Related papers: All you need is spin: SU(2) equivariant variationa…
We show that quantum circuits restricted by a symmetry inherit the properties of the whole special unitary group $SU(2^n)$, in particular composition, algebraic and topological closedness and connectedness. It extends prior work on…
A new method for compiling quantum algorithms is proposed and tested for a three qubit system. The proposed method is to decompose a a unitary matrix U, into a product of simpler U j via a neural network. These U j can then be decomposed…
Symmetries and equivariance are fundamental to the generalization of neural networks on domains such as images, graphs, and point clouds. Existing work has primarily focused on a small number of groups, such as the translation, rotation,…
Parametrised quantum circuits are a central framework for near term quantum machine learning. However, it remains challenging to determine in advance how architectural choices, such as encoding strategies, gate placement, and entangling…
Scalable quantum technologies will require an unprecedented combination of precision and complexity for designing stable structures of well-controllable quantum systems. It is a challenging task to find a suitable elementary building block,…
Quantum physics-informed neural networks (QPINNs) have recently emerged as a promising framework for the solution of partial differential equations (PDEs), with several studies reporting improved convergence and accuracy relative to…
We construct lattice gauge theories in which the elements of the link matrices are represented by non-commuting operators acting in a Hilbert space. These quantum link models are related to ordinary lattice gauge theories in the same way as…
A school of thought contends that human decision making exhibits quantum-like logic. While it is not known whether the brain may indeed be driven by actual quantum mechanisms, some researchers suggest that the decision logic is…
We present a neural network wavefunction framework for solving non-Abelian lattice gauge theories in a continuous group representation. Using a combination of $SU(2)$ equivariant neural networks alongside an $SU(2)$ invariant,…
Equivariant neural networks have shown improved performance, expressiveness and sample complexity on symmetrical domains. But for some specific symmetries, representations, and choice of coordinates, the most common point-wise activations,…
We investigate the application of hybrid quantum tensor networks to aeroelastic problems, harnessing the power of Quantum Machine Learning (QML). By combining tensor networks with variational quantum circuits, we demonstrate the potential…
We consider quantum transition amplitudes, partition functions and observables for 3D spin foam models within $SU(2)$ quantum group deformation symmetry, where the deformation parameter is a complex fifth root of unity. By considering…
Quantum networks offer a realistic and practical scheme for generating multiparticle entanglement and implementing multiparticle quantum communication protocols. However, the correlations that can be generated in networks with quantum…
Recently, deep neural networks have proven capable of predicting some output properties of relevant random quantum circuits, indicating a strategy to emulate quantum computers alternative to direct simulation methods such as, e.g.,…
Reversing unitary operations is a key task in quantum computing and quantum control. In this work, we introduce and develop the framework of shadow unitary inversion, a relaxed variant of unitary inversion in which the goal is to reproduce…
We consider lambda and anisotropic deformations of the SU(2) principal chiral model and show how they can be quantized in the Hamiltonian formalism on a lattice as a suitable spin chain. The spin chain is related to the higher spin XXZ…
We introduce a variational manifold of simple tensor network states for the study of a family of constrained models that describe spin-1/2 systems as realized by Rydberg atom arrays. Our manifold permits analytical calculation via…
We provide a general self-attention formulation to impose group equivariance to arbitrary symmetry groups. This is achieved by defining positional encodings that are invariant to the action of the group considered. Since the group acts on…
While quantum machine learning (ML) has been proposed to be one of the most promising applications of quantum computing, how to build quantum ML models that outperform classical ML remains a major open question. Here, we demonstrate a…
Discrete translational symmetry plays a fundamental role in condensed matter physics and lattice gauge theories, enabling the analysis of systems that would otherwise be intractable. Despite this, many open problems remain. Quantum…