Nuclear quantum effects such as zero-point energy and hydrogen tunneling play a central role in many biological and chemical processes. The nuclear-electronic orbital (NEO) approach captures these effects by treating selected nuclei quantum mechanically on the same footing as electrons. On classical computers, the resources required for an exact solution of NEO-based models grow exponentially with system size. By contrast, quantum computers offer a means of solving this problem with polynomial scaling. However, due to the limitations of current quantum devices, NEO simulations are confined to the smallest systems described by minimal basis sets, whereas realistic simulations beyond the Born-Oppenheimer approximation require more sophisticated basis sets. For this purpose, we herein extend a hardware-efficient ADAPT-VQE method to the NEO framework in the frozen natural orbital (FNO) basis. We demonstrate on H2 and D2 molecules that the NEO-FNO-ADAPT-VQE method reduces the CNOT count by several orders of magnitude relative to the NEO unitary coupled cluster method with singles and doubles while maintaining the desired accuracy. This extreme reduction in the CNOT gate count is sufficient to permit practical computations employing the NEO method─an important step toward accurate simulations involving nonclassical nuclei and non-Born-Oppenheimer effects on near-term quantum devices. We further show that the method can capture isotope effects, and we demonstrate that inclusion of correlation energy systematically improves the prediction of difference in the zero-point energy (ΔZPE) between isotopes.

Coupled quantum electron-nuclear dynamics is oftenassociatedwith the Born-Huang expansion of the molecular wave functionand the appearance of nonadiabatic effects as a perturbation. On theother hand, native multicomponent representations of electrons andnuclei also exist, which do not rely on any a priori approximation.However, their implementation is hampered by prohibitive scaling.Consequently, quantum computers offer a unique opportunity for extendingtheir use to larger systems. Here, we propose a quantum algorithmfor simulating the time-evolution of molecular systems and apply itto proton transfer dynamics in malonaldehyde, described as a rigidscaffold. The proposed quantum algorithm can be easily generalizedto include the explicit dynamics of the classically described molecularscaffold. We show how entanglement between electronic and nucleardegrees of freedom can persist over long times if electrons do notfollow the nuclear displacement adiabatically. The proposed quantumalgorithm may become a valid candidate for the study of such phenomenawhen sufficiently powerful quantum computers become available.

Several areas have been improved with Deep Learning during the past years. For non-safety related products adoption of AI and ML is not an issue, whereas in safety critical applications, robustness of such approaches is still an issue. A common challenge for Deep Neural Networks (DNN) occur when exposed to out-of-distribution samples that are previously unseen, where DNNs can yield high confidence predictions despite no prior knowledge of the input. In this paper we analyse two supervisors on two well-known DNNs with varied setups of training and find that the outlier detection performance improves with the quality of the training procedure. We analyse the performance of the supervisor after each epoch during the training cycle, to investigate supervisor performance as the accuracy converges. Understanding the relationship between training results and supervisor performance is valuable to improve robustness of the model and indicates where more work has to be done to create generalized models for safety critical applications.

Deep Neural Networks (DNN) have improved the quality of several non-safety related products in the past years. However, before DNNs should be deployed to safety-critical applications, their robustness needs to be systematically analyzed. A common challenge for DNNs occurs when input is dissimilar to the training set, which might lead to high confidence predictions despite proper knowledge of the input. Several previous studies have proposed to complement DNNs with a supervisor that detects when inputs are outside the scope of the network. Most of these supervisors, however, are developed and tested for a selected scenario using a specific performance metric. In this work, we emphasize the need to assess and compare the performance of supervisors in a structured way. We present a framework constituted by four datasets organized in six test cases combined with seven evaluation metrics. The test cases provide varying complexity and include data from publicly available sources as well as a novel dataset consisting of images from simulated driving scenarios. The latter we plan to make publicly available. Our framework can be used to support DNN supervisor evaluation, which in turn could be used to motive development, validation, and deployment of DNNs in safety-critical applications.

Traffic sign identification using camera images from vehicles plays a critical role in autonomous driving and path planning. However, the front camera images can be distorted due to blurriness, lighting variations and vandalism which can lead to degradation of detection performances. As a solution, machine learning models must be trained with data from multiple domains, and collecting and labeling more data in each new domain is time consuming and expensive. In this work, we present an end-to-end framework to augment traffic sign training data using optimal reinforcement learning policies and a variety of Generative Adversarial Network (GAN) models, that can then be used to train traffic sign detector modules. Our automated augmenter enables learning from transformed nightime, poor lighting, and varying degrees of occlusions using the LISA Traffic Sign and BDD-Nexar dataset. The proposed method enables mapping training data from one domain to another, thereby improving traffic sign detection precision/recall from 0.70/0.66 to 0.83/0.71 for nighttime images.

We propose an offline method to match tracked objects from two sensors in complex and real life traffic scenarios, which can be used to build an automatic system for offline sensor verification of advanced driver assistance systems and autonomous driving. Detected objects in each of the sensors are described by a dynamic state vector representing their position, speed, and the physical shape of the object. The proposed method is based on a weighted Euclidean distance between a set of features derived from these descriptors. The performance of the developed method is evaluated using a manually labeled data set, where the obtained overall true positive and negative rates are around 85% and 95%, respectively, while substantially better results were obtained considering specific traffic situations such as highways. Additionally, we propose a new method to statistically evaluate the performance of the matching method by running it on the labeled data set and on a larger unlabeled data set.

Quantum fluctuations of the vacuum are both a surprising and fundamental phenomenon of nature. Understood as virtual photons, they still have a very real impact, for instance, in the Casimir effects and the lifetimes of atoms. Engineering vacuum fluctuations is therefore becoming increasingly important to emerging technologies. Here, we shape vacuum fluctuations using a superconducting circuit analogue of a mirror, creating regions in space where they are suppressed. Moving an artificial atom through these regions and measuring the spontaneous emission lifetime of the atom provides us with the spectral density of the vacuum fluctuations. Using the paradigm of waveguide quantum electrodynamics, we significantly improve over previous studies of the interaction of an atom with its mirror image, observing a spectral density as low as 0.02 quanta, a factor of 50 below the mirrorless result. This demonstrates that we can hide the atom from the vacuum, even though it is exposed in free space.

The ability to nondestructively detect the presence of a single, traveling photon has been a long-standing goal in optics, with applications in quantum information and measurement. Realizing such a detector is complicated by the fact that photon-photon interactions are typically very weak. At microwave frequencies, very strong effective photon-photon interactions in a waveguide have recently been demonstrated. Here we show how this type of interaction can be used to realize a quantum nondemolition measurement of a single propagating microwave photon. The scheme we propose uses a chain of solid-state three-level systems (transmons) cascaded through circulators which suppress photon backscattering. Our theoretical analysis shows that microwave-photon detection with fidelity around 90% can be realized with existing technologies.

We demonstrate the active suppression of transmon qubit dephasing induced by dispersive measurement, using parametric amplification and analog feedback. By real-time processing of the homodyne record, the feedback controller reverts the stochastic quantum phase kick imparted by the measurement on the qubit. The feedback operation matches a model of quantum trajectories with a measurement efficiency (eta) over tilde approximate to 0.5, consistent with the result obtained by postselection. We overcome the bandwidth limitations of the amplification chain by numerically optimizing the signal processing in the feedback loop and provide a theoretical model explaining the optimization result.

We analyze a direct parity measurement of the state of three superconducting qubits in circuit quantum electrodynamics. The parity is inferred from a homodyne measurement of the reflected/transmitted microwave radiation and the measurement is direct in the sense that the parity is measured without the need for any quantum circuit operations or for ancilla qubits. Qubits are coupled to two resonant cavity modes, allowing the steady state of the emitted radiation to satisfy the necessary conditions to act as a pointer state for the parity. However, the transient dynamics violates these conditions and we analyze this detrimental effect and show that it can be overcome in the limit of weak measurement signal. Our analysis shows that, with a moderate degree of post-selection, it is possible to achieve post-measurement states with fidelity of order 95%. We believe that this type of measurement could serve as a benchmark for future error-correction protocols in a scalable architecture.

We present a scheme for the dissipative preparation of an entangled steady state of two superconducting qubits in a circuit quantum electrodynamics (QED) setup. Combining resonator photon loss---a dissipative process already present in the setup---with an effective two-photon microwave drive, we engineer an effective decay mechanism which prepares a maximally entangled state of the two qubits. This state is then maintained as the steady state of the driven, dissipative evolution. The performance of the dissipative state preparation protocol is studied analytically and verified numerically. In view of the experimental implementation of the presented scheme we investigate the effects of potential experimental imperfections and show that our scheme is robust to small deviations in the parameters. We find that high fidelities with the target state can be achieved both with state-of-the-art three-dimensional, as well as with the more commonly used two-dimensional transmons. The promising results of our study thus open a route for the demonstration of a highly entangled steady state in circuit QED.

We investigate the effective interaction between two microwave fields, mediated by a transmon-type superconducting artificial atom which is strongly coupled to a coplanar transmission line. The interaction between the fields and atom produces an effective cross-Kerr coupling. We demonstrate average cross-Kerr phase shifts of up to 20 degrees per photon with both coherent microwave fields at the single-photon level. Our results provide an important step toward quantum applications with propagating microwave photons.

We realize indirect partial measurement of a transmon qubit in circuit quantum electrodynamics by interaction with an ancilla qubit and projective ancilla measurement with a dedicated readout resonator. Accurate control of the interaction and ancilla measurement basis allows tailoring the measurement strength and operator. The tradeoff between measurement strength and qubit backaction is characterized through the distortion of a qubit Rabi oscillation imposed by ancilla measurement in different bases. Combining partial and projective qubit measurements, we provide the solid-state demonstration of the correspondence between a nonclassical weak value and the violation of a Leggett-Garg inequality.

We realize indirect partial measurement of a transmon qubit in circuit quantum electrodynamics by interaction with an ancilla qubit and projective ancilla measurement with a dedicated readout resonator. Accurate control of the interaction and ancilla measurement basis allows tailoring the measurement strength and operator. The tradeoff between measurement strength and qubit back-action is characterized through the distortion of a qubit Rabi oscillation imposed by ancilla measurement in different bases. Combining partial and projective qubit measurements, we provide the solid-state demonstration of the correspondence between a non-classical weak value and the violation of a Leggett-Garg inequality.

We analyze the backaction of homodyne detection and photodetection on superconducting qubits in circuit quantum electrodynamics. Although both measurement schemes give rise to backaction in the form of stochastic phase rotations, which leads to dephasing, we show that this can be perfectly undone provided that the measurement signal is fully accounted for. This result improves on an earlier one [Phys. Rev. A 82, 012329 (2010)], showing that the method suggested can be made to realize a perfect two-qubit parity measurement. We propose a benchmarking experiment on a single qubit to demonstrate the method using homodyne detection. By analyzing the limited measurement efficiency of the detector and bandwidth of the amplifier, we show that the parameter values necessary to see the effect are within the limits of existing technology.

In quantum chemistry, one is often interested in the static properties of a molecular quantum system, such its electronic structure, or its energy eigenvalues and eigenstates. In this chapter we describe the Abrams-Lloyd and Kitaev eigenvalue estimation algorithms. These provide efficient algorithms for determining the exact eigenvalue associated with a given eigenstate, a feat that is exponentially more difficult to do classically to the same precision.

We analyze a two qubit parity measurement based on dispersive read-out in circuit quantum electrodynamics. The back-action on the qubits has two qualitatively different contributions. One is an unavoidable dephasing in one of the parity subspaces, arising during the transient time of switching on the measurement. The other part is a stochastic rotation of the phase in the same subspace, which persists during the whole measurement. The latter can be determined from the full measurement record, using the method of state estimation. Our main result is that the outcome of this phase determination process is {\em independent} of the initial state in the state estimation procedure. The procedure can thus be used in a measurement situation, where the initial state is unknown. We discuss how this feed-back method can be used to achieve a high fidelity parity measurement for realistic values of the cavity-qubit coupling strength. Finally, we discuss the robustness of the feed-back procedure towards errors in the measurement record.