Related papers: When Less is More: Approximating the Quantum Geome…
Quantum kernel methods offer significant theoretical benefits by rendering classically inseparable features separable in quantum space. Yet, the practical application of Quantum Machine Learning (QML), currently constrained by the…
In this paper, we show how the restriction of the Quantum Geometric Tensor to manifolds of states that can be generated through local interactions provides a new tool to understand the consequences of locality in physics. After a review of…
Quantum computing has been revolutionizing the development of algorithms. However, only noisy intermediate-scale quantum devices are available currently, which imposes several restrictions on the circuit implementation of quantum…
Quantum algorithms for electronic-structure simulations are actively being developed, yet many hybrid quantum-classical approaches are bottlenecked by the measurement overhead associated with large molecular Hamiltonians. Here we introduce…
Quantum computing (QC) promises theoretical advantages, benefiting computational problems that would not be efficiently classically simulatable. However, much of this theoretical speedup depends on the quantum circuit design solving the…
This paper presents a quantum algorithm for solving the fractional Poisson equation \((-\Delta)^s u = f\) with \(s \in (0,1)\) on bounded domains. The proposed approach combines rational approximation techniques with quantum linear system…
In the NISQ (Noisy intermediate-scale quantum) area, Quantum computers can be utilized for deep learning by treating variational quantum circuits as neural network models. This can be achieved by first encoding the input data onto quantum…
In this work, we propose Natural Hypergradient Descent (NHGD), a new method for solving bilevel optimization problems. To address the computational bottleneck in hypergradient estimation--namely, the need to compute or approximate Hessian…
The constantly increasing dimensionality of artificial quantum systems demands for highly efficient methods for their characterization and benchmarking. Conventional quantum tomography fails for larger systems due to the exponential growth…
The finite element method (FEM) is a cornerstone numerical technique for solving partial differential equations (PDEs). Here, we present $\textbf{Qu-FEM}$, a fault-tolerant era quantum algorithm for the finite element method. In contrast to…
The implementation and practicality of quantum algorithms highly hinge on the quality of operations within a quantum processor. Therefore, including realistic error models in quantum computing simulation platforms is crucial for testing…
Variational Quantum Computing (VQC) faces fundamental scalability barriers, primarily due to barren plateaus and sensitivity to quantum noise. To address these challenges, we introduce TensorHyper-VQC, a novel tensor-train (TT)-guided…
Reconstructing quantum states is an important task for various emerging quantum technologies. The process of reconstructing the density matrix of a quantum state is known as quantum state tomography. Conventionally, tomography of arbitrary…
Tensor networks represent the state-of-the-art in computational methods across many disciplines, including the classical simulation of quantum many-body systems and quantum circuits. Several applications of current interest give rise to…
Computational Fluid Dynamics (CFD) is central to science and engineering, but faces severe scalability challenges, especially in high-dimensional, multiscale, and turbulent regimes. Traditional numerical methods often become prohibitively…
The development of efficient machine learning models for molecular systems representation is becoming crucial in scientific research. We introduce TensorNet, an innovative O(3)-equivariant message-passing neural network architecture that…
Machine learning has been increasingly utilized in the field of biomedical research to accelerate the drug discovery process. In recent years, the emergence of quantum computing has been followed by extensive exploration of quantum machine…
We investigate the quantum geometric tensor, which is comprised of the Berry curvature and quantum metric, in a generalized Dirac two-band system with non-integer dispersion $E(\mathbf{k})\sim k^{\alpha}$. Our analysis reveals that this…
One of the apparent advantages of quantum computers over their classical counterparts is their ability to efficiently contract tensor networks. In this article, we study some implications of this fact in the case of topological tensor…
The computation of the ground state (i.e. the eigenvector related to the smallest eigenvalue) is an important task in the simulation of quantum many-body systems. As the dimension of the underlying vector space grows exponentially in the…