Realization of a quantum autoencoder for lossless compression of quantum data

One-qubit pure states, living on the surface of Bloch sphere, can be mapped onto the usual complex plane by using stereographic projection. In this paper, after reviewing the entanglement of two-qubit pure state, it is shown that the \emph{quaternionic} stereographic projection is related to concurrence measure. This is due to the fact that every two-qubit state, in ordinary complex field, corresponds to the one-qubit state in quaternionic skew field, called quaterbit. Like the one-qubit states in complex field, the stereographic projection maps every quaterbit onto a quaternion number whose complex and quaternionic parts are related to Schmidt and concurrence terms respectively. Rather, the same relation is established for three-qubit state under \emph{octonionic} stereographic projection which means that if the state is bi-separable then, quaternionic and octonionic terms vanish. Finally, we generalize recent consequences to $2 \otimes N$ and $4\otimes N$ dimensional Hilbert spaces ($N\geq 2$) and show that, after stereographic projection, the quaternionic and octonionic terms are entanglement sensitive. These trends are easily confirmed by direct computation for general multi-particle W- and GHZ-states.

In multi-label learning, each object belongs to multiple class labels simultaneously. In the data explosion age, the size of data is often huge, i.e., large number of instances, features and class labels. The high dimension of both the feature and label spaces has posed great challenges to multi-label learning problems, e.g., high time and memory costs. In this paper, we propose a new framework for multi-label learning with a large number of class labels and features, i.e., M ulti- L abel L earning via F eature and L abel S pace D imension R eduction, namely MLL-FLSDR. Specifically, both the feature space and label space are reduced to low dimensional spaces respectively, in which the local structure of data points is utilized to constrain the geometrical structure on both the learned low dimensional spaces and guarantee the qualities of them. Then, an effective multi-label classifier is constructed from the low dimensional feature space to the latent label space. Last, the final prediction for new test data examples can be obtained by recovering from their prediction results in the latent label space with an encoding matrix learned in the previous stage. Extensive comparison experiments with the state-of-the-art approaches manifest the effectiveness of the proposed method MLL-FLSDR.

We show how the quantum Zeno effect can be exploited to control quantum many-body dynamics for quantum information and computation purposes. In particular, we consider a one dimensional array of three level systems interacting via a nearest-neighbour interaction. By encoding the qubit on two levels and using simple projective frequent measurements yielding the quantum Zeno effect, we demonstrate how to implement a well defined quantum register, quantum state transfer on demand, universal two-qubit gates and two-qubit parity measurements. Thus, we argue that the main ingredients for universal quantum computation can be achieved in a spin chain with an {\em always-on} and {\em constant} many-body Hamiltonian. We also show some possible modifications of the initially assumed dynamics in order to create maximally entangled qubit pairs and single qubit gates.

4 - Introduction to NMR quantum computing

Linear-optical-based quantum information processing has attached much attention since photon is an ideal medium for transmitting quantum information remotely. Until now, there are some important works in quantum state remote preparation, the method for reconstructing quantum state deterministically via linear optics. However, most of the methods are protocols to prepare single-qubit states remotely via linear-optical elements. In this article, we investigate the methods to prepare two-qubit hybrid states remotely. We present a deterministic remote state preparation scheme for an arbitrary two-qubit hybrid state via a hyperentangled Bell state, resorting to linear-optical elements only. The sender rotates the spatial-mode state and polarization state of the hyperentangled photon respectively in accordance with his knowledge of the two-qubit hybrid state, and the receiver can reconstruct the original two-qubit hybrid state by applying appropriate recovery operations. Moreover, we discuss the remote state preparation scheme for the two-qubit hybrid state via partially hyperentangled Bell state.

The novel field of quantum computation and quantum information has gathered significant momentum in the last few years. It has the potential to radically impact the future of information technology and influence the development of modern society. The construction of practical, general purpose quantum computers has been challenging, but quantum cryptographic and communication devices have been available in the commercial marketplace for several years. Quantum networks have been built in various cities around the world and a dedicated satellite has been launched by China to provide secure quantum communication. Such new technologies demand rigorous analysis and verification before they can be trusted in safety- and security-critical applications. Experience with classical hardware and software systems has shown the difficulty of achieving robust and reliable implementations. We present CCS q , a concurrent language for describing quantum systems, and develop verification techniques for checking equivalence between CCS q processes. CCS q has well-defined operational and superoperator semantics for protocols that are functional , in the sense of computing a deterministic input-output relation for all interleavings arising from concurrency in the system. We have implemented QEC (Quantum Equivalence Checker), a tool that takes the specification and implementation of quantum protocols, described in CCS q , and automatically checks their equivalence. QEC is the first fully automatic equivalence checking tool for concurrent quantum systems. For efficiency purposes, we restrict ourselves to Clifford operators in the stabilizer formalism, but we are able to verify protocols over all input states. We have specified and verified a collection of interesting and practical quantum protocols, ranging from quantum communication and quantum cryptography to quantum error correction.

Quantum computers are known to efficiently solve problems that remain unsolved by classical von Neumann-type computers. However, in the research and development phase within the field of information science, quantum information theory is prioritized, and the extent of information processing achievable at the experimental stage is generally not well understood. In particular, data compression is a key concept and challenge in image processing and multimedia processing within quantum information processing. A prime example of data compression in quantum computing is the quantum Fourier transform. With the advent of experimental environments enabling simplified simulations using quantum simulators developed by Google and IBM, we considered that verification might now be possible. Still images captured by 360 degree cameras are full-sky images, requiring pixel counts equivalent to 4K to 8K. This results in significantly larger data volumes compared to standard high-definition still images. Therefore, when encoding these images, it is desirable to efficiently reduce the information volume while preserving quality as much as possible. We considered whether insights from quantum information computing science could be applied to achieve this. Therefore, in this study, we experimentally investigated the effectiveness, usefulness, and potential of quantum information science for image compression by simulating the quantum Fourier transform using Qiskit during the data compression process of 360 degree camera images.

A generative-discriminative framework that integrates imaging, genetic, and diagnosis into coupled low dimensional space

Data compression is a ubiquitous aspect of modern information technology, and the advent of quantum information raises the question of what types of compression are feasible for quantum data, where it is especially relevant given the extreme difficulty involved in creating reliable quantum memories. We present a protocol in which an ensemble of quantum bits (qubits) can in principle be perfectly compressed into exponentially fewer qubits. We then experimentally implement our algorithm, compressing three photonic qubits into two. This protocol sheds light on the subtle differences between quantum and classical information. Furthermore, since data compression stores all of the available information about the quantum state in fewer physical qubits, it could allow for a vast reduction in the amount of quantum memory required to store a quantum ensemble, making even today's limited quantum memories far more powerful than previously recognized.

BackgroundAlzheimer’s disease (AD) usually appears in mid‐60s (Late‐Onset AD, LOAD), but also rarely appears in patients younger than 65 (Early‐Onset AD, EOAD), while showing distinct features. Tau shows high correlation with AD prognosis and can be detected through positron emission tomography (PET) scan. Tau data mapped into a low dimensional latent space will help detect longitudinal change pattern along AD spectrum. Furthermore, fitting tensors using individual line segments will enable us to track individual tau trajectory in the latent space.MethodWe recruited 74 healthy controls, 75 mild cognitive impairment patients, and 38 AD patients with two PET scans ([18F]Flortaucipir for tau and [18F]Florbetaben for Aβ) with two‐year follow‐up. We used standardized uptake value ratios (SUVRs) for tau PET data. All patients’ tau data went through autoencoder and principal component analysis, pretrained using baseline (BL) tau data. Using only amyloid positive AD patients’ BL – follow‐up (FU) line segments, we fit tensors and tracked individual trajectories in the latent space using a tensor tracing algorithm.ResultIn the 2‐dimensional latent space the points dispersed toward the upper‐ and right‐side as the disease deteriorated. Reconstructed SUVR maps showed tau accumulation pattern of EOAD through x‐axis, such as tau spreading in temporal, prefrontal, and parietal lobes. Reconstructed map of 1st quartile group in y‐axis showed tau spreading dominance in parietal lobe and 4th quartile group showed dominance in prefrontal, temporal lobe. Each patient’s trajectory, predicted based on the latent space, showed reconstructed map following individual tau accumulation pattern. In addition, EOAD tau spreading trajectory tend to precede LOAD tau spreading trajectory.ConclusionWe decomposed high dimensional tau accumulation pattern into 2 independent components through deep‐learning methods. X‐axis showed EOAD tau accumulation pattern and y‐axis was divided into LOAD tau accumulation pattern and non‐prefrontal dominant pattern. In addition, tensor fitting of the longitudinal vector field enables us to find individual tau spreading trajectories which can be used to predict future and past spreading. Even though this study was done using only one factor, tau, it has the potential to be expanded to other factors such as amyloid or neurodegeneration data.

A register of quantum bits with fixed transition frequencies and weakly coupled to one another through simple linear circuit elements is an experimentally minimal architecture for a small-scale superconducting quantum information processor. Presently, the known schemes for implementing two-qubit gates in this system require microwave signals having amplitudes and frequencies precisely tuned to meet a resonance condition, leaving only the signal phases as free experimentally adjustable parameters. Here, we report a minimal and robust microwave scheme to generate fast, tunable universal two-qubit gates: simply irradiate one qubit (the ``control'') at the transition frequency of another (the ``target''). The effective coupling between them is then switched on by tuning only the frequency of this single drive tone; the drive amplitude adjusts the effective coupling strength; and the drive phase selects the particular two-qubit gate implemented. This cross-resonance effect turns on linearly with the ratio of the drive amplitude $\ensuremath{\Omega}$ to the qubit-qubit detuning $\ensuremath{\Delta}$, as compared with earlier proposals that turn on as ${(\ensuremath{\Omega}/\ensuremath{\Delta})}^{4}$.

The scheme for joint remote state preparation of two different one-qubit states according to requirement is proposed by using one four-dimensional spatial-mode-entangled KLM state as quantum channel. The scheme for joint remote state preparation of two different two-qubit states according to requirement is also proposed by using one four-dimensional spatial-mode-entangled KLM state and one three-dimensional spatial-mode-entangled GHZ state as quantum channels. Quantum non-demolition measurement, Hadamard gate operation, projective measurement and unitary transformation are included in the schemes.

Extraction of low-dimensional latent space from high-dimensional observation data is essential to construct a real-time robot controller with a world model on the extracted latent space. However, there is no established method for tuning the dimension size of the latent space automatically, suffering from finding the necessary and sufficient dimension size, i.e. the minimal realization of the world model. In this study, we analyze and improve Tsallis-based variational autoencoder (q-VAE), and reveal that, under an appropriate configuration, it always facilitates making the latent space sparse. Even if the dimension size of the pre-specified latent space is redundant compared to the minimal realization, this sparsification collapses unnecessary dimensions, allowing for easy removal of them. We experimentally verified the benefits of the sparsification by the proposed method that it can easily find the necessary and sufficient six dimensions for a reaching task with a mobile manipulator that requires a six-dimensional state space. Moreover, by planning with such a minimal-realization world model learned in the extracted dimensions, the proposed method was able to exert a more optimal action sequence in real-time, reducing the reaching accomplishment time by around 20%.

Social recommendations assume that users with social networks tend to have similar pReferences and leverage the social network of users to improve personalized recommendations. However, the scarcity of interactive and social data, along with the presence of irrelevant or fake social connections, poses challenges in accurately predicting user preferences. Recent research has leveraged diffusion models to eliminate invalid social connections from the social relation graph, but this approach incurs high resource costs for large-scale item prediction. To address these issues, we propose an efficient latent space diffusion model for social recommendation named latent diffusion method for social recommendation (LDSR), which can reduce resource costs by clustering user social relationships and performing diffusion in a low-dimensional space. During the diffusion process, we inject and eliminate Gaussian noise and residuals in multiple steps, enhancing the model’s ability to recognize noise while ensuring output diversity and determinism. Additionally, we design a reconstruction strategy to capture latent social relationships, which helps to densify the social relation graph. The nonsmooth nature of the latent space can disrupt downstream task outputs, so we introduce variation constraints to smooth the latent space, reducing the impact of latent perturbations during generation. Furthermore, we incorporate user-item collaborative information to guide the reverse process, enhancing the controllability of the generated content to provide reasonable denoising. Extensive experiments on four publicly available datasets demonstrate that LDSR outperforms the state-of-the-art models, exhibiting superior training efficiency, robustness against sparsity and noise, and enhanced interpretability.

In the past few years, there has been an increasingly active exchange of ideas and methods between the formerly rather disjunct fields of quantum information and many-body physics. This has been due, on the one hand, to the growing sophisti- cation of methods and the increasing complexity of problems treated in quantum information theory, and, on the other, to the recognition that a number of central issues in many-body quantum systems can fruitfully be approached from the quan- tum information point of view. Nowhere has this been more evident than in the context of the family of numerical methods that go under the rubric density-matrix renormalization group. In particular, the concept of entanglement and its definition, measurement, and manipulation lies at the heart of much of quantum information theory (1). The density-matrix renormalization group (DMRG) methods use proper- ties of the entanglement of a bipartite system to build up an accurate approximation to particular many-body wave functions. The cross-fertilization between the two fields has led to improvements in the understanding of interacting quantum systems in general and the DMRG method in particular, has led to new algorithms related to and generalizing the DMRG, and has opened up the possibility of studying many new physical problems, ones of interest both for quantum information theory and for understanding the behavior of strongly correlated quantum systems (2). In this line, we discuss some relevant concepts in quantum information theory, including the relation between the DMRG and data compression and entanglement. As an application, we will use the quantum information entropy calculated with the DMRG to study quantum phase transitions, in particular in the bilinear-biquadratic spin-one chain and in the frustrated spin-1/2 Heisenberg chain.