Explicability and Inexplicability in the Interpretation of Quantum Neural Networks

Interpretability of artificial intelligence (AI) methods, particularly deep neural networks, is of great interest due to the widespread use of AI-backed systems, which often have unexplainable behavior. The interpretability of such models is a crucial component of building trusted systems. Many methods exist to approach this problem, but they do not obviously generalize to the quantum setting. Here we explore the interpretability of quantum neural networks using local model-agnostic interpretability measures of quantum and classical neural networks. We introduce the concept of the band of inexplicability, representing the interpretable region in which data samples have no explanation, likely victims of inherently random quantum measurements. We see this as a step toward understanding how to build responsible and accountable quantum AI models

Energy transport and optimal design of noisy Platonic quantum networks

Optimal transport is one of the primary goals for designing efficient quantum networks. In this work, the maximum transport is investigated for three-dimensional quantum networks with Platonic geometries affected by dephasing and dissipative Markovian noise. The network and the environmental characteristics corresponding the optimal design are obtained and investigated for five Platonic networks with 4, 6, 8, 12, and 20 number of sites that one of the sites is connected to a sink site through a dissipative process. Such optimal designs could have various applications like switching and multiplexing in quantum circuits.Comment: 10 pages, 6 figure

Adaptive quantum state tomography improves accuracy quadratically

We introduce a simple protocol for adaptive quantum state tomography, which reduces the worst-case infidelity between the estimate and the true state from $O(N^{-1/2})$ to $O(N^{-1})$. It uses a single adaptation step and just one extra measurement setting. In a linear optical qubit experiment, we demonstrate a full order of magnitude reduction in infidelity (from $0.1$ to $0.01$) for a modest number of samples ($N=3\times10^4$).Comment: 8 pages, 7 figure

Sub-universal variational circuits for combinatorial optimization problems

Quantum variational circuits have gained significant attention due to their applications in the quantum approximate optimization algorithm and quantum machine learning research. This work introduces a novel class of classical probabilistic circuits designed for generating approximate solutions to combinatorial optimization problems constructed using two-bit stochastic matrices. Through a numerical study, we investigate the performance of our proposed variational circuits in solving the Max-Cut problem on various graphs of increasing sizes. Our classical algorithm demonstrates improved performance for several graph types to the quantum approximate optimization algorithm. Our findings suggest that evaluating the performance of quantum variational circuits against variational circuits with sub-universal gate sets is a valuable benchmark for identifying areas where quantum variational circuits can excel.Comment: 10 pages, 7 figure

Experimental single-setting quantum state tomography

Quantum computers solve ever more complex tasks using steadily growing system sizes. Characterizing these quantum systems is vital, yet becoming increasingly challenging. The gold-standard is quantum state tomography (QST), capable of fully reconstructing a quantum state without prior knowledge. Measurement and classical computing costs, however, increase exponentially in the system size - a bottleneck given the scale of existing and near-term quantum devices. Here, we demonstrate a scalable and practical QST approach that uses a single measurement setting, namely symmetric informationally complete (SIC) positive operator-valued measures (POVM). We implement these nonorthogonal measurements on an ion trap device by utilizing more energy levels in each ion - without ancilla qubits. More precisely, we locally map the SIC POVM to orthogonal states embedded in a higher-dimensional system, which we read out using repeated in-sequence detections, providing full tomographic information in every shot. Combining this SIC tomography with the recently developed randomized measurement toolbox ("classical shadows") proves to be a powerful combination. SIC tomography alleviates the need for choosing measurement settings at random ("derandomization"), while classical shadows enable the estimation of arbitrary polynomial functions of the density matrix orders of magnitudes faster than standard methods. The latter enables in-depth entanglement studies, which we experimentally showcase on a 5-qubit absolutely maximally entangled (AME) state. Moreover, the fact that the full tomography information is available in every shot enables online QST in real time. We demonstrate this on an 8-qubit entangled state, as well as for fast state identification. All in all, these features single out SIC-based classical shadow estimation as a highly scalable and convenient tool for quantum state characterization.Comment: 34 pages, 15 figure

The clustering of risk behaviours in adolescence and health consequences in middle age.

INTRODUCTION: There is increasing interest in the clustering of risk behaviours in adolescence. However, few studies have examined what clusters of risk behaviours exist among adolescents, their early-life predictors, and their associations with later health. METHODS: We analysed data derived from 8754 participants (women 53.3%) in the 1970 British Cohort Study. Latent class analysis was used to identify clusters of risk behaviours at age 16. Regression modelling was then used to examine predictors of clusters and their consequences of risk behaviours and health outcomes at age 42. RESULTS: We identified two latent classes: a risky-behaviour (men: 20.0%, women: 23.6%) and less-risky-behaviour class. Among men, those in the risky-behaviour class were more likely to report smoking, multiple binge drinking, sexual debut before 16, involvement in fights and delinquency than were women. Membership in risky-behaviour class was mainly predicted by sociodemographic and parental risk behaviours and monitoring. The risky-behaviour class at age 16 was associated with the following outcome age 42: smoking status (more strongly among women), excessive alcohol consumption (more strongly among men), worse self-rated health (more strongly among men), and psychological distress (only among women). CONCLUSIONS: Engagement in multiple risk behaviours in adolescence is an important driver of health inequalities later in life. Early life intervention, for example via school-based interventions, may be warranted for favourable lifelong health

MATHGAMES! (Years 7-12)

Mathematics is embedded into every element of our daily lives – it is omnipresent and essential to our world but understanding its language and processes can sometimes be tricky. A team of fun and creative mathematicians are here to help! This colourful stage show will take students on a fun and exciting journey of mind-blowing numerical puzzles and games using problem solving and logic to convert any mathematical sceptic into a math lover. Don’t miss out! This event is recommended for school students in Years 7-12. This program addresses key curriculum, including General Capabilities: Numeracy