Superposition Of States Research Articles

Survey Paper on Quantum Deep Reinforcement Learning for Robot Navigation Tasks

Abstract: Quantum deep reinforcement learning is an integration of the principles of quantum computing with deep reinforcement learning in an effort to advance robot navigation tasks. Due to the explosion of the state and action spaces, traditionally DRL methods are limited in scalability and efficiency. QDRL, however, uses quantum superposition and entanglement for more efficient processing of big amounts of information-it enables robots to learn optimal policies for navigating complex environments. We introduce here a new QDRL framework in which quantum neural networks encode policy functions and value estimates. We demonstrate how quantum circuits can take advantage of multi-dimensional state representations in order to strengthen the power of a robot in changing its environment over time. Benchmark experiments on navigation tasks reflect phenomenal acceleration in learning performance along with better decision-making accuracy compared to classical DRL methods. We then consider integrating such quantum algorithms, as Grover's search, to improve exploration strategies in sparse reward settings. The experiments show that QDRL speeds up convergence rates and provides robots with the possibility to react more rapidly to unexpected obstacles. It discusses new applications for quantum computing of autonomous systems, potentially applied to robotics, autonomous vehicles, and other environments which require complex decision making. Some lines of work in the future are optimization of the resources needed for quantum computers and hybrid architectures for the resolution of classical problems in navigation

Universal limit on spatial quantum superpositions with massive objects due to phonons

It has been a long-standing goal to bring massive objects into a superposition of different locations in real space, not only to confirm quantum theory in new regimes, but also to explore the interface with gravity. The main challenge is usually thought to arise from forces or scattering due to environmental fields and particles that decohere the large object's wave function into a statistical mixture. We unveil a decoherence channel which cannot be eliminated by improved isolation from the environment. It originates from sound waves within the object, which are excited as part of any splitting process and carry partial information. This puts stringent constraints on future spatial superpositions of large objects. Published by the American Physical Society 2024

Spin-bearing molecules as optically addressable platforms for quantum technologies

Abstract Efforts to harness quantum hardware relying on quantum mechanical principles have been steadily progressing. The search for novel material platforms that could spur the progress by providing new functionalities for solving the outstanding technological problems is however still active. Any physical property presenting two distinct energy states that can be found in a long-lived superposition state can serve as a quantum bit (qubit), the basic information processing unit in quantum technologies. Molecular systems that can feature electron and/or nuclear spin states together with optical transitions are one of the material platforms that can serve as optically addressable qubits. The attractiveness of molecular systems for quantum technologies relies on the fact that molecular structures of atomically defined nature can be obtained in endless diversity of chemical compositions. Crucially, by harnessing the molecular design protocols, the optical and spin (electronic and nuclear) properties of molecules can be tailored, aiding the design of optically addressable spin qubits and quantum sensors. In this contribution, we present a concise and collective discussion of optically addressable spin-bearing molecules – namely, organic molecules, transition metal (TM) and rare-earth ion (REI) complexes – and highlight recent results such as chemical tuning of optical and electron spin quantum coherence, optical spin initialization and readout, intramolecular quantum teleportation, optical coherent storage, and photonic-enhanced optical addressing. We envision that optically addressable spin-carrying molecules could become a scalable building block of quantum hardware for applications in the fields of quantum sensing, quantum communication and quantum computing.

Quantum networks theory

The formalism of quantum theory over discrete systems is extended in two significant ways. First, quantum evolutions are generalized to act over entire network configurations, so that nodes may find themselves in a quantum superposition of being connected or not, and be allowed to merge, split and reconnect coherently in a superposition. Second, tensors and traceouts are generalized, so that systems can be partitioned according to almost arbitrary logical predicates in a robust manner. The hereby presented mathematical framework is anchored on solid grounds through numerous lemmas. Indeed, one might have feared that the familiar interrelations between the notions of unitarity, complete positivity, trace-preservation, non-signalling causality, locality and localizability that are standard in quantum theory be jeopardized as the neighbourhood and partitioning between systems become both quantum, dynamical, and logical. Such interrelations in fact carry through, albeit two new notions become instrumental: consistency and comprehension.

Generation of ultrarelativistic vortex leptons with large orbital angular momenta

We put forward a novel method for generating ultrarelativistic vortex positrons and electrons with intrinsic orbital angular momenta (OAM) through nonlinear Breit-Wheeler (NBW) scattering of vortex γ photons. A complete angular momentum-resolved scattering theory has been formulated, introducing angular momenta of laser photons and vortex particles into the conventional NBW scattering framework. We find that vortex positron (electron) can be produced when the outgoing electron (positron) is generated along the collision axis. By unveiling the angular momentum transfer mechanism, we clarify that the OAM of the γ photon and the large angular momenta due to multiple laser photons are entirely transferred to the generated vortex leptons. Furthermore, the cone opening angle and superposition state of the vortex γ photon can be determined via the angular distribution of created pairs in NBW processes. Published by the American Physical Society 2024

Teaching quantum mechanics using Ant–Man

Abstract The integration of popular culture, particularly superhero films, into physics education has gained traction as a means to enhance student engagement and comprehension. In this paper, we present a pedagogical approach aimed at introducing quantum mechanics concepts to high school students using the superhero paradigm, focusing on Ant–Man. Our approach addresses the lack of resources utilizing quantum physics in superhero films by outlining a sequence of activities centred around the Uncertainty Principle, position, momentum, superposition of states, and the Planck scale. Through a series of classroom activities, students were encouraged to reflect on quantum mechanical concepts, propose solutions to fictional scenarios inspired by superhero narratives, and apply their understanding to new problem–solving situations. Analysis of student responses indicates that the activities effectively stimulated introductory discussions and curiosity about quantum mechanics, suggesting potential for further exploration and adaptation in physics education.

Observation of quantum superposition of topological defects in a trapped-ion quantum simulator.

Topological defects are discontinuities of a system protected by global properties, with wide applications in mathematics and physics. While previous experimental studies mostly focused on their classical properties, it has been predicted that topological defects can exhibit quantum superposition. Despite the fundamental interest and potential applications in understanding symmetry-breaking dynamics of quantum phase transitions, its experimental realization still remains a challenge. Here, we report the observation of quantum superposition of topological defects in a trapped-ion quantum simulator. By engineering long-range spin-spin interactions, we observe a spin kink splitting into a superposition of kinks at different positions, creating a "Schrodinger kink" that manifests nonlocality and quantum interference. Furthermore, by preparing superposition states of neighboring kinks with different phases, we observe the propagation of the wave packet in different directions, thus unambiguously verifying the quantum coherence in the superposition states. Our work provides useful tools for nonequilibrium dynamics in quantum Kibble-Zurek physics.

Optimal circular states

Abstract In quantum optics, superpositions of coherent states, such as Schr"odinger cat states and compass states, and more generally, circular states, have attracted widespread attention due to their nice properties and significant applications. Concerning circular states, a natural question arises as what are the optimal parameters in these states for maximally achieving certain specified quantum features such as average photon number and nonclassicality. It turns out this issue is highly nontrivial and subtle. In this work, we investigate optimal circular states for average photon number, and determine the optimal parameters by a combination of theoretical and numerical methods. In particular, we establish several analytical results and also some rather detailed numerical results. We tabulate some numerical results, which may be useful in both theoretical and experimental studies of superpositions of coherent states.

Observing Quantum Measurement Collapse as a Learnability Phase Transition

During a quantum measurement, superpositions of states with different observable properties probabilistically collapse into one with a sharp value of the measured observable. In macroscopic quantum systems, this collapse arises via a continuous measurement-induced phase transition (MIPT) at a critical value of the strength of interaction with the measurement apparatus. MIPTs lie outside established paradigms for equilibrium or nonequilibrium critical phenomena and delineate distinct, stable dynamical and computational phases of matter. Quantum computers enable programmable simulation of the interaction of a measurement apparatus with a dynamical quantum system, to explore MIPT phenomena over a range of system sizes while retaining quantum coherence. Yet, existing experimental protocols rely on fundamentally nonscalable postselection techniques or direct classical simulation of quantum circuits. Here, we report the scalable observation of finite-size scaling evidence for an observable-sharpening MIPT in monitored quantum circuits in a chain of Yb+171 ions in Quantinuum’s H1-1 trapped-ion quantum processor. By leveraging an equivalent description as a statistical physics problem, we implement scalable classical algorithms to infer the value of the measured observable from a single experimental shot. This technique enables a truly scalable protocol to observe observable-sharpening MIPTs in generic classes of circuits that cannot be directly classically simulated and also provides enhanced means to detect and suppress errors in the quantum simulation. Published by the American Physical Society 2024

Locally distinguishing genuinely nonlocal sets with entanglement resource

A set of orthogonal product states is deemed genuinely nonlocal if they remain locally indistinguishable under any bipartition. In this paper, we first construct a genuinely nonlocal product basis B I(5, 3) in C5⨂C5⨂C5 using a set of nonlocal product states in C3⨂C4 . Then, we obtain a genuinely nonlocal product basis B II(5, 3) by replacing certain states in B I(5, 3) with some superposition states. We achieve perfect discrimination of the constructed genuinely nonlocal product basis, separately employing two EPR states and one GHZ state. Our protocol is more efficient than quantum teleportation.

Hierarchical graph contrastive learning framework based on quantum neural networks for sentiment analysis

Existing multi-modal sentiment analysis (MSA) methods typically achieve interaction by connecting different layers or designing special structures, but rarely consider the synergistic effects among data. Moreover, most sentiment analysis research tends to focus solely on single sentiment polarity analysis, without considering the intensity and directional attributes of emotions. Addressing these issues, we propose a framework called Hierarchical Graph Contrastive Learning based on Quantum Neural Network (HGCL-QNN) to remedy these shortcomings. Specifically, a graph structure is established within and between modalities. In the quantum fuzzy neural network module, fuzzy quantum encoding is implemented by using complex-valued, then quantum superposition and entanglement are utilized to consider the intensity and directional attributes of emotions while analyzing emotional polarity. In the quantum multi-modal fusion neural network module, methods such as amplitude encoding and quantum entanglement are employed to further integrate information from different modalities, thereby enhancing the model's power to express emotional information. To enhance the model's understanding of fine-grained and global features, and to better align and integrate features from different modalities, hierarchical graph contrastive learning is employed on different levels. The experimental results demonstrate that HGCL-QNN outperforms the existing baseline methods on MOSI and MOSEI datasets, achieving significant efficacy improvements.

Quantum lozenge tiling and entanglement phase transition

While volume violation of area law has been exhibited in several quantum spin chains, the construction of a corresponding ground state in higher dimensions, entangled in more than one direction, has been an open problem. Here we construct a 2D frustration-free Hamiltonian with maximal violation of the area law. We do so by building a quantum model of random surfaces with color degree of freedom that can be viewed as a collection of colored Dyck paths. The Hamiltonian may be viewed as a 2D generalization of the Fredkin spin chain. It relates all the colored random surface configurations subject to a Dirichlet boundary condition and hard wall constraint from below to one another, and the ground state is therefore a superposition of all such classical states and non-degenerate. Its entanglement entropy between subsystems undergoes a quantum phase transition as the deformation parameter is tuned. The area- and volume-law phases are similar to the one-dimensional model, while the critical point scales with the linear size of the system L as Llog⁡L. Further it is conjectured that similar models with entanglement phase transitions can be built in higher dimensions with even softer area law violations at the critical point.

Relativity of the event: examples in JT gravity and linearized GR

Observables in quantum gravity are famously defined asymptotically, at the boundary of AdS or Minkowski spaces. However, by gauge fixing a coordinate system or suitably dressing the field operators, an approximate, “quasi-local” approach is also possible, that can give account of the measurements performed by a set of observers living inside the spacetime. In particular, one can attach spatial coordinates to the worldlines of these observers and use their proper times as a time coordinate. Here we highlight that any such local formulation has to face the relativity of the event, in that changing frame (= set of observers) implies a reshuffling of the point-events and the way they are identified. As a consequence, coordinate transformations between different frames become probabilistic in quantum gravity. We give a concrete realization of this mechanism in Jackiw-Teitelboim gravity, where a point in the bulk can be defined operationally with geodesics anchored to the boundary. We describe different ways to do so, each corresponding to a different frame, and compute the variances of the transformations relating some of these frames. In particular, we compute the variance of the location of the black hole horizon, which appears smeared in most frames. We then suggest how to calculate this effect in Einstein gravity, assuming knowledge of the wavefunction of the metric. The idea is to expand the latter on a basis of semiclassical states. Each element of this basis enjoys standard/deterministic coordinate transformations and the result is thus obtained by superposition. As a divertissement, we sabotage Lorentz boosts by adding to Minkoswki space a quantum superposition of gravitational waves and compute the probabilistic coordinate transformation to a boosted frame at linear order. Finally, we attempt to translate the relativity of the event into the language of dressed operators.

Quantum superpositions of current states in Rydberg-atom networks

Quantum simulation of many-body quantum systems using Rydberg-atom platforms has become of extreme interest in the last years. The possibility to realize spin Hamiltonians and the accurate control at the single atom level paved the way for the study of quantum phases of matter and dynamics. Here, we propose a quantum optimal control protocol to engineer current states: quantum states characterized by Rydberg excitations propagating in a given spatially closed tweezer networks. Indeed, current states with different winding numbers can be generated on demand. Besides those ones with single winding number, superposition of quantum current states characterized by more winding numbers can be obtained. The single current states are eigenstates of the current operator that therefore can define an observable that remains persistent at any time. In particular, the features of the excitations dynamics reflects the nature of current states, a fact that in principle can be used to characterize the nature of the flow experimentally without the need of accessing high order correlators. Published by the American Physical Society 2024

Modern quantum materials

Quantum phenomena, including entanglement, superposition, tunneling, and spin–orbit interactions, among others, are foundational to the development of recent innovations in quantum computing, teleportation, encryption, sensing, and new modalities of electronics, such as spintronics, spin-orbitronics, caloritronics, magnonics, twistronics, and valleytronics. These emerging technologies provide disruptive influences to global commercial markets. These remarkable advances in quantum technologies are nearly always enabled by the discovery of materials and their quantum behaviors. Such advances are governed by quantum principles that are strongly influenced by environmental, physical, topological, and morphological conditions such as very small length scales, short time durations, ultrahigh pressures, ultralow temperatures, etc., which lead to quantum behaviors that manifest as quantum tunneling, entanglement, superpositioning, superfluidity, low-dimensional, high-temperature and high-pressure superconductivity, quantum fluctuations, Bose–Einstein condensates, topological effects, and other phenomena that are not yet fully understood nor adequately explored. Here, we provide a review of quantum materials developed up to 2023. Remarkable advances in quantum materials occur daily, and therefore, by the time of publication, new and exciting breakthroughs will have occurred that are regrettably not covered herein.

Hyperfine-Enhanced Gyroscope Based on Solid-State Spins.

Solid-state platforms based on electronuclear spin systems are attractive candidates for rotation sensing due to their excellent sensitivity, stability, and compact size, compatible with industrial applications. Conventional spin-based gyroscopes measure the accumulated phase of a nuclear spin superposition state to extract the rotation rate and thus suffer from spin dephasing. Here, we propose a gyroscope protocol based on a two-spin system that includes a spin intrinsically tied to the host material, while the other spin is isolated. The rotation rate is then extracted by measuring the relative rotation angle between the two spins starting from their population states, robust against spin dephasing. In particular, the relative rotation rate between the two spins can be enhanced by their hyperfine coupling by more than an order of magnitude, further boosting the achievable sensitivity. The ultimate sensitivity of the gyroscope is limited by the lifetime of the spin system and compatible with a broad dynamic range, even in the presence of magnetic noise or control errors due to initialization and qubit manipulations. Our result enables precise measurement of slow rotations and exploration of fundamental physics.

Block Cipher Doubling for a Post-Quantum World

In order to maintain a similar security level in a post-quantum setting, many symmetric primitives should have to double their keys and increase their state sizes. So far, no generic way for doing this is known that would provide convincing quantum security guarantees. In this paper we propose a new generic construction, QuEME, that allows one to double the key and the state size of a block cipher in such a way that a decent level of quantum security is guaranteed. The QuEME design is inspired by the ECB-Mix-ECB (EME) construction, but is defined for a different choice of mixing function than what we have seen before, in order to withstand a new quantum superposition attack that we introduce as a side result: this quantum superposition attack exhibits a periodic property found in collisions and breaks EME and a large class of its variants. We prove that QuEME achieves n-bit security in the classical setting, where n is the block size of the underlying block cipher, and at least (n/6)-bit security in the quantum setting. We finally propose a concrete instantiation of this construction, called Double-AES, that is built with variants of the standardized AES-128 block cipher.

Quantum Representation based Preference Evolution Network for E-commerce recommendation

Quantum theory, originally developed to explain microscopic physical systems, has recently emerged as a novel conceptual and mathematical framework in information science. This paper applies quantum theory to address challenges in E-commerce recommendation, specifically those involving sequential behavior, aiming to mine effective patterns of preference evolution and more accurately predict user interests. Current recommender systems are limited by the sequence length and underutilize side information such as item attributes. To address these issues, we propose a Quantum Representation-based Preference Evolution Network (QRPEN) for E-commerce recommendations. Unlike traditional methods that focus solely on item-ID, our approach integrates a comprehensive set of side information, including both item-ID and attribute data, at each timestamp. We represent item attributes using quantum superposition states and employ density matrices to describe the probability distribution of same-type attributes. These matrices are then transformed into vectors through a quantum measurement-inspired process and fed into a Quasi-RNN model, enabling parallelization and the modeling of longer sequences. This approach effectively captures the dynamic evolution of user preferences. Experiments on public E-commerce datasets demonstrate that QRPEN achieves competitive performance.

QSIM: A Quantum-inspired hierarchical semantic interaction model for text classification

Semantic interaction modeling is a fundamental technology in natural language understanding that guides models to extract deep semantic information from text. Currently, the attention mechanism is one of the most effective techniques in semantic interaction modeling, which learns word-level attention representation by measuring the relevance between different words. However, the attention mechanism is limited to word-level semantic interaction, it cannot meet the needs of fine-grained interactive information for some text classification tasks. In recent years, quantum-inspired language modeling methods have successfully constructed quantized representations of language systems in Hilbert spaces, which use density matrices to achieve fine-grained semantic interaction modeling.This paper presents a Quantum-inspired hierarchical Semantic Interaction Model (QSIM), which follows the sememe-word-sentence language construction principle and utilizes quantum entanglement theory to capture hierarchical semantic interaction information in Hilbert space. Our work builds on the idea of the attention mechanism and extends it. Specifically, we explore the original semantic space from a quantum theory perspective and derive the core semantic space using the Schmidt decomposition technique, where: (1) Sememe is represented as the unit vector in the two-dimensional minimum semantic space; (2) Word is represented as reduced density matrices in the core semantic space, where Schmidt coefficients quantify sememe-level semantic interaction. Compared to density matrices, reduced density matrices capture fine-grained semantic interaction information with lower computational cost; (3) Sentence is represented as quantum superposition states of words, and the degree of word-level semantic interaction is measured using entanglement entropy.To evaluate the model’s performance, we conducted experiments on 15 text classification datasets. The experimental results demonstrate that our model is superior to classical neural network models and traditional quantum-inspired language models. Furthermore, the experiment also confirms two distinct advantages of QISM: (1) flexibility, as it can be integrated into various mainstream neural network text classification architectures; and (2) practicability, as it alleviates the problem of parameter growth inherent in density matrix calculation in quantum language model.

Quantum computing enhanced knowledge tracing: Personalized KT research for mitigating data sparsity

With the development of artificial intelligence in education, knowledge tracing (KT) has become a current research hotspot and is the key to the success of personalized instruction. However, data sparsity remains a significant challenge in the KT domain. To address this challenge, this paper applies quantum computing (QC) technology to KT for the first time. It proposes two personalized KT models incorporating quantum mechanics (QM): quantum convolutional enhanced knowledge tracing (QCE-KT) and quantum variational enhanced knowledge tracing (QVE-KT). Through quantum superposition and entanglement properties, QCE-KT and QVE-KT effectively alleviate the data sparsity problem in the KT domain through quantum convolutional layers and variational quantum circuits, respectively, and significantly improve the quality of the representation and prediction accuracy of students’ knowledge states. Experiments on three datasets show that our models outperform ten benchmark models. On the most sparse dataset, QCE-KT and QVE-KT improve their performance by 16.44% and 14.78%, respectively, compared to DKT. Although QC is still in the developmental stage, this study reveals the great potential of QM in personalized KT, which provides new perspectives for solving personalized instruction problems and opens up new directions for applying QC in education.