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Air-lasing from single ionized N$_2^+$ molecules induced by laser filamentation in air has been intensively investigated and the mechanisms responsible for lasing are currently highly debated. We use ultrafast nitrogen K-edge spectroscopy to follow the strong field ionization and fragmentation dynamics of N$_2$ upon interaction with an ultrashort 800 nm laser pulse. Using probe pulses generated by extreme high-order harmonic generation, we observe transitions indicative of the formation of the electronic ground X$^2\Sigma_{g}^{+}$, first excited A$^2\Pi_u$ and second excited B$^2\Sigma^+_u$ states of N$_2^+$ on femtosecond time scales, from which we can quantitatively determine the time-dependent electronic state population distribution dynamics of N$_2^+$. Our results show a remarkably low population of the A$^2\Pi_u$ state, and nearly equal populations of the X$^2\Sigma_{g}^{+}$ and B$^2\Sigma^+_u$ states. In addition, we observe fragmentation of N$_2^+$ into N and N$^+$ on a time scale of several tens of picoseconds that we assign to significant collisional dynamics in the plasma, resulting in dissociative excitation of N$_2^+$.

Prethermalization occurs as an important phase in the dynamics of many-body systems when strong coupling drives a quasi-equilibrium in a subspace separated from the thermodynamic equilibrium by the restriction of a gap in energy or other conserved quantity. Here, we report the signature of an enduring prethermal regime of arrested relaxation in the molecular ultracold plasma that forms following the avalanche of a state-selected Rydberg gas of nitric oxide. Electron collisions mix orbital angular momentum, scattering Rydberg molecules to states of very high-$\ell$. Spontaneous predissociation purifies this non-penetrating character, creating an extraordinary gap between the plasma states of $n \approx \ell$, with measured $n>200$ and penetrating states of $\ell = 0, ~1$ and 2. Evolution to a statistically equilibrated state of N and O atoms cannot occur without Rydberg electron penetration, and this gap blocks relaxation for a millisecond or more. Evolving through the critical phase, electrons that balance the NO$^+$ charge behave as though localized in the prethermal phase and play an ineffective role in bridging this gap. However, the application of a weak radiofrequency (RF) field promotes a dramatic degree of relaxation owing to electron collisions. On an entirely different scale, exciting a quantum-state transition in an exceedingly small fraction of the molecules in the prethermalized ensemble acts with even greater effect to drive the entire system toward equilibrium. We ascribe this to dissipative character added to a small fraction of the states in the prethermally localized ensemble. Using the Lindblad master equation, we illustrate qualitatively similar dynamics for a toy model of an open quantum system that consists of a localized set of spins on which dissipation acts locally at a single site.

The variational quantum eigensolver (or VQE) uses the variational principle to compute the ground state energy of a Hamiltonian, a problem that is central to quantum chemistry and condensed matter physics. Conventional computing methods are constrained in their accuracy due to the computational limits. The VQE may be used to model complex wavefunctions in polynomial time, making it one of the most promising near-term applications for quantum computing. Finding a path to navigate the relevant literature has rapidly become an overwhelming task, with many methods promising to improve different parts of the algorithm. Despite strong theoretical underpinnings suggesting excellent scaling of individual VQE components, studies have pointed out that their various pre-factors could be too large to reach a quantum computing advantage over conventional methods. This review aims to provide an overview of the progress that has been made on the different parts of the algorithm. All the different components of the algorithm are reviewed in detail including representation of Hamiltonians and wavefunctions on a quantum computer, the optimization process, the post-processing mitigation of errors, and best practices are suggested. We identify four main areas of future research:(1) optimal measurement schemes for reduction of circuit repetitions; (2) large scale parallelization across many quantum computers;(3) ways to overcome the potential appearance of vanishing gradients in the optimization process, and how the number of iterations required for the optimization scales with system size; (4) the extent to which VQE suffers for quantum noise, and whether this noise can be mitigated. The answers to these open research questions will determine the routes for the VQE to achieve quantum advantage as the quantum computing hardware scales up and as the noise levels are reduced., Comment: 156 pages, 19 figures

Specialized applications of nanoparticles often call for particular, well-characterized particle size distributions in solution. But, this property can prove difficult to measure. High-throughput methods, such as dynamic light scattering, detect nanoparticles in solution with an efficiency that scales with diameter to the sixth power. This diminishes the accuracy of any determination that must span a range of particle sizes. The accurate classification of broadly distributed systems thus requires very large numbers of measurements. Mass-filtered particle-sensing techniques offer a better dynamic range, but are labor-intensive and so have low throughput. Progress in many areas of nanotechnology requires a faster, lower-cost, and more accurate measure of particle size distributions, particularly for diameters smaller than 20 nm. Here, we present a tailored interferometric microscope system, combined with a high-speed image-processing strategy, optimized for real-time particle tracking that determines accurate size distributions in nominal 5, 10, and 15 nm colloidal gold nanoparticle systems by automatically sensing and classifying thousands of single particles sampled from solution at rates as high as 4,000 particles per minute. We demonstrate this method by sensing the irreversible binding of gold nanoparticles to poly-D-lysine functionalized coverslips. Variations in the single-particle signal as a function of time and mass, calibrated by TEM, show clear evidence for the presence of diffusion-limited transport that most affects larger particles in solution.

We investigate fully self-consistent multiscale quantum-classical algorithms on current generation superconducting quantum computers, in a unified approach to tackle the correlated electronic structure of large systems in both quantum chemistry and condensed matter physics. In both of these contexts, a strongly correlated quantum region of the extended system is isolated and self-consistently coupled to its environment via the sampling of reduced density matrices. We analyze the viability of current generation quantum devices to provide the required fidelity of these objects for a robust and efficient optimization of this subspace. We show that with a simple error mitigation strategy and optimization of compact tensor product bases to minimize the number of terms to sample, these self-consistent algorithms are indeed highly robust, even in the presence of significant noises on quantum hardware. Furthermore, we demonstrate the use of these density matrices for the sampling of non-energetic properties, including dipole moments and Fermi liquid parameters in condensed phase systems, achieving a reliable accuracy with sparse sampling. It appears that uncertainties derived from the iterative optimization of these subspaces is smaller than variances in the energy for a single subspace optimization with current quantum hardware. This boosts the prospect for routine self-consistency to improve the choice of correlated subspaces in hybrid quantum-classical approaches to electronic structure for large systems in this multiscale fashion.

Solving for molecular excited states remains one of the key challenges of modern quantum chemistry. Traditional methods are constrained by existing computational capabilities, limiting the complexity of the molecules that can be studied or the accuracy of the results that can be obtained. Several quantum computing methods have been suggested to address this limitation. However, these typically have hardware requirements which may not be achieved in the near term. We propose a variational quantum machine learning based method to determine molecular excited states aiming at being as resilient as possible to the defects of early Noisy Intermediate Scale Quantum (NISQ) computers and demonstrate an implementation for H2 on IBMQ. Our method uses a combination of two parametrized quantum circuits, working in tandem, combined with a Variational Quantum Eigensolver (VQE) to iteratively find the eigenstates of a molecular Hamiltonian.

Quantum error correcting codes protect quantum computation from errors caused by decoherence and other noise. Here we study the problem of designing logical operations for quantum error correcting codes. We present an automated procedure which generates logical operations given known encoding and correcting procedures. Our technique is to use variational circuits for learning both the logical gates and the physical operations implementing them. This procedure can be implemented on near-term quantum computers via quantum process tomography. It enables automatic discovery of logical gates from analytically designed error correcting codes and can be extended to error correcting codes found by numerical optimizations. We test the procedure by simulation on classical computers on small quantum codes of four qubits to fifteen qubits and show that it finds most logical gates known in the current literature. Additionally, it generates logical gates not found in the current literature for the [[5,1,2]] code, the [[6,3,2]] code, and the [[8,3,2]] code., Comment: 17 pages

Patient outcomes in the medical field are improving through the use and incorporation of robotics technology and laser physics, e.g., the use of optical fibers and lasers in micro-surgery. This paper describes the design and implementation of a new optical fiber laser micro-surgery system, one that is the first to use closed-loop feedback control. In this computerassisted laser scanning tool the laser beam is controlled by four magnetic actuators. After attaching permanent magnets to the free end of the optical fiber, it is the control of these four magnets that produces an accurate laser scanning system, one suited to micro-surgery applications. The interaction between the electromagnetic fields generated by the external magnetic coils and the flux of the internal permanent magnets, produces the control torques required to produce the desired movement of the optic fiber. The tracking error of the optic fiber is compensated for by using a photo-detector sensor as the feedback transducer in the control system. The magnetic torque bends the optical fiber and the feedback from the photodetector gives automated control and high-speed laser scanning of the fiber tip. The simulation and the experimental results are accurate and are co-related., Comment: Since some of the experimental results from the paper should be modified, one of the authors asked me to withdrawal the paper until we modify the paper with new results

Machine learning is seen as a promising application of quantum computation. For near-term noisy intermediate-scale quantum (NISQ) devices, parametrized quantum circuits (PQCs) have been proposed as machine learning models due to their robustness and ease of implementation. However, the cost function is normally calculated classically from repeated measurement outcomes, such that it is no longer encoded in a quantum state. This prevents the value from being directly manipulated by a quantum computer. To solve this problem, we give a routine to embed the cost function for machine learning into a quantum circuit, which accepts a training dataset encoded in superposition or an easily preparable mixed state. We also demonstrate the ability to evaluate the gradient of the encoded cost function in a quantum state.

Resonant mm-wave fields drive $n_0f(2) \rightarrow (n_0 \pm 1)g(2)$ transitions in a state-selected $n_0f(2)$ Rydberg gas of NO. This transformation produces a clear signature in the selected field ionization spectrum and dramatically increases the intensity of corresponding features in the spectrum of the $n_0f(2)$ Rydberg series observed in UV-UV double resonant transitions via the $A ~^2\Sigma^+, ~N'=0$ state. Here, $n_0$ refers to the principal quantum number of an $f$ Rydberg state converging to the $N^+=2$ rotational state of NO$^+ X~ ^1\Sigma^+$. Enhancement owing to transitions from $\ell=3$ ($f$) to $\ell=4$ ($g$) appears both in the electron signal detected at early time by the field ionization of Rydberg molecules and, 40 $\mu$s later, as the late-peak signal of plasma in a state of arrested relaxation. Similar stabilization and enhanced intensity also occurs for shorter-lived interloping complex resonances, $44p(0) - 43d(1)$ and $43p(0) - 42d(1)$. We conclude from these observations that avalanche alone does not guarantee a plasma state of arrested relaxation. But rather, the formation of an arrested phase requires both avalanche-produced NO$^+$ ions and a persistent population of long-lived Rydberg molecules.

An ellipsoidal volume of Rydberg molecules, entrained in a supersonic molecular beam, evolves on a nanosecond timescale to form a strongly coupled ultracold plasma. We present coupled rate-equation simulations that model the underlying kinetic processes and molecular dissociation channels in both a uniformly distributed plasma and under the conditions dictated by our experimental geometry. Simulations predict a fast electron-driven collisional avalanche to plasma followed by slow electron-ion recombination. Within 20 $\mu$s, release of Rydberg binding energy raises the electron temperature of a static plasma to $T_e = 100$ K. Providing for a quasi-self-similar expansion, the hot electron gas drives ion radial motion, reducing $T_e$. These simulations provide a classical baseline model from which to consider quantum effects in the evolution of charge gradients and ambipolar forces in an experimental system undergoing responsive avalanche dynamics.

We propose an efficient method for simultaneously optimizing both the structure and parameter values of quantum circuits with only a small computational overhead. Shallow circuits that use structure optimization perform significantly better than circuits that use parameter updates alone, making this method particularly suitable for noisy intermediate-scale quantum computers. We demonstrate the method for optimizing a variational quantum eigensolver for finding the ground states of Lithium Hydride and the Heisenberg model in simulation, and for finding the ground state of Hydrogen gas on the IBM Melbourne quantum computer., Comment: 13 pages, 6 figures. Added section "Optimization of circuits with limited expressibility". The previous version was titled "Quantum circuit structure learning"

Parametrized quantum circuits initialized with random initial parameter values are characterized by barren plateaus where the gradient becomes exponentially small in the number of qubits. In this technical note we theoretically motivate and empirically validate an initialization strategy which can resolve the barren plateau problem for practical applications. The technique involves randomly selecting some of the initial parameter values, then choosing the remaining values so that the circuit is a sequence of shallow blocks that each evaluates to the identity. This initialization limits the effective depth of the circuits used to calculate the first parameter update so that they cannot be stuck in a barren plateau at the start of training. In turn, this makes some of the most compact ans\"atze usable in practice, which was not possible before even for rather basic problems. We show empirically that variational quantum eigensolvers and quantum neural networks initialized using this strategy can be trained using a gradient based method.

The exploration of large-scale many-body phenomena in quantum materials has produced many important experimental discoveries, including novel states of entanglement, topology and quantum order as found for example in quantum spin ices, topological insulators and semimetals, complex magnets, and high-$T_c$ superconductors. Yet, the sheer scale of solid-state systems and the difficulty of exercising exacting control of their quantum mechanical degrees of freedom limit the pace of rational progress in advancing the properties of these and other materials. With extraordinary effort to counteract natural processes of dissipation, precisely engineered ultracold quantum simulators could point the way to exotic new materials. Here, we look instead to the quantum mechanical character of the arrested state formed by a quenched ultracold molecular plasma. This novel class of system arises spontaneously, without a deliberate engineering of interactions, and evolves naturally from state-specified initial conditions, to a long-lived final state of canonical density, in a process that conflicts with classical notions of plasma dissipation and neutral dissociation. We take information from experimental observations to develop a conceptual argument that attempts to explain this state of arrested relaxation in terms of a minimal phenomenological model of randomly interacting dipoles of random energies. This model of the plasma forms a starting point to describe its observed absence of relaxation in terms of many-body localization (MBL). The large number of accessible Rydberg and excitonic states gives rise to an unconventional web of many-body interactions that vastly exceeds the complexity of MBL in a conventional few-level scheme. This experimental platform thus opens an avenue for the coupling of dipoles in disordered environments that will demand the development of new theoretical tools., Comment: 27 pages, 6 figures, 2 tables

Quantum systems interacting with an unknown environment are notoriously difficult to model, especially in presence of non-Markovian and non-perturbative effects. Here we introduce a neural network based approach, which has the mathematical simplicity of the Gorini-Kossakowski-Sudarshan-Lindblad master equation, but is able to model non-Markovian effects in different regimes. This is achieved by using recurrent neural networks for defining Lindblad operators that can keep track of memory effects. Building upon this framework, we also introduce a neural network architecture that is able to reproduce the entire quantum evolution, given an initial state. As an application we study how to train these models for quantum process tomography, showing that recurrent neural networks are accurate over different times and regimes., Comment: 10 pages, 8 figures

Adversarial learning is one of the most successful approaches to modelling high-dimensional probability distributions from data. The quantum computing community has recently begun to generalize this idea and to look for potential applications. In this work, we derive an adversarial algorithm for the problem of approximating an unknown quantum pure state. Although this could be done on universal quantum computers, the adversarial formulation enables us to execute the algorithm on near-term quantum computers. Two parametrized circuits are optimized in tandem: One tries to approximate the target state, the other tries to distinguish between target and approximated state. Supported by numerical simulations, we show that resilient backpropagation algorithms perform remarkably well in optimizing the two circuits. We use the bipartite entanglement entropy to design an efficient heuristic for the stopping criterion. Our approach may find application in quantum state tomography., Comment: 14 pages, 6 figures. Minor revisions. As published in New J. Phys

Quantum circuits with hierarchical structure have been used to perform binary classification of classical data encoded in a quantum state. We demonstrate that more expressive circuits in the same family achieve better accuracy and can be used to classify highly entangled quantum states, for which there is no known efficient classical method. We compare performance for several different parameterizations on two classical machine learning datasets, Iris and MNIST, and on a synthetic dataset of quantum states. Finally, we demonstrate that performance is robust to noise and deploy an Iris dataset classifier on the ibmqx4 quantum computer.

We demonstrate the applicability of 2-photon Rydberg excitations of nitric oxide (NO) at room temperature in a gas mixture with helium (He) as an optogalvanic gas sensor. The charges created initially from succeeding collisions of excited NO Rydberg molecules with free electrons are measured as a current on metallic electrodes inside a glass cell and amplified using a custom-designed highbandwidth transimpedance amplifier attached to the cell. We fnd that this gas sensing method is capable of detecting NO concentrations lower than 10 ppm even at atmospheric pressures, currently only limited by the way we prepare the gas dilutions.

This paper demonstrates a method for tensorizing neural networks based upon an efficient way of approximating scale invariant quantum states, the Multi-scale Entanglement Renormalization Ansatz (MERA). We employ MERA as a replacement for the fully connected layers in a convolutional neural network and test this implementation on the CIFAR-10 and CIFAR-100 datasets. The proposed method outperforms factorization using tensor trains, providing greater compression for the same level of accuracy and greater accuracy for the same level of compression. We demonstrate MERA layers with 14000 times fewer parameters and a reduction in accuracy of less than 1% compared to the equivalent fully connected layers, scaling like O(N)., Comment: 8 pages, 2 figures

Studying general quantum many-body systems is one of the major challenges in modern physics because it requires an amount of computational resources that scales exponentially with the size of the system.Simulating the evolution of a state, or even storing its description, rapidly becomes intractable for exact classical algorithms. Recently, machine learning techniques, in the form of restricted Boltzmann machines, have been proposed as a way to efficiently represent certain quantum states with applications in state tomography and ground state estimation. Here, we introduce a new representation of states based on variational autoencoders. Variational autoencoders are a type of generative model in the form of a neural network. We probe the power of this representation by encoding probability distributions associated with states from different classes. Our simulations show that deep networks give a better representation for states that are hard to sample from, while providing no benefit for random states. This suggests that the probability distributions associated to hard quantum states might have a compositional structure that can be exploited by layered neural networks. Specifically, we consider the learnability of a class of quantum states introduced by Fefferman and Umans. Such states are provably hard to sample for classical computers, but not for quantum ones, under plausible computational complexity assumptions. The good level of compression achieved for hard states suggests these methods can be suitable for characterising states of the size expected in first generation quantum hardware., Comment: v2: 9 pages, 3 figures, journal version with major edits with respect to v1 (rewriting of section "hard and easy quantum states", extended discussion on comparison with tensor networks)

We argue that the quenched ultracold plasma presents an experimental platform for studying quantum many-body physics of disordered systems in the long-time and finite energy-density limits. We consider an experiment that quenches a plasma of nitric oxide to an ultracold system of Rydberg molecules, ions and electrons that exhibits a long-lived state of arrested relaxation. The qualitative features of this state fail to conform with classical models. Here, we develop a microscopic quantum description for the arrested phase based on an effective many-body spin Hamiltonian that includes both dipole-dipole and van der Waals interactions. This effective model appears to offer a way to envision the essential quantum disordered non-equilibrium physics of this system., Comment: 6 pages main text + 9 pages supplemental materials, 2 figures main text + 7 figures and 2 tables supplemental materials

We introduce a convolutional neural network for inferring a compact disentangled graphical description of objects from 2D images that can be used for volumetric reconstruction. The network comprises an encoder and a twin-tailed decoder. The encoder generates a disentangled graphics code. The first decoder generates a volume, and the second decoder reconstructs the input image using a novel training regime that allows the graphics code to learn a separate representation of the 3D object and a description of its lighting and pose conditions. We demonstrate this method by generating volumes and disentangled graphical descriptions from images and videos of faces and chairs.

Judgments about personality based on facial appearance are strong effectors in social decision making, and are known to have impact on areas from presidential elections to jury decisions. Recent work has shown that it is possible to predict perception of memorability, trustworthiness, intelligence and other attributes in human face images. The most successful of these approaches require face images expertly annotated with key facial landmarks. We demonstrate a Convolutional Neural Network (CNN) model that is able to perform the same task without the need for landmark features, thereby greatly increasing efficiency. The model has high accuracy, surpassing human-level performance in some cases. Furthermore, we use a deconvolutional approach to visualize important features for perception of 22 attributes and demonstrate a new method for separately visualizing positive and negative features.