Optical trapping of molecules with long coherence times is crucial for many protocols in quantum information and metrology. However, the factors that limit the lifetimes of the trapped molecules remain elusive and require improved understanding of the underlying molecular structure. Here we show that measurements of vibronic line strengths in weakly and deeply bound $^{88}$Sr$_2$ molecules, combined with \textit{ab initio} calculations, allow for unambiguous identification of vibrational quantum numbers. This, in turn, enables the construction of refined excited potential energy curves that inform the selection of magic wavelengths which facilitate long vibrational coherence. We demonstrate Rabi oscillations between far-separated vibrational states that persist for nearly 100 ms.

As quantum key distribution becomes increasingly practical, questions of how to effectively employ it in large-scale networks and over large distances becomes increasingly important. To that end, in this work, we model the performance of the E91 entanglement based QKD protocol when operating in a network consisting of both quantum repeaters and trusted nodes. We propose a number of routing protocols for this network and compare their performance under different usage scenarios. Through our modeling, we investigate optimal placement and number of trusted nodes versus repeaters depending on device performance (e.g., quality of the repeater's measurement devices). Along the way we discover interesting lessons determining what are the important physical aspects to improve for upcoming quantum networks in order to improve secure communication rates.

Highly excited Rydberg states are usually extremely polarizable and exceedingly sensitive to electric fields. Because of this Rydberg ions confined in electric fields have state-dependent trapping potentials. We engineer a Rydberg state that is insensitive to electric fields by coupling two Rydberg states with static polarizabilities of opposite sign, in this way we achieve state-independent magic trapping. We show that the magically-trapped ion can be coherently excited to the Rydberg state without the need for control of the ion's motion.

Several architectures have been proposed for quantum neural networks (QNNs), with the goal of efficiently performing machine learning tasks on quantum data. Rigorous scaling results are urgently needed for specific QNN constructions to understand which, if any, will be trainable at a large scale. Here, we analyze the gradient scaling (and hence the trainability) for a recently proposed architecture that we called dissipative QNNs (DQNNs), where the input qubits of each layer are discarded at the layer's output. We find that DQNNs can exhibit barren plateaus, i.e., gradients that vanish exponentially in the number of qubits. Moreover, we provide quantitative bounds on the scaling of the gradient for DQNNs under different conditions, such as different cost functions and circuit depths, and show that trainability is not always guaranteed.

Bayesian Networks (BN) are probabilistic graphical models that are widely used for uncertainty modeling, stochastic prediction and probabilistic inference. A Quantum Bayesian Network (QBN) is a quantum version of the Bayesian network that utilizes the principles of quantum mechanical systems to improve the computational performance of various analyses. In this paper, we experimentally evaluate the performance of QBN on various IBM QX hardware against Qiskit simulator and classical analysis. We consider a 4-node BN for stock prediction for our experimental evaluation. We construct a quantum circuit to represent the 4-node BN using Qiskit, and run the circuit on nine IBM quantum devices: Yorktown, Vigo, Ourense, Essex, Burlington, London, Rome, Athens and Melbourne. We will also compare the performance of each device across the four levels of optimization performed by the IBM Transpiler when mapping a given quantum circuit to a given device. We use the root mean square percentage error as the metric for performance comparison of various hardware.

We numerically investigate the quench expansion dynamics of an initially confined state in a two-dimensional Gross-Pitaevskii lattice in the presence of external disorder. The expansion dynamics is conveniently described in the control parameter space of the energy and norm densities. The expansion can slow down substantially if the expected final state is a non-ergodic non-Gibbs one, regardless of the disorder strength. Likewise stronger disorder delays expansion. We compare our results with recent studies for quantum many body quench experiments.

Recently a certain conceptual puzzle in the AdS/CFT correspondence, concerning the growth of quantum circuit complexity and the wormhole volume, has been identified by Bouland-Fefferman-Vazirani and Susskind. In this note, we propose a resolution of the puzzle and save the quantum Extended Church-Turing thesis by arguing that there is no computational shortcut in measuring the volume due to gravitational backreaction from bulk observers. A certain strengthening of the firewall puzzle from the computational complexity perspective, as well as its potential resolution, is also presented.

Linear response theory (LRT) is a key tool in investigating the quantum matter, for quantum systems perturbed by a weak probe, it connects the dynamics of experimental observable with the correlation function of unprobed equilibrium states. Entanglement entropy(EE) is a measure of quantum entanglement, it is a very important quantity of quantum physics and quantum information science. While EE is not an observable, developing the LRT of it is an interesting thing. In this work, we develop the LRT of von Neumann entropy for an open quantum system. Moreover, we found that the linear response of von Neumann entanglement entropy is determined by the linear response of an observable. Using this observable, we define the Kubo formula and susceptibility of EE, which have the same properties of its conventional counterpart. Through using the LRT of EE, we further found that the linear response of EE will be zero for maximally entangled or separable states, this is a unique feature of entanglement dynamics. A numerical verification of our analytical derivation is also given using XX spin chain model. The LRT of EE provides a useful tool in investigating and understanding EE.

Entanglement properties of IBM Q 53 qubit quantum computer are carefully examined with the noisy intermediate-scale quantum (NISQ) technology. We study GHZ-like states with multiple qubits (N=2 to N=7) on IBM Rochester and compare their maximal violation values of Mermin polynomials with analytic results. A rule of N-qubits orthogonal measurements is taken to further justify the entanglement less than maximal values of local realism (LR). The orthogonality of measurements is another reliable criterion for entanglement except the maximal values of LR. Our results indicate that the entanglement of IBM 53-qubits is reasonably good when N <= 4 while for the longer entangle chains the entanglement is only valid for some special connectivity.

One of the greatest challenges for current quantum computing hardware is how to obtain reliable results from noisy devices. A recent paper [A. Kandala et al., Nature 567, 491 (2019)] described a method for injecting noise by stretching gate times, enabling the calculation of quantum expectation values as a function of the amount of noise in the IBM-Q devices. Extrapolating to zero noise led to excellent agreement with exact results. Here an alternative scheme is described that employs the intentional addition of identity pulses, pausing the device periodically in order to gradually subject the quantum computation to increased levels of noise. The scheme is implemented in a one qubit circuit on an IBM-Q device. It is determined that this is an effective method for controlled addition of noise, and further, that using noisy results to perform extrapolation can lead to improvements in the final output, provided careful attention is paid to how the extrapolation is carried out.

The hybrid quantum-classical algorithm is actively examined as a technique applicable even to intermediate-scale quantum computers. To execute this algorithm, the hardware efficient ansatz is often used, thanks to its implementability and expressibility; however, this ansatz has a critical issue in its trainability in the sense that it generically suffers from the so-called gradient vanishing problem. This issue can be resolved by limiting the circuit to the class of shallow alternating layered ansatz. However, even though the high trainability of this ansatz is proved, it is still unclear whether it has rich expressibility in state generation. In this paper, with a proper definition of the expressibility found in the literature, we show that the shallow alternating layered ansatz has almost the same level of expressibility as that of hardware efficient ansatz. Hence the expressibility and the trainability can coexist, giving a new designing method for quantum circuits in the intermediate-scale quantum computing era.

Ghost fields in quantum field theory have been a long-standing problem. Specifically, theories with higher derivatives involve ghosts that appear in the Hamiltonian in the form of linear momenta term, which is commonly known as the Ostrogradski ghost. Higher derivative theories may involve both types of constraints i.e. first class and second class. Interestingly, these higher derivative theories may have non-Hermitian Hamiltonian respecting $\mathcal{PT}-$symmetries. In this paper, we have considered the $\mathcal{PT}-$symmetric nature of the extended Maxwell-Chern-Simon's theory and employed the second class constraints to remove the linear momenta terms causing the instabilities. We found that the removal is not complete rather conditions arise among the coefficients of the operator ${Q}$.

Quantum simulations are one of the pillars of quantum technologies. These simulations provide insight in fields as varied as high energy physics, many-body physics, or cosmology to name only a few. Several platforms, ranging from ultracold-atoms to superconducting circuits through trapped ions have been proposed as quantum simulators. This article reviews recent developments in another well established platform for quantum simulations: polaritons in semiconductor microcavities. These quasiparticles obey a nonlinear Schr\"odigner equation (NLSE), and their propagation in the medium can be understood in terms of quantum hydrodynamics. As such, they are considered as "fluids of light". The challenge of quantum simulations is the engineering of configurations in which the potential energy and the nonlinear interactions in the NLSE can be controlled. Here, we revisit some landmark experiments with polaritons in microcavities, discuss how the various properties of these systems may be used in quantum simulations, and highlight the richness of polariton systems to explore non-equilibrium physics

Despite previous extensive analysis of open quantum systems described by the Lindblad equation, it is unclear whether correlated topological states, such as fractional quantum Hall states, are maintained even in the presence of the jump term. In this paper, we introduce the pseudo-spin Chern number of the Liouvillian which is computed by twisting the boundary conditions only for one of the subspaces of the doubled Hilbert space. The existence of such a topological invariant elucidates that the topological properties remain unchanged even in the presence of the jump term which does not close the gap of the effective non-Hermitian Hamiltonian (obtained by neglecting the jump term). In other words, the topological properties are encoded into an effective non-Hermitian Hamiltonian rather than the full Liouvillian. This is particularly useful when the jump term can be written as a strictly block-upper (-lower) triangular matrix in the doubled Hilbert space, in which case the presence or absence of the jump term does not affect the spectrum of the Liouvillian. With the pseudo-spin Chern number, we address the characterization of fractional quantum Hall states with two-body loss but without gain, elucidating that the topology of the non-Hermitian fractional quantum Hall states is preserved even in the presence of the jump term. This numerical result also supports the use of the non-Hermitian Hamiltonian which significantly reduces the numerical cost. Similar topological invariants can be extended to treat correlated topological states for other spatial dimensions and symmetry (e.g., one-dimensional open quantum systems with inversion symmetry), indicating the high versatility of our approach.

Quantum mechanical effects at the macroscopic level were first explored in Josephson junction-based superconducting circuits in the 1980's. In the last twenty years, the emergence of quantum information science has intensified research toward using these circuits as qubits in quantum information processors. The realization that superconducting qubits can be made to strongly and controllably interact with microwave photons, the quantized electromagnetic fields stored in superconducting circuits, led to the creation of the field of circuit quantum electrodynamics (QED), the topic of this review. While atomic cavity QED inspired many of the early developments of circuit QED, the latter has now become an independent and thriving field of research in its own right. Circuit QED allows the study and control of light-matter interaction at the quantum level in unprecedented detail. It also plays an essential role in all current approaches to quantum information processing with superconducting circuits. In addition, circuit QED enables the study of hybrid quantum systems interacting with microwave photons. Here, we review the coherent coupling of superconducting qubits to microwave photons in high-quality oscillators focussing on the physics of the Jaynes-Cummings model, its dispersive limit, and the different regimes of light-matter interaction in this system. We discuss coupling of superconducting circuits to their environment, which is necessary for coherent control and measurements in circuit QED, but which also invariably leads to decoherence. Dispersive qubit readout, a central ingredient in almost all circuit QED experiments, is also described. Following an introduction to these fundamental concepts that are at the heart of circuit QED, we discuss important use cases of these ideas in quantum information processing and in quantum optics.

We present the formation of homonuclear Cs2, K2, and heteronuclear CsK long-range Rydberg molecules in a dual-species magneto-optical trap for 39K and 133Cs by one-photon UV photoassociation. The different ground-state-density dependence of homo- and heteronuclear photoassociation rates and the detection of stable molecular ions resulting from auto-ionization provide an unambiguous assignment. We perform bound-bound millimeter-wave spectroscopy of long-range Rydberg molecules to access molecular states not accessible by one-photon photoassociation. A comparison to binding energies calculated with the most recent theoretical model and atomic parameters reveals the inadequacy of this approach to correctly describe the full set of our observations from homo- and heteronuclear long-range Rydberg molecules. We show that the data from photoassociation spectroscopy of heteronuclear long-range Rydberg molecules provides a benchmark for the development of theoretical models which facilitate the accurate extraction of low-energy electron-neutral scattering phase shifts.

We analyse a proposition which considers quantum theory as a mere tool for calculating probabilities for sequences of outcomes of observations made by an Observer, who him/herself remains outside the scope of the theory. Predictions are possible, provided a sequence includes at least two such observations. Complex valued probability amplitudes, each defined for an entire sequence of outcomes, are attributed to Observer's reasoning, and the problem of wave function's collapse is dismissed as a purely semantic one. Our examples include quantum "weak values", and a simplified version of the "delayed quantum eraser".

Simulations of field theories on noisy quantum computers must contend with errors introduced by that noise. For gauge theories, a large class of errors violate gauge symmetry, and thus may result in unphysical processes occurring in the simulation. We present a method, applicable to non-Abelian gauge theories, for suppressing coherent gauge drift errors through the repeated application of pseudorandom gauge transformation. In cases where the dominant errors are gauge-violating, we expect this method to be a practical way to improve the accuracy of NISQ-era simulations.

We introduce the method of maximum likelihood fragment tomography (MLFT) as an improved circuit cutting technique for running clustered quantum circuits on quantum devices with limited quantum resources. In addition to minimizing the classical computing overhead of circuit cutting methods, MLFT finds the most likely probability distribution over measurement outcomes at the output of a quantum circuit, given the data obtained from running the circuit's fragments. Unlike previous circuit cutting methods, MLFT guarantees that all reconstructed probability distributions are strictly non-negative and normalized. We demonstrate the benefits of MLFT with classical simulations of clustered random unitary circuits. Finally, we provide numerical evidence and theoretical arguments that circuit cutting can estimate the output of a clustered circuit with higher fidelity than full circuit execution, thereby motivating the use of circuit cutting as a standard tool for running clustered circuits on quantum hardware.

The imaginary-time evolution method is widely known to be efficient for obtaining the ground state in quantum many-body problems on a classical computer. A recently proposed quantum imaginary-time evolution method (QITE) faces problems of deep circuit depth and difficulty in the implementation on noisy intermediate-scale quantum (NISQ) devices. In this study, a nonlocal approximation is developed to tackle this difficulty. We found that by removing the locality condition or local approximation (LA), which was imposed when the imaginary-time evolution operator is converted to a unitary operator, the quantum circuit depth is significantly reduced. We propose two-step approximation methods based on a nonlocality condition: extended LA (eLA) and nonlocal approximation (NLA). To confirm the validity of eLA and NLA, we apply them to the max-cut problem of an unweighted 3-regular graph and a weighted fully connected graph; we comparatively evaluate the performances of LA, eLA, and NLA. The eLA and NLA methods require far fewer circuit depths than LA to maintain the same level of computational accuracy. Further, we developed a ``compression'' method of the quantum circuit for the imaginary-time steps as a method to further reduce the circuit depth in the QITE method. The eLA, NLA, and the compression method introduced in this study allow us to reduce the circuit depth and the accumulation of error caused by the gate operation significantly and pave the way for implementing the QITE method on NISQ devices.