Related papers: Variational decision diagrams for quantum-inspired…
In reliability engineering, we need to understand system dependencies, cause-effect relations, identify critical components, and analyze how they trigger failures. Three prominent graph models commonly used for these purposes are fault…
Invariant manifolds provide the geometric structures for describing and understanding dynamics of nonlinear systems. The theory of invariant manifolds for both finite and infinite dimensional autonomous deterministic systems, and for…
Quantum Extreme Learning Machine (QELM) is an emerging hybrid quantum machine learning framework that leverages quantum system dynamics to enhance classical models. However, QELM can suffer from the exponential concentration problem, where…
Decision diagrams (DDs) are powerful tools to represent effectively propositional formulas, which are largely used in many domains, in particular in formal verification and in knowledge compilation. Some forms of DDs (e.g., OBDDs, SDDs) are…
Determinantal point processes (DPPs) are elegant probabilistic models of repulsion that arise in quantum physics and random matrix theory. In contrast to traditional structured models like Markov random fields, which become intractable and…
Quantum query complexity plays an important role in studying quantum algorithms, which captures the most known quantum algorithms, such as search and period finding. A query algorithm applies $U_tO_x\cdots U_1O_xU_0$ to some input state,…
Variational representations of quantum states abound and have successfully been used to guess ground-state properties of quantum many-body systems. Some are based on partial physical insight (Jastrow, Gutzwiller projected, and fractional…
Decision diagram (DD)-based quantum circuit simulators represent quantum states and gates using DDs, enabling memory-efficient and fast simulations for some quantum circuits like Shor. Although it is known that DD size and processing time…
To understand the chemical properties of molecules, it is often important to study derivatives of energies with respect to nuclear coordinates or external fields. Quantum algorithms for computing energy derivatives have been proposed, but…
Modeling non-Hermitian Hamiltonians is increasingly important in classical and quantum domains, especially when studying open systems, $PT$ symmetry, and resonances. However, the quantum simulation of these models has been limited by the…
Representing and learning from graphs is essential for developing effective machine learning models tailored to non-Euclidean data. While Graph Neural Networks (GNNs) strive to address the challenges posed by complex, high-dimensional graph…
The barren plateau phenomenon, characterized by loss gradients that vanish exponentially with system size, poses a challenge to scaling variational quantum algorithms. Here we explore the potential of warm starts, whereby one initializes…
For a large class of variational quantum circuits, we show how arbitrary-order derivatives can be analytically evaluated in terms of simple parameter-shift rules, i.e., by running the same circuit with different shifts of the parameters. As…
Variational Quantum Algorithms (VQAs), such as the Variational Quantum Eigensolver (VQE) and the Quantum Approximate Optimization Algorithm (QAOA), are widely studied as candidates for near-term quantum advantage. Recent work has shown that…
Dynamic graph learning has gained significant attention as it offers a powerful means to model intricate interactions among entities across various real-world and scientific domains. Notably, graphs serve as effective representations for…
A new method for learning variational autoencoders (VAEs) is developed, based on Stein variational gradient descent. A key advantage of this approach is that one need not make parametric assumptions about the form of the encoder…
Quantum machine learning models that leverage quantum circuits as quantum feature maps (QFMs) are recognized for their enhanced expressive power in learning tasks. Such models have demonstrated rigorous end-to-end quantum speedups for…
The simulation of quantum dynamics calls for quantum algorithms working in first quantized grid encodings. Here, we propose a variational quantum algorithm for performing quantum dynamics in first quantization. In addition to the usual…
In recent years, variational quantum circuits (VQCs) have been widely explored to advance quantum circuits against classic models on various domains, such as quantum chemistry and quantum machine learning. Similar to classic…
Quantum machine learning (QML) has recently made significant advancements in various topics. Despite the successes, the safety and interpretability of QML applications have not been thoroughly investigated. This work proposes using…