相关论文: Topological Signal Processing on Quantum Computers…

We present a new approach, the Topograph, which reconstructs underlying physics processes, including the intermediary particles, by leveraging underlying priors from the nature of particle physics decays and the flexibility of message…

We present a quantum algorithm that additively approximates the value of a tensor network to a certain scale. When combined with existing results, this provides a complete problem for quantum computation. The result is a simple new way of…

Quantum networks providing shared entanglement over a mesh of quantum nodes will revolutionize the field of quantum information science by offering novel applications in quantum computation, enhanced precision in networks of sensors and…

Topological deep learning (TDL) is a rapidly growing field that seeks to leverage topological structure in data and facilitate learning from data supported on topological objects, ranging from molecules to 3D shapes. Most TDL architectures…

The Harrow-Hassidim-Lloyd (HHL) quantum algorithm for sampling from the solution of a linear system provides an exponential speed-up over its classical counterpart. The problem of solving a system of linear equations has a wide scope of…

Verifying quantum advantage for practical problems, particularly the ground state energy estimation (GSEE) problem, is one of the central challenges in quantum computing theory. For that purpose, dequantization algorithms play a central…

Hybrid Tensor Networks (hTN) offer a promising solution for encoding variational quantum states beyond the capabilities of efficient classical methods or noisy quantum computers alone. However, their practical usefulness and many…

Despite significant advances in quantum algorithms, quantum programs in practice are often expressed at the circuit level, forgoing helpful structural abstractions common to their classical counterparts. Consequently, as many quantum…

The development of numerically efficient computational methods has facilitated in depth studies of various correlated phases of matter including critical and topological phases. A quantum Monte-Carlo study of an extended Bose-Hubbard ladder…

Several aspects of managing a sensor network (e.g., motion planning for data mules, serial data fusion and inference) benefit once the network is linearized to a path. The linearization is often achieved by constructing a space filling…

Higher order data is modeled using matrices whose entries are numerical arrays of a fixed size. These arrays, called t-scalars, form a commutative ring under the convolution product. Matrices with elements in the ring of t-scalars are…

Our previous multiscale graph basis dictionaries/graph signal transforms -- Generalized Haar-Walsh Transform (GHWT); Hierarchical Graph Laplacian Eigen Transform (HGLET); Natural Graph Wavelet Packets (NGWPs); and their relatives -- were…

Topological orders can be used as media for topological quantum computing --- a promising quantum computation model due to its invulnerability against local errors. Conversely, a quantum simulator, often regarded as a quantum computing…

Recently, message-passing Neural networks (MPNN) provide a promising tool for dealing with molecular graphs and have achieved remarkable success in facilitating the discovery and materials design with desired properties. However, the…

The discovery of nontrivial topology in quantum critical states has introduced a new paradigm for classifying quantum phase transitions and challenges the conventional belief that topological phases are typically associated with a bulk…

We elaborate the idea of quantum computation through measuring the correlation of a gapped ground state, while the bulk Hamiltonian is utilized to stabilize the resource. A simple computational primitive, by pulling out a single spin…

The hidden subgroup problem~(HSP) is one of the most important problems in quantum computation. Many problems for which quantum algorithm achieves exponential speedup over its classical counterparts can be reduced to the Abelian HSP.…

The interplay of quantum and classical simulation and the delicate divide between them is in the focus of massively parallelized tensor network state (TNS) algorithms designed for high performance computing (HPC). In this contribution, we…

The preparation of the ground state of a Hamiltonian $H$ with a large spectral radius has applications in many areas such as electronic structure theory and quantum field theory. Given an initial state with a constant overlap with the…

Topological data analysis can reveal higher-order structure beyond pairwise connections between vertices in complex networks. We present a new method based on discrete Morse theory to study topological properties of unweighted and…