Related papers: Quantum Natural Gradient
Optimization in large language models (LLMs) unfolds over high-dimensional parameter spaces with non-Euclidean structure. Information geometry frames this landscape using the Fisher information metric, enabling more principled learning via…
The quantum geometric tensor (QGT) characterizes the local geometry of quantum states, and its components directly account for the dynamical effects observed, e.g., in condensed matter systems. In this work, we address the problem of…
Variational Quantum Algorithms have emerged as a leading paradigm for near-term quantum computation. In such algorithms, a parameterized quantum circuit is controlled via a classical optimization method that seeks to minimize a…
This paper presents a global optimization approach to quantum mechanics, which describes the most fundamental dynamics of the universe. It suggests that the wave-like behavior of (sub)atomic particles could be the critical characteristic of…
Natural gradient descent is an optimization method traditionally motivated from the perspective of information geometry, and works well for many applications as an alternative to stochastic gradient descent. In this paper we critically…
Variational quantum circuits characterise the state of a quantum system through the use of parameters that are optimised using classical optimisation procedures that typically rely on gradient information. The circuit-execution complexity…
We use differential equations based approaches to provide some {\it \textbf{physics}} insights into analyzing the dynamics of popular optimization algorithms in machine learning. In particular, we study gradient descent, proximal gradient…
Gate-based quantum computations represent an essential to realize near-term quantum computer architectures. A gate-model quantum neural network (QNN) is a QNN implemented on a gate-model quantum computer, realized via a set of unitaries…
Quantum Variational Circuits (QVCs) are often claimed as one of the most potent uses of both near term and long term quantum hardware. The standard approaches to optimizing these circuits rely on a classical system to compute the new…
Designing quantum circuits for ground state preparation is a fundamental task in quantum information science. However, standard Variational Quantum Algorithms (VQAs) are often constrained by limited ansatz expressivity and difficult…
We present a gradient-based optimal-control technique for open quantum systems that utilizes quantum trajectories to simulate the quantum dynamics during optimization. Using trajectories allows for optimizing open systems with less…
The expectation that quantum computation might bring performance advantages in machine learning algorithms motivates the work on the quantum versions of artificial neural networks. In this study, we analyze the learning dynamics of a…
When the gate set has continuous parameters, synthesizing a unitary operator as a quantum circuit is always possible using exact methods, but finding minimal circuits efficiently remains a challenging problem. The landscape is very…
The simulation of quantum dynamics on a digital quantum computer with parameterized circuits has widespread applications in fundamental and applied physics and chemistry. In this context, using the hybrid quantum-classical algorithm,…
Optimization with constraints is a typical problem in quantum physics and quantum information science that becomes especially challenging for high-dimensional systems and complex architectures like tensor networks. Here we use ideas of…
Quantum control is valuable for various quantum technologies such as high-fidelity gates for universal quantum computing, adaptive quantum-enhanced metrology, and ultra-cold atom manipulation. Although supervised machine learning and…
We show that energy dissipation in slowly-driven, Markovian quantum systems at low temperature is linked to the geometry of the driving protocol through the quantum (or Fubini-Study) metric. Utilizing these findings, we establish lower…
Efficient optimization of quantum systems is a necessity for reaching fault tolerant thresholds. A standard tool for optimizing simulated quantum dynamics is the gradient-based \textsc{grape} algorithm, which has been successfully applied…
Gradient Descent (GD) is a ubiquitous algorithm for finding the optimal solution to an optimization problem. For reduced computational complexity, the optimal solution $\mathrm{x^*}$ of the optimization problem must be attained in a minimum…
The quantum geometric tensor (QGT) is a fundamental quantity for characterizing the geometric properties of quantum states and plays an essential role in elucidating various physical phenomena. The traditional QGT, defined only for pure…