Related papers: Matrix Inversion by Quantum Walk
In the current framework of Geometric Quantum Machine Learning, the canonical method for constructing a variational ansatz that respects the symmetry of some group action is by forcing the circuit to be equivariant, i.e., to commute with…
In this work, we generalize the recently-introduced graph composition framework to the non-boolean setting. A quantum algorithm in this framework is represented by a hypergraph, where each hyperedge is adjacent to multiple vertices. The…
The standard quantum annealing algorithm tries to approach the ground state of a classical system by slowly decreasing the hopping rates of a quantum random walk in the configuration space of the problem, where the on-site energies are…
Hierarchical matrices approximate a given matrix by a decomposition into low-rank submatrices that can be handled efficiently in factorized form. $\mathcal{H}^2$-matrices refine this representation following the ideas of fast multipole…
We present a detailed circuit implementation of Szegedy's quantization of the Metropolis-Hastings walk. This quantum walk is usually defined with respect to an oracle. We find that a direct implementation of this oracle requires costly…
Transition amplitudes and transition probabilities are relevant to many areas of physics simulation, including the calculation of response properties and correlation functions. These quantities can also be related to solving linear systems…
Quantum walks are quantum counterparts of Markov chains. In this article, we give a brief overview of quantum walks, with emphasis on their algorithmic applications.
Machine learning has emerged as a promising approach to study the properties of many-body systems. Recently proposed as a tool to classify phases of matter, the approach relies on classical simulation methods$-$such as Monte Carlo$-$which…
We address the properties of continuous-time quantum walks with Hamiltonians of the form $\mathcal{H}= L + \lambda L^2$, being $L$ the Laplacian matrix of the underlying graph and being the perturbation $\lambda L^2$ motivated by its…
This paper presents a novel methodology that transforms discrete-time quantum walks into a graph embedding technique, offering a fresh perspective on graph representation methods.Through mathematical manipulations, the approach of this…
Suppose we have k matrices of size n by n. We are given an oracle that knows all the entries of k matrices, that is, we can query the oracle an (i,j) entry of the l-th matrix. The goal is to test if each pair of k matrices commute with each…
We present classical sublinear-time algorithms for solving low-rank linear systems of equations. Our algorithms are inspired by the HHL quantum algorithm for solving linear systems and the recent breakthrough by Tang of dequantizing the…
Very much as its classical counterpart, quantum cellular automata are expected to be a great tool for simulating complex quantum systems. Here we introduce a partitioned model of quantum cellular automata and show how it can simulate, with…
In this paper, we introduce a discrete quantum walk model called bipartite walks. Bipartite walks include many known discrete quantum walk models, like arc-reversal walks, vertex-face walks. For the transition matrix of a quantum walk,…
Many promising quantum applications depend on the efficient quantum simulation of an exponentially large sparse Hamiltonian, a task known as sparse Hamiltonian simulation, which is fundamentally important in quantum computation. Although…
With photonics, the quantum computational advantage has been demonstrated on the task of boson sampling. Next, developing quantum-enhanced approaches for practical problems becomes one of the top priorities for photonic systems. Quantum…
We analyze the performance of the Harrow-Hassidim-Lloyd algorithm (HHL algorithm) for solving linear problems and of a variant of this algorithm (HHL variant) commonly encountered in literature. This variant relieves the algorithm of…
Integer linear programming (ILP) remains computationally challenging due to its NP-complete nature despite its central role in scheduling, logistics, and design optimization. We introduce a fully quantum Metropolis-Hastings algorithm for…
The efficient resolution of optimization problems is one of the key issues in today's industry. This task relies mainly on classical algorithms that present scalability problems and processing limitations. Quantum computing has emerged to…
Random walk algorithms are crucial for sampling and approximation problems in statistical physics and theoretical computer science. The mixing property is necessary for Markov chains to approach stationary distributions and is facilitated…