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Using tools from the representation theory of compact Lie groups, we formulate a theory of Barren Plateaus (BPs) for parameterized quantum circuits whose observables lie in their dynamical Lie algebra (DLA), a setting that we term Lie…

We consider continuous structures which are obtained from finite dimensional Hilbert spaces over $\mathbb{C}$ by adding some unitary operators. Quantum automata and circuits are naturally interpretable in such structures. We consider…

Contrary to the conventional view point of quantization that breaks the gauge symmetry, a gauge invariant formulation of quantum electrodynamics is proposed. Instead of fixing the gauge, some frame is chosen to yield the locally invariant…

Variational quantum algorithms (VQAs) hold great potentials for near-term applications and are promising to achieve quantum advantage on practical tasks. However, VQAs suffer from severe barren plateau problem as well as have a large…

We give an efficient algorithm for learning a binary function in a given class C of bounded VC dimension, with training data distributed according to P and test data according to Q, where P and Q may be arbitrary distributions over X. This…

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…

Features in machine learning problems are often time-varying and may be related to outputs in an algebraic or dynamical manner. The dynamic nature of these machine learning problems renders current higher order accelerated gradient descent…

Our examination of existing deep generative models (DGMs), including VAEs and GANs, reveals two problems. First, their capability in handling discrete observations and latent codes is unsatisfactory, though there are interesting efforts.…

Quantum algorithms on near-term quantum processors are typically executed using shallow quantum circuits composed of one- and two-qubit gates. However, as circuit depth and gate number increase, gate imperfections and qubit decoherence…

Incorporating inductive biases is a promising approach for tackling challenging robot learning domains with sample-efficient solutions. This paper identifies partially observable domains where symmetries can be a useful inductive bias for…

The individual optimization of quantum circuit parameters is currently one of the main practical bottlenecks in variational quantum eigensolvers for electronic systems. To this end, several machine learning approaches have been proposed to…

Machine learning (ML) is a promising approach for performing challenging quantum-information tasks such as device characterization, calibration and control. ML models can train directly on the data produced by a quantum device while…

The article proposes and theoretically analyses a \emph{computationally efficient} multi-task learning (MTL) extension of popular principal component analysis (PCA)-based supervised learning schemes…

Parameterised quantum circuit (PQC) based Quantum Reinforcement Learning (QRL) has emerged as a promising paradigm at the intersection of quantum computing and reinforcement learning (RL). By design, PQCs create hybrid quantum-classical…

Although deep learning (DL) has already become a state-of-the-art technology for various data processing tasks, data security and computational overload problems often arise due to their high data and computational power dependency. To…

Uncertainty quantification (UQ) is critical for assessing the reliability of machine learning interatomic potentials (MLIPs) in molecular dynamics (MD) simulations, identifying extrapolation regimes and enabling uncertainty-aware workflows…

Replication of experimental results has been a challenge faced by many scientific disciplines, including the field of machine learning. Recent work on the theory of machine learning has formalized replicability as the demand that an…

Recent work in equivariant deep learning bears strong similarities to physics. Fields over a base space are fundamental entities in both subjects, as are equivariant maps between these fields. In deep learning, however, these maps are…

Machine learning algorithms with empirical risk minimization are vulnerable under distributional shifts due to the greedy adoption of all the correlations found in training data. Recently, there are robust learning methods aiming at this…

This paper surveys various results in the field of Quantum Learning theory, specifically focusing on learning quantum-encoded classical concepts in the Probably Approximately Correct (PAC) framework. The cornerstone of this work is the…