Dynamical quantum phase transitions of the Schwinger model: real-time dynamics on IBM Quantum

Simulating real-time dynamics of gauge theories represents a paradigmatic use case to test the hardware capabilities of a quantum computer, since it can involve non-trivial input states preparation, discretized time evolution, long-distance entanglement, and measurement in a noisy environment. We implement an algorithm to simulate the real-time dynamics of a few-qubit system that approximates the Schwinger model in the framework of lattice gauge theories, with specific attention to the occurrence of a dynamical quantum phase transition. Limitations in the simulation capabilities on IBM Quantum are imposed by noise affecting the application of single-qubit and two-qubit gates, which combine in the decomposition of Trotter evolution. The experimental results collected in quantum algorithm runs on IBM Quantum are compared with noise models to characterize the performance in the absence of error mitigation

Bound states and entanglement generation in waveguide quantum electrodynamics

We investigate the behavior of two quantum emitters (two-level atoms) embedded in a linear waveguide, in a quasi-one-dimensional configuration. Since the atoms can emit, absorb and reflect radiation, the pair can spontaneously relax towards an entangled bound state, under conditions in which a single atom would instead decay. We analyze the properties of these bound states, which occur for resonant values of the interatomic distance, and discuss their relevance with respect to entanglement generation. The stability of such states close to the resonance is studied, as well as the properties of non resonant bound states, whose energy is below the threshold for photon propagation

Advancement study of CancerMath model as prognostic tools for predicting Sentinel lymph node metastasis in clinically negative T1 breast cancer patients

Purpose: Sentinel lymph node biopsy (SLNB) is an invasive surgical procedure and although it has fewer complications and is less severe than axillary lymph node dissection, it is not a risk-free procedure. Large prospective trials have documented SLNB that it is considered non-therapeutic in early stage breast cancer. Methods: Web-calculator CancerMath (CM) allows you to estimate the probability of having positive lymph nodes valued on the basis of tumour size, age, histologic type, grading, expression of estrogen receptor, progesterone receptor. We collected 595 patients referred to our Institute resulting clinically negative T1 breast cancer characterized by sentinel lymph node status, prognostic factors defined by CM and also HER2 and Ki-67. We have compared classification performances obtained by online CM application with those obtained after training its algorithm on our database. Results: By training CM model on our dataset and using the same feature, adding HER2 or ki67 we reached a sensitivity median value of 71.4%, 73%, 70.4%, respectively, whereas the online one was equal to 61%, without losing specificity. The introduction of the prognostic factors Her2 and Ki67 could help improving performances on the classification of particularly type of patients. Conclusions: Although the training of the model on the sample of T1 patients has brought a significant improvement in performance, the general performance does not yet allow a clinical application of the algorithm. However, the experimental results encourage future developments aimed at introducing features of a different nature in the CM model

Multiscale Entanglement Renormalization Ansatz: Causality and Error Correction

Computational complexity reduction is at the basis of a new formulation of many-body quantum states according to tensor network ansatz, originally framed in one-dimensional lattices. In order to include long-range entanglement characterizing phase transitions, the multiscale entanglement renormalization ansatz (MERA) defines a sequence of coarse-grained lattices, obtained by targeting the map of a scale-invariant system into an identical coarse-grained one. The quantum circuit associated with this hierarchical structure includes the definition of causal relations and unitary extensions, leading to the definition of ground subspaces as stabilizer codes. The emerging error correcting codes are referred to logical indices located at the highest hierarchical level and to physical indices yielded by redundancy, framed in the AdS-CFT correspondence as holographic quantum codes with bulk and boundary indices, respectively. In a use-case scenario based on errors consisting of spin erasure, the correction is implemented as the reconstruction of a bulk local operator

Correlated photon emission by two excited atoms in a waveguide

Systems of atoms coupled to a single or a few waveguide modes provide a test-bed for physically and practically interesting interference effects. We consider the dynamics of a pair of atoms, approximated as two-level quantum emitters, coupled to a linear guided mode. In particular, we analyze the evolution of an initial state in which both atoms are excited, which is expected to decay into an asymptotic two-photon state. We investigate the lifetime of the initial configuration and the properties of the asymptotic photon correlations, and analyze the probability that the two photons are emitted in the same or in opposite directions. We find that the ratio R between parallel and antiparallel emission probabilities is maximal when the interatomic distance is an odd multiple of a quarter wavelength of the emitted light. In such a case, R = 3 in the small-coupling regime

A Proposal of Quantum-Inspired Machine Learning for Medical Purposes: An Application Case

Learning tasks are implemented via mappings of the sampled data set, including both the classical and the quantum framework. Biomedical data characterizing complex diseases such as cancer typically require an algorithmic support for clinical decisions, especially for early stage tumors that typify breast cancer patients, which are still controllable in a therapeutic and surgical way. Our case study consists of the prediction during the pre-operative stage of lymph node metastasis in breast cancer patients resulting in a negative diagnosis after clinical and radiological exams. The classifier adopted to establish a baseline is characterized by the result invariance for the order permutation of the input features, and it exploits stratifications in the training procedure. The quantum one mimics support vector machine mapping in a high-dimensional feature space, yielded by encoding into qubits, while being characterized by complexity. Feature selection is exploited to study the performances associated with a low number of features, thus implemented in a feasible time. Wide variations in sensitivity and specificity are observed in the selected optimal classifiers during cross-validations for both classification system types, with an easier detection of negative or positive cases depending on the choice between the two training schemes. Clinical practice is still far from being reached, even if the flexible structure of quantum-inspired classifier circuits guarantees further developments to rule interactions among features: this preliminary study is solely intended to provide an overview of the particular tree tensor network scheme in a simplified version adopting just product states, as well as to introduce typical machine learning procedures consisting of feature selection and classifier performance evaluation

A Roadmap towards Breast Cancer Therapies Supported by Explainable Artificial Intelligence

In recent years personalized medicine reached an increasing importance, especially in the design of oncological therapies. In particular, the development of patients’ profiling strategies suggests the possibility of promising rewards. In this work, we present an explainable artificial intelligence (XAI) framework based on an adaptive dimensional reduction which (i) outlines the most important clinical features for oncological patients’ profiling and (ii), based on these features, determines the profile, i.e., the cluster a patient belongs to. For these purposes, we collected a cohort of 267 breast cancer patients. The adopted dimensional reduction method determines the relevant subspace where distances among patients are used by a hierarchical clustering procedure to identify the corresponding optimal categories. Our results demonstrate how the molecular subtype is the most important feature for clustering. Then, we assessed the robustness of current therapies and guidelines; our findings show a striking correspondence between available patients’ profiles determined in an unsupervised way and either molecular subtypes or therapies chosen according to guidelines, which guarantees the interpretability characterizing explainable approaches to machine learning techniques. Accordingly, our work suggests the possibility to design data-driven therapies to emphasize the differences observed among the patients