相关论文: A Lie Algebraic Theory of Barren Plateaus for Deep…
Deep learning methods continue to have a decided impact on machine learning, both in theory and in practice. Statistical theoretical developments have been mostly concerned with approximability or rates of estimation when recovering…
Structured variational quantum algorithms such as the Quantum Approximate Optimisation Algorithm (QAOA) have emerged as leading candidates for exploiting advantages of near-term quantum hardware. They interlace classical computation, in…
In this work, we highlight an unforeseen behavior of the expressivity of Parameterized Quantum Circuits (PQCs) for machine learning. A large class of these models, seen as Fourier Series which frequencies are derived from the encoding…
Currently available quantum computers suffer from constraints including hardware noise and a limited number of qubits. As such, variational quantum algorithms that utilise a classical optimiser in order to train a parameterised quantum…
We compare the non-linear matter power spectrum in real space calculated analytically from 3rd-order perturbation theory with N-body simulations at 1<z<6. We find that the perturbation theory prediction agrees with the simulations to better…
Quantifying the flatness of the objective-function landscape associated with unstructured parameterized quantum circuits is important for understanding the performance of variational algorithms utilizing a "hardware-efficient ansatz",…
Quantum Machine Learning (QML) is fundamentally limited by two challenges: barren plateaus (exponentially vanishing gradients) and the fragility of parameterized quantum circuits under noise. Despite extensive empirical studies, a unified…
Perturbation theory (PT) might be one of the most powerful and fruitful tools for both physicists and chemists, which evoked an explosion of applications with the blooming of atomic and subatomic physics. Even though PT is well-used today,…
Parameterized quantum circuits (PQCs), as one of the most promising schemes to realize quantum machine learning algorithms on near-term quantum computers, have been designed to solve machine earning tasks with quantum advantages. In this…
We derive and analyze three feature map representations of parametrized quantum dynamics, which generalize variational quantum circuits. These are (i) a Lie-Fourier partial sum, (ii) a Taylor expansion, and (iii) a finite-dimensional sinc…
Computing circuits composed of noisy logical gates and their ability to represent arbitrary Boolean functions with a given level of error are investigated within a statistical mechanics setting. Bounds on their performance, derived in the…
In the quest to harness the power of quantum computing, training quantum neural networks (QNNs) presents a formidable challenge. This study introduces an innovative approach, integrating the Bees Optimization Algorithm (BOA) to overcome one…
Quantum computing devices require exceptional control of their experimental parameters to prepare quantum states and simulate other quantum systems. Classical optimization procedures used to find such optimal control parameters, have…
Bayesian neural networks (BNNs) promise improved generalization under covariate shift by providing principled probabilistic representations of epistemic uncertainty. However, weight-based BNNs often struggle with high computational…
The optimization of quantum circuits can be hampered by a decay of average gradient amplitudes with increasing system size. When the decay is exponential, this is called the barren plateau problem. Considering explicit circuit…
Variational quantum algorithms (VQA) have emerged as a promising quantum alternative for solving optimization and machine learning problems using parameterized quantum circuits (PQCs). The design of these circuits influences the ability of…
Parametrized Quantum Circuits (PQCs) enable a novel method for machine learning (ML). However, from a computational point of view they present a challenge to existing eXplainable AI (xAI) methods. On the one hand, measurements on quantum…
Quantum Neural Networks (QNNs), or the so-called variational quantum circuits, are important quantum applications both because of their similar promises as classical neural networks and because of the feasibility of their implementation on…
Quantum data loading plays a central role in quantum algorithms and quantum information processing. Many quantum algorithms hinge on the ability to prepare arbitrary superposition states as a subroutine, with claims of exponential speedups…
Instantaneous quantum polynomial quantum circuit Born machines (IQP-QCBMs) have been proposed as quantum generative models with a classically tractable training objective based on the maximum mean discrepancy (MMD) and a potential quantum…