Related papers: Efficient Quantum Tensor Product Expanders and k-d…
Suitable discretizations through tensor product formulas of popular multidimensional operators (diffusion or diffusion--advection, for instance) lead to matrices with $d$-dimensional Kronecker sum structure. For evolutionary Partial…
$E(3)$-equivariant neural networks have demonstrated success across a wide range of 3D modelling tasks. A fundamental operation in these networks is the tensor product, which interacts two geometric features in an equivariant manner to…
Free categorical constructions characterise quantum computing as the combination of two copies of a reversible classical model, glued by the complementarity equations of classical structures. This recipe effectively constructs a…
Image-based data is a popular arena for testing quantum machine learning algorithms. A crucial factor in realizing quantum advantage for these applications is the ability to efficiently represent images as quantum states. Here we present a…
We introduce a new tool for quantum algorithms called quantum fast-forwarding (QFF). The tool uses quantum walks as a means to quadratically fast-forward a reversible Markov chain. More specifically, with $P$ the Markov chain transition…
Quantum annealing processors typically control qubits in unison, attenuating quantum fluctuations uniformly until the applied system Hamiltonian is diagonal in the computational basis. This simplifies control requirements, allowing…
We present the time-dependent Quantum Geometric Tensor (tQGT) as a comprehensive tool for capturing the geometric character of insulators observable within linear response. We show that tQGT describes the zero-point motion of bound…
Quantum pseudorandomness, also known as unitary designs, comprise a powerful resource for quantum computation and quantum engineering. While it is known in theory that pseudorandom unitary operators can be constructed efficiently, realizing…
Quantum Bit String Comparators (QBSC) operate on two sequences of n-qubits, enabling the determination of their relationships, such as equality, greater than, or less than. This is analogous to the way conditional statements are used in…
Regular graphs find broad applications ranging from quantum communication to quantum computation. Motivated by this, we investigate the design of a quantum battery based on a K-regular graph, where K denotes the number of edges incident on…
We give a test that can distinguish efficiently between product states of n quantum systems and states which are far from product. If applied to a state psi whose maximum overlap with a product state is 1-epsilon, the test passes with…
The increasingly complex quantum electronic circuits with a number of coupled quantum degrees of freedom will become intractable to be simulated on classical computers, and requires quantum computers for an efficient simulation. In turn, it…
Quantum random walks are constructed on operator spaces with the aid of matrix-space lifting, a type of ampliation intermediate between those provided by spatial and ultraweak tensor products. Using a form of Wiener-Ito decomposition, a…
We present a novel Adaptive Distribution Generator that leverages a quantum walks-based approach to generate high precision and efficiency of target probability distributions. Our method integrates variational quantum circuits with…
Motivated by the novel applications of the mathematical formalism of quantum theory and its generalizations in cognitive science, psychology, social and political sciences, and economics, we extend the notion of the tensor product and…
This paper is contributed to a fast algorithm for Hankel tensor-vector products. For this purpose, we first discuss a special class of Hankel tensors that can be diagonalized by the Fourier matrix, which is called \emph{anti-circulant}…
Quantum walks are the quantum mechanical analogue of classical random walks and an extremely powerful tool in quantum simulations, quantum search algorithms, and even for universal quantum computing. In our work, we have designed and…
Optimal parameter setting for applications problems embedded into hardware graphs is key to practical quantum annealers (QA). Embedding chains typically crop up as harmful Griffiths phases, but can be used as a resource as we show here: to…
The Gottesman-Knill theorem states that a Clifford circuit acting on stabilizer states can be simulated efficiently on a classical computer. Recently, this result has been generalized to cover inputs that are close to a coherent…
This paper presents the definition and implementation of a quantum computer architecture to enable creating a new computational device - a quantum computer as an accelerator In this paper, we present explicitly the idea of a quantum…