S12 - Real-World Applications I

Dissipation and irreversibility are central to most physical processes, yet they lead to non-unitary dynamics that are challenging to realise on quantum processors. Splitting methods (i.e. Trotterization) are popular for simulating unitary dynamics because the simulation problem becomes one of finding an efficient decomposition into simpler problems that can be efficiently simulated. This readily extends to high-order compositions, which introduce negative time steps beyond order 2 [1], since backward unitary evolutions are also unitary. However, when it comes to simulating dissipative dynamics, backward evolutions are amplifications, which are numerically unstable and cannot be directly block-encoded into unitary operators without rescaling. We show how splitting compositions with complex coefficients overcome this problem, bringing the simplicity and accuracy of high-order operator splitting to simulating dissipative dynamics on quantum computers. 

Distributed control systems in industrial cyber-physical environments, such as water treatment processes, rely on tightly coupled interactions among sensors, actuators, and controllers. As demonstrated in a three-tank system model, even minor faults or cyber-attacks at critical nodes can propagate rapidly, affecting overall system stability and safety. Identifying such high-impact components is therefore essential for reliable monitoring and control. Traditional centrality measures provide useful structural insights but often fail to capture hidden vulnerabilities, particularly in systems with sparse or hierarchical connectivity where dangling or weakly connected nodes influence system behavior disproportionately.
Building on prior work in centrality-based fault detection and secure monitoring in cyber-physical systems, this study extends the framework by incorporating dangling centrality within a quantum-inspired fuzzy logic approach. The proposed method aims to better capture structural fragility and influence propagation under uncertainty. Quantum-inspired techniques enable efficient exploration of complex network states, while fuzzy logic supports decision-making in the presence of incomplete or imprecise information.
The relevance of this problem lies in its direct application to real-world industrial control systems, where improved identification of critical nodes enhances fault detection, strengthens cybersecurity strategies, and increases system resilience. This work contributes toward bridging theoretical network analysis with practical control system optimization, aligning with the need for robust and adaptive solutions in next-generation cyber-physical infrastructures.

Matrix functions, for example, computing the exponential, inverse, square root or logarithm of a matrix, are ubiquitous across computational science and engineering. They transform the eigenvalues of the input matrix by the target function. We present a general method for directly synthesising block encodings of matrix functions with exponential convergence in the number of unitaries. Beyond a target error, we exploit redundancy in the Fourier extension basis to produce a bounded, near-optimal subnormalisation, i.e. the scaling of the block within the unitary matrix. The method can be applied to implementing non-unitary operators, solving systems of linear equations, solving partial differential equations, and computing covariance matrices on quantum computers, for example.