This paper covers some new results from the theory of time optimal quantum control, with particular application to relativistic particles including Majorana fermions. We give a brief review of the state of affairs regarding experimental results, and a concise overview of the methodology of time optimal control and unitary transformation. This technique is then applied to the Majorana particle and used to derive four dimensional conservation laws. We then discuss the nature of time transformation in these systems and some simple scattering problems.

We present a new interpretation of quantum mechanics, called the double-scale theory, which expends on the de Broglie-Bohm (dBB) theory. It is based, for any quantum system, on the simultaneous existence of two wave functions in the laboratory reference frame : an external wavefunction and an internal one. The external wave function corresponds to a field that pilots the center-of-mass of the quantum system. The external wave spreads out in space over time. Mathematically, the Schr\"odinger equation converges to the Hamilton-Jacobi statistical equations when the Planck constant tends towards zero and the Newton trajectories are therefore approximations of the dBB trajectories.

The internal wave function corresponds to the interpretation proposed by Edwin Schr\"odinger for whom the particle is extended. Then, the internal wave remains confined in space. Its converges, when h -> 0, to a Dirac distribution. Furthermore, we show that non-stationary solutions can exist such that the 3N-dimensional configuration space of the internal wave function can be rewritten as the product of N individual 3-dimensional internal wave functions.

We present an algorithm leading to some general versions of the Weyl and Wigner function. It is based on the use of certain tight frames instead of orthonormal bases. In the case of qubit quantum mechanics, there exist (among others) a phase space formulation using the Bloch sphere as a phase space, the formulation using {0, 1} x {0, 1} proposed independently by Feynman and Wootters, and the formulation using {0, 1, 2, 3} x {0, 1, 2, 3} proposed by Leonhardt. In order to illustrate our algorithm, we present explicitly a formulation using {0, 1, 2} x {0, 1, 2} as a phase space of qubit.

Simulating properties of quantum materials is one of the most promising applications of quantum computation, both near- and long-term. While real-time dynamics can be straightforwardly implemented, the finite temperature ensemble involves non-unitary operators that render an implementation on a near-term quantum computer extremely challenging. Recently, [Lu, Ba\~nuls and Cirac, PRX Quantum 2, 020321 (2021)] suggested a "time-series quantum Monte Carlo method" which circumvents this problem by extracting finite temperature properties from real-time simulations via Wick's rotation and Monte Carlo sampling of easily preparable states. In this paper, we address the challenges associated with the practical applications of this method, using the two-dimensional transverse field Ising model as a testbed. We demonstrate that estimating Boltzmann weights via Wick's rotation is very sensitive to time-domain truncation and statistical shot noise. To alleviate this problem, we introduce a technique that imposes constraints on the density of states, most notably its non-negativity, and show that this way, we can reliably extract Boltzmann weights from noisy time series. In addition, we show how to reduce the statistical errors of Monte Carlo sampling via a reweighted version of the Wolff cluster algorithm. Our work enables the implementation of the time-series algorithm on present-day quantum computers to study finite temperature properties of many-body quantum systems.

Catalysis plays a key role in many scientific areas, most notably in chemistry and biology. Here we present a catalytic process in a paradigmatic quantum optics setup, namely the Jaynes-Cummings model, where an atom interacts with an optical cavity. The atom plays the role of the catalyst, and allows for the deterministic generation of non-classical light in the cavity. Considering a cavity prepared in a "classical'' coherent state, and choosing appropriately the atomic state and the interaction time, we obtain an evolution with the following properties. First, the state of the cavity has been modified, and now features non-classicality, as witnessed by sub-Poissonian statistics or Wigner negativity. Second, the process is catalytic, in the sense that the atom is deterministically returned to its initial state exactly, and could then in principle be re-used multiple times. We investigate the mechanism of this catalytic process, in particular highlighting the key role of correlations and quantum coherence.

To quantify the interplay between decoherence and quantum chaos away from the semi-classical limit, we investigate the properties of the survival probability of an initial Coherent Gibbs State (CGS), extending the notion of the Spectral Form Factor (SFF) to arbitrary open systems. The relation of this generalized SFF with the corresponding coherence monotones reveals how the manifestation of level repulsion in the correlation hole is suppressed by the decay of the density matrix's off-diagonal elements in the energy eigenbasis. As a working example, we introduce Parametric Quantum Channels (PQC), a discrete-time model of unitary evolution, periodically interrupted by the effects of measurements or transient interactions with an environment, in the context of the axiomatic theory of operations. The maximally incoherent Energy Dephasing (ED) dynamics arises as a special case in the Markovian limit. We demonstrate our results in a series of random matrix models.

Quantum information scrambling (QIS), from the perspective of quantum information theory, is generally understood as local non-retrievability of information evolved through some dynamical process, and is often quantified via entropic quantities such as the tripartite information. We argue that this approach comes with a number of issues, in large part due to its reliance on quantum mutual informations, which do not faithfully quantify correlations directly retrievable via measurements, and in part due to the specific methodology used to compute tripartite informations of the studied dynamics. We show that these issues can be overcome by using accessible mutual informations, defining corresponding ``accessible tripartite informations'', and provide explicit examples of dynamics whose scrambling properties are not properly quantified by the standard tripartite information. Our results lay the groundwork for a more profound understanding of what QIS represents, and reveal a number of promising, as of yet unexplored, venues for futher research.

We present a construction of the Wigner function for a bosonic quantum field theory that has well-defined ultraviolet (UV) and infrared (IR) properties. Our construction uses the local mode formalism in algebraic quantum field theory that is valid in any globally hyperbolic curved spacetimes, i.e., without invoking the path integral formalism. The idea is to build $N$ quantum harmonic oscillators degrees of freedom from $2N$ smeared field operators and use them to "tile" a Cauchy surface of the spacetime manifold. The smallest support of the smearing functions that define each local mode define the UV scale and the number of modes local modes fix the IR scale. This construction can be viewed as a form of "covariant discretization" of the quantum field in curved spacetimes, since the tiling of the Cauchy surface does not depend on any choice of coordinate systems or foliation.

Quantum processors can already execute tasks beyond the reach of classical simulation, albeit for artificial problems. At this point, it is essential to design error metrics that test the experimental accuracy of quantum algorithms with potential for a practical quantum advantage. The distinction between coherent errors and incoherent errors is crucial, as they often involve different error suppression tools. The first class encompasses miscalibrations of control signals and crosstalk, while the latter is usually related to stochastic events and unwanted interactions with the environment. We introduce the incoherent infidelity as a measure of incoherent errors and present a scalable method for measuring it. This method is applicable to generic quantum evolutions subjected to time-dependent Markovian noise. Moreover, it provides an error quantifier for the target circuit, rather than an error averaged over many circuits or quantum gates. The estimation of the incoherent infidelity is suitable to assess circuits with sufficiently low error rates, regardless of the circuit size, which is a natural requirement to run useful computations.

Sentiment classification is one the best use case of classical natural language processing (NLP) where we can witness its power in various daily life domains such as banking, business and marketing industry. We already know how classical AI and machine learning can change and improve technology. Quantum natural language processing (QNLP) is a young and gradually emerging technology which has the potential to provide quantum advantage for NLP tasks. In this paper we show the first application of QNLP for sentiment analysis and achieve perfect test set accuracy for three different kinds of simulations and a decent accuracy for experiments ran on a noisy quantum device. We utilize the lambeq QNLP toolkit and $t|ket>$ by Cambridge Quantum (Quantinuum) to bring out the results.

The field of indefinite causal order (ICO) has seen a recent surge in interest. Much of this research has focused on the quantum SWITCH, wherein multiple parties act in a superposition of different orders in a manner transcending the quantum circuit model. This results in a new resource for quantum protocols, and is exciting for its relation to issues in foundational physics. The quantum SWITCH is also an example of a higher-order quantum operation, in that it not only transforms quantum states, but also other quantum operations. To date, no higher-order quantum operation has been completely experimentally characterized. Indeed, past work on the quantum SWITCH has confirmed its ICO by measuring causal witnesses or demonstrating resource advantages, but the complete process matrix has only been described theoretically. Here, we perform higher-order quantum process tomography. However, doing so requires exponentially many measurements with a scaling worse than standard process tomography. We overcome this challenge by creating a new passively-stable fiber-based quantum SWITCH using active optical elements to deterministically generate and manipulate time-bin encoded qubits. Moreover, our new architecture for the quantum SWITCH can be readily scaled to multiple parties. By reconstructing the process matrix, we estimate its fidelity and tailor different causal witnesses directly for our experiment. To achieve this, we measure a set of tomographically complete settings, that also spans the input operation space. Our tomography protocol allows for the characterization and debugging of higher-order quantum operations with and without an ICO, while our experimental time-bin techniques could enable the creation of a new realm of higher-order quantum operations with an ICO.

We experimentally and theoretically study the dynamics of a one-dimensional array of pendula with a mild spatial gradient in their self-frequency and where neighboring pendula are connected with weak and alternating coupling. We map their dynamics to the topological Su-Schrieffer-Heeger (SSH) model of charged quantum particles on a lattice with alternating hopping rates in an external electric field. By directly tracking the dynamics of a wavepacket in the bulk of the lattice, we observe Bloch oscillations, Landau-Zener transitions, and coupling between the isospin (i.e. the inner wave function distribution within the unit cell) and the spatial degrees of freedom (the distribution between unit cells). We then use Bloch oscillations in the bulk to directly measure the non-trivial global topological phase winding and local geometric phase of the band. We measure an overall evolution of 3.1 $\pm$ 0.2 radians for the geometrical phase during the Bloch period, consistent with the expected Zak phase of $\pi$. Our results demonstrate the power of classical analogs of quantum models to directly observe the topological properties of the band structure, and sheds light on the similarities and the differences between quantum and classical topological effects.

In the standard homodyne configuration, an unknown optical state is combined with a local oscillator (LO) on a beam splitter (BS). Good quadrature measurements require a high-amplitude LO and two high-efficiency photodiodes whose signals are subtracted and normalized. By changing the LO phase, it is then possible to infer the optical state in the mode matching the LO. For quantum information processing, the states of interest are in well-separated modes, corresponding to a pulsed configuration with one relevant LO mode per measurement. We theoretically investigate what can be learned about the unknown optical state by counting photons in one or both outgoing paths after the BS, keeping the LO mode fixed but choosing its phase and magnitude. We consider measurement configurations where the BS acts differently on different sets of matching modes. When the BS acts identically on all matching modes it is possible to determine the content of the unknown optical state in the mode matching the LO conditional on each number of photons in the orthogonal modes on the same path. In particular, if both the phase and the intensity of the LO can be varied, then the statistics of just one of the counters is enough to infer these parameters, while in the case of an LO with fixed intensity both detectors are needed to accomplish this. Our results are derived by demonstrating a bijection, or lack thereof, between the probability distributions over the space of outcomes of the counter(s) and certain parameters of the unknown state for different measurement configuration. We report an experiment that was conducted to demonstrate the theory in the case where the BS acts differently depending on the polarization.

Large integer factorization is a prominent research challenge, particularly in the context of quantum computing. The classical computation of prime factors for an integer entails exponential time complexity. Quantum computing offers the potential for significantly faster computational processes compared to classical processors. We proposed a new quantum algorithm, Shallow Depth Factoring (SDF), to factor an integer. SDF consists of three steps. First, it converts a factoring problem to an optimization problem without an objective function. Then, we use a Quantum Feasibility Labeling (QFL) to label every possible solution according to whether it is feasible or infeasible for the optimization problem. Finally, the Variational Quantum Search (VQS) is used to find all feasible solutions. The SDF algorithm utilizes shallow-depth quantum circuits for efficient factorization, with the circuit depth scaling linearly as the integer to be factorized increases. Through minimizing the number of gates in the circuit, the algorithm enhances feasibility and reduces vulnerability to errors.

We develop a framework for characterizing quantum temporal correlations in a general temporal scenario, in which an initial quantum state is measured, sent through a quantum channel, and finally measured again. This framework does not make any assumptions on the system nor on the measurements, namely, it is device-independent. It is versatile enough, however, to allow for the addition of further constraints in a semi-device-independent setting. Our framework serves as a natural tool for quantum certification in a temporal scenario when the quantum devices involved are uncharacterized or partially characterized. It can hence also be used for characterizing quantum temporal correlations when one assumes an additional constraint of no-signaling in time, there are upper bounds on the involved systems' dimensions, rank constraints -- for which we prove genuine quantum separations over local hidden variable models -- or further linear constraints. We present a number of applications, including bounding the maximal violation of temporal Bell inequalities, quantifying temporal steerability, bounding the maximum successful probability in a scenario of quantum randomness access codes.

We introduce a quantum algorithm for simulating the time-dependent Dirac equation in 3+1 dimensions using discrete-time quantum walks. Thus far, promising quantum algorithms have been proposed to simulate quantum dynamics in non-relativistic regimes efficiently. However, only some studies have attempted to simulate relativistic dynamics due to its theoretical and computational difficulty. By leveraging the convergence of discrete-time quantum walks to the Dirac equation, we develop a quantum spectral method that approximates smooth solutions with exponential convergence. This mitigates errors in implementing potential functions and reduces the overall gate complexity that depends on errors. We demonstrate that our approach does not require additional operations compared to the asymptotic gate complexity of non-relativistic real-space algorithms. Our findings indicate that simulating relativistic dynamics is achievable with quantum computers and can provide insights into relativistic quantum physics and chemistry.

The burgeoning fields of machine learning (ML) and quantum machine learning (QML) have shown remarkable potential in tackling complex problems across various domains. However, their susceptibility to adversarial attacks raises concerns when deploying these systems in security sensitive applications. In this study, we present a comparative analysis of the vulnerability of ML and QML models, specifically conventional neural networks (NN) and quantum neural networks (QNN), to adversarial attacks using a malware dataset. We utilize a software supply chain attack dataset known as ClaMP and develop two distinct models for QNN and NN, employing Pennylane for quantum implementations and TensorFlow and Keras for traditional implementations. Our methodology involves crafting adversarial samples by introducing random noise to a small portion of the dataset and evaluating the impact on the models performance using accuracy, precision, recall, and F1 score metrics. Based on our observations, both ML and QML models exhibit vulnerability to adversarial attacks. While the QNNs accuracy decreases more significantly compared to the NN after the attack, it demonstrates better performance in terms of precision and recall, indicating higher resilience in detecting true positives under adversarial conditions. We also find that adversarial samples crafted for one model type can impair the performance of the other, highlighting the need for robust defense mechanisms. Our study serves as a foundation for future research focused on enhancing the security and resilience of ML and QML models, particularly QNN, given its recent advancements. A more extensive range of experiments will be conducted to better understand the performance and robustness of both models in the face of adversarial attacks.

There is a strong interest in quantum search algorithms, particularly in problems with multiple adjacent solutions. In the hypercube, part of the energy of the quantum system is retained in states adjacent to the target states, decreasing the chances of the target states being observed. This paper applies the Multiself-loop Lackadaisical Quantum Walk with Partial Phase Inversion to search for multiple adjacent marked vertices on the hypercube. Aspects like the type of marked vertices are considered in addition to using multiple self-loops and weight compositions. Two scenarios are analyzed. Firstly, the relative position of non-adjacent marked vertices together with adjacent marked vertices. Secondly, only adjacent marked vertices are analyzed. Here, we show experimentally that, with partial phase inversion, a quantum walk can amplify the probability amplitudes of the target states, reaching success probabilities of values close to $1$. We also show that the relative position of non-adjacent marked vertices does not significantly influence the search results. Our results demonstrate that the partial phase inversion of target states is a promising alternative to search adjacent solutions with quantum walks, which is a key capacity for real search applications.

We report on the existence of exceptional points (EPs) in single-resonance autoionization and provide analytical expressions for their positions in parameter space, in terms of the Fano asymmetry parameter. We additionally propose a reliable method for the experimental determination of EPs, based solely on information about their ionization probability as a function of the system parameters. The links between EPs, the maxima of the asymmetric profile and the effective decay rate of the ground state are investigated in detail. Quantitative numerical examples pertaining to the doubly excited $2s2p({}^1P)$ state of Helium confirm the validity of our formulation and results.

Precision navigation and timing, very-long-baseline interferometry, next-generation communication, sensing, and tests of fundamental physics all require a highly synchronized network of clocks. With the advance of highly-accurate optical atomic clocks, the precision requirements for synchronization are reaching the limits of classical physics (i.e. the standard quantum limit, SQL). Efficiently overcoming the SQL to reach the fundamental Heisenberg limit can be achieved via the use of squeezed or entangled light. Although approaches to the Heisenberg limit are well understood in theory, a practical implementation, such as in space-based platforms, requires that the advantage outweighs the added costs and complexity. Here, we focus on the question: can entanglement yield a quantum advantage in clock synchronization over lossy satellite-to-satellite channels? We answer in the affirmative, showing that the redundancy afforded by the two-mode nature of entanglement allows recoverability even over asymmetrically lossy channels. We further show this recoverability is an improvement over single-mode squeezing sensing, thereby illustrating a new complexity-performance trade-off for space-based sensing applications.