 2D Fermi gas with a single $s$-wave scattering length is not adequate to describe the experiments in the 2D limit, as commonly believed. A more complete description of quasi-2D leads to a much weaker quantum anomaly, consistent with the experimental observations. We clarify that the reduced quantum anomaly is due to the significant confinement-induced effective range of interactions.

We present a technique for reducing the computational requirements by several orders of magnitude in the evaluation of semidefinite relaxations for bounding the set of quantum correlations arising from finite-dimensional Hilbert spaces. The technique, which we make publicly available through a user-friendly software package, relies on the exploitation of symmetries present in the optimization problem to reduce the number of variables and the block sizes in semidefinite relaxations. It is widely applicable in problems encountered in quantum information theory and enables computations that were previously too demanding. We demonstrate its advantages and general applicability in several physical problems. In particular, we use it to robustly certify the nonprojectiveness of high-dimensional measurements in a black-box scenario based on self-tests of $d$-dimensional symmetric informationally complete positive-operator-valued measurements.

The eigenstate thermalization hypothesis (ETH) is one of the cornerstones of contemporary quantum statistical mechanics. The extent to which ETH holds for nonlocal operators is an open question that we partially address in this Letter. We report on the construction of highly nonlocal operators, behemoths, that are building blocks for various kinds of local and nonlocal operators. The behemoths have a singular distribution and width $w\sim {\mathcal{D}}^{-1}$ ($\mathcal{D}$ being the Hilbert space dimension). From there, one may construct local operators with the ordinary Gaussian distribution and $w\sim {\mathcal{D}}^{-1/2}$ in agreement with ETH. Extrapolation to even larger widths predicts sub-ETH behavior of typical nonlocal operators with $w\sim {\mathcal{D}}^{-\delta }$, $0<\delta <1/2$. This operator construction is based on a deep analogy with random matrix theory and shows striking agreement with numerical simulations of nonintegrable many-body systems.

We present two quantum algorithms based on evolution randomization, a simple variant of adiabatic quantum computing, to prepare a quantum state $|x⟩$ that is proportional to the solution of the system of linear equations $A\overrightarrow{x}=\overrightarrow{b}$. The time complexities of our algorithms are $O\mathbf{(}{\kappa }^2\log (\kappa )/\epsilon \mathbf{)}$ and $O\mathbf{(}\kappa \log (\kappa )/\epsilon \mathbf{)}$, where $\kappa$ is the condition number of $A$ and $\epsilon$ is the precision. Both algorithms are constructed using families of Hamiltonians that are linear combinations of products of $A$, the projector onto the initial state $|b⟩$, and single-qubit Pauli operators. The algorithms are conceptually simple and easy to implement. They are not obtained from equivalences between the gate model and adiabatic quantum computing. They do not use phase estimation or variable-time amplitude amplification, and do not require large ancillary systems. We discuss a gate-based implementation via Hamiltonian simulation and prove that our second algorithm is almost optimal in terms of $\kappa$. Like previous methods, our techniques yield an exponential quantum speed-up under some assumptions. Our results emphasize the role of Hamiltonian-based models of quantum computing for the discovery of important algorithms.

Population annealing is a powerful tool for large-scale Monte Carlo simulations. We adapt this method to molecular dynamics simulations and demonstrate its excellent accelerating effect by simulating the folding of a short peptide commonly used to gauge the performance of algorithms. The method is compared to the well established parallel tempering approach and is found to yield similar performance for the same computational resources. In contrast to other methods, however, population annealing scales to a nearly arbitrary number of parallel processors, and it is thus a unique tool that enables molecular dynamics to tap into the massively parallel computing power available in supercomputers that is so much needed for a range of difficult computational problems.

The limits of frequency resolution in nano-NMR experiments have been discussed extensively in recent years. It is believed that there is a crucial difference between the ability to resolve a few frequencies and the precision of estimating a single one. Whereas the efficiency of single frequency estimation gradually increases with the square root of the number of measurements, the ability to resolve two frequencies is limited by the specific timescale of the signal and cannot be compensated for by extra measurements. Here we show theoretically and demonstrate experimentally that the relationship between these quantities is more subtle and both are only limited by the Cramér-Rao bound of a single frequency estimation.

The information-carrying capacity of a memory is known to be a thermodynamic resource facilitating the conversion of heat to work. Szilard’s engine explicates this connection through a toy example involving an energy-degenerate two-state memory. We devise a formalism to quantify the thermodynamic value of memory in general quantum systems with nontrivial energy landscapes. Calling this the thermal information capacity, we show that it converges to the nonequilibrium Helmholtz free energy in the thermodynamic limit. We compute the capacity exactly for a general two-state (qubit) memory away from the thermodynamic limit, and find it to be distinct from known free energies. We outline an explicit memory-bath coupling that can approximate the optimal qubit thermal information capacity arbitrarily well.

We show that genuine multipartite entanglement of all multipartite pure states in arbitrary finite dimension can be detected in a device-independent way by employing bipartite Bell inequalities on states that are deterministically generated from the initial state via local operations. This leads to an efficient scheme for large classes of multipartite states that are relevant in quantum computation or condensed-matter physics, including cluster states and the ground state of the Affleck-Kennedy-Lieb-Tasaki (AKLT) model. For cluster states the detection of genuine multipartite entanglement involves only measurements on a constant number of systems with an overhead that scales linearly with the system size, while for the AKLT model the overhead is polynomial. In all cases our approach shows some robustness against experimental imperfections.

We introduce a class of non-Hermitian Hamiltonians that offers a dynamical approach to a shortcut to adiabaticity (DASA). In particular, in our proposed $2\times 2$ Hamiltonians, one eigenvalue is absolutely real and the other one is complex. This specific form of eigenvalues helps us to exponentially decay the population in an undesired eigenfunction or amplify the population in the desired state while keeping the probability amplitude in the other eigenfunction conserved. This provides us with a powerful method to have a diabatic process with the same outcome as its corresponding adiabatic process. In contrast to standard shortcuts to adiabaticity, our Hamiltonians have a much simpler form with a lower thermodynamic cost. Furthermore, we show that DASA can be extended to higher dimensions using the parameters associated with our $2\times 2$ Hamiltonians. Our proposed Hamiltonians not only have application in DASA but also can be used for tunable mode selection and filtering in acoustics, electronics, and optics.

We study the spontaneously broken phase of the $XY$ model in three dimensions, with boundary conditions enforcing the presence of a vortex line. Comparing Monte Carlo and field-theoretic determinations of the magnetization and energy density profiles, we numerically determine the mass of the vortex particle in the underlying O(2)-invariant quantum field theory. The result shows, in particular, that the obstruction posed by Derrick’s theorem to the existence of stable topological particles in scalar theories in more than two dimensions does not in general persist beyond the classical level.

The possibility of effectively inverting the sign of the dipole-dipole interaction, by fast rotation of the dipole polarization, is examined within a harmonically trapped dipolar Bose-Einstein condensate. Our analysis is based on the stationary states in the Thomas-Fermi limit, in the corotating frame, as well as direct numerical simulations in the Thomas-Fermi regime, explicitly accounting for the rotating polarization. The condensate is found to be inherently unstable due to the dynamical instability of collective modes. This ultimately prevents the realization of robust and long-lived rotationally tuned states. Our findings have major implications for experimentally accessing this regime.

Quantum measurements based on mutually unbiased bases are commonly used in quantum information processing, as they are generally viewed as being maximally incompatible and complementary. Here we quantify precisely the degree of incompatibility of mutually unbiased bases (MUB) using the notion of noise robustness. Specifically, for sets of $k$ MUB in dimension $d$, we provide upper and lower bounds on this quantity. Notably, we get a tight bound in several cases, in particular for complete sets of $k=d+1$ MUB (using the standard construction for $d$ being a prime power). On the way, we also derive a general upper bound on the noise robustness for an arbitrary set of quantum measurements. Moreover, we prove the existence of sets of $k$ MUB that are operationally inequivalent, as they feature different noise robustness, and we provide a lower bound on the number of such inequivalent sets up to dimension 32. Finally, we discuss applications of our results for Einstein-Podolsky-Rosen steering.

Aiming at a better understanding of anomalous and topological effects in gauge theories out of equilibrium, we study the real-time dynamics of a prototype model for $CP$ violation, the massive Schwinger model with a $\theta$ term. We identify dynamical quantum phase transitions between different topological sectors that appear after sufficiently strong quenches of the $\theta$ parameter. Moreover, we establish a general dynamical topological order parameter, which can be accessed through fermion two-point correlators and, importantly, which can be applied for interacting theories. Enabled by this result, we show that the topological transitions persist beyond the weak-coupling regime. Finally, these effects can be observed with tabletop experiments based on existing cold-atom, superconducting-qubit, and trapped-ion technology. Our Letter thus presents a significant step towards quantum simulating topological and anomalous real-time phenomena relevant to nuclear and high-energy physics.

We present a method for performing multithermal-multibaric molecular dynamics simulations that sample entire regions of the temperature-pressure (TP) phase diagram. The method uses a variational principle [Valsson and Parrinello, Phys. Rev. Lett. 113, 090601 (2014)] in order to construct a bias that leads to a uniform sampling in energy and volume. The intervals of temperature and pressure are taken as inputs and the relevant energy and volume regions are determined on the fly. In this way the method guarantees adequate statistics for the chosen TP region. We show that our multithermal-multibaric simulations can be used to calculate all static physical quantities for all temperatures and pressures in the targeted region of the TP plane. We illustrate our approach by studying the density anomaly of TIP4P/ice water.

An isolated quantum gas with a localized loss features a nonmonotonic behavior of the particle loss rate as an incarnation of the quantum Zeno effect, as recently shown in experiments with cold atomic gases. While this effect can be understood in terms of local, microscopic physics, we show that novel many-body effects emerge when nonlinear gapless quantum fluctuations become important. To this end, we investigate the effect of a local dissipative impurity on a one-dimensional gas of interacting fermions. We show that the escape probability for modes close to the Fermi energy vanishes for an arbitrary strength of the dissipation. In addition, transport properties across the impurity are qualitatively modified, similarly to the Kane-Fisher barrier problem. We substantiate these findings using both a microscopic model of spinless fermions and a Luttinger liquid description.

Quantum nonlocality is usually associated with entangled states by their violations of Bell-type inequalities. However, even unentangled systems, whose parts may have been prepared separately, can show nonlocal properties. In particular, a set of product states is said to exhibit “quantum nonlocality without entanglement” if the states are locally indistinguishable; i.e., it is not possible to optimally distinguish the states by any sequence of local operations and classical communication. Here, we present a stronger manifestation of this kind of nonlocality in multiparty systems through the notion of local irreducibility. A set of multiparty orthogonal quantum states is defined to be locally irreducible if it is not possible to locally eliminate one or more states from the set while preserving orthogonality of the postmeasurement states. Such a set, by definition, is locally indistinguishable, but we show that the converse does not always hold. We provide the first examples of orthogonal product bases on ${\mathbb{C}}^d\otimes {\mathbb{C}}^d\otimes {\mathbb{C}}^d$ for $d=3$, 4 that are locally irreducible in all bipartitions, where the construction for $d=3$ achieves the minimum dimension necessary for such product states to exist. The existence of such product bases implies that local implementation of a multiparty separable measurement may require entangled resources across all bipartitions.

Out-of-time-ordered correlators (OTOCs) have received considerable recent attention as qualitative witnesses of information scrambling in many-body quantum systems. Theoretical discussions of OTOCs typically focus on closed systems, raising the question of their suitability as scrambling witnesses in realistic open systems. We demonstrate empirically that the nonclassical negativity of the quasiprobability distribution (QPD) behind the OTOC is a more sensitive witness for scrambling than the OTOC itself. Nonclassical features of the QPD evolve with timescales that are robust with respect to decoherence and are immune to false positives caused by decoherence. To reach this conclusion, we numerically simulate spin-chain dynamics and three measurement protocols (the interferometric, quantum-clock, and weak-measurement schemes) for measuring OTOCs. We target experiments based on quantum-computing hardware such as superconducting qubits and trapped ions.