Related papers: Quantum Algorithm of the GLMY Homology on Digraphs
One of the distinct features of quantum mechanics is that the probability amplitude can have both positive and negative signs, which has no classical counterpart as the classical probability must be positive. Consequently, one possible way…
Quantum search algorithms offer a remarkable advantage of quadratic reduction in query complexity using quantum superposition principle. However, how an actual architecture may access and handle the database in a quantum superposed state…
Topological data analysis (TDA) is an emergent field of data analysis. The critical step of TDA is computing the persistent Betti numbers. Existing classical algorithms for TDA are limited if we want to learn from high-dimensional…
Recent results by Harrow et. al. and by Ta-Shma, suggest that quantum computers may have an exponential advantage in solving a wealth of linear algebraic problems, over classical algorithms. Building on the quantum intuition of these…
In a topological quantum computer, braids of non-Abelian anyons in a (2+1)-dimensional space-time form quantum gates, whose fault tolerance relies on the topological, rather than geometric, properties of the braids. Here we propose to…
Too often, quantum computer scientists seek to create new algorithms entirely fresh from new cloth when there are extensive and optimized classical algorithms that can be generalized wholesale. At the same time, one may seek to maintain…
We present a novel benchmark application of a quantum algorithm to Feynman loop integrals. The two on-shell states of a Feynman propagator are identified with the two states of a qubit and a quantum algorithm is used to unfold the causal…
Quantum simulation has emerged as a key application of quantum computing, with significant progress made in algorithms for simulating both closed and open quantum systems. The simulation of open quantum systems, particularly those governed…
Topological quantum error-correcting codes are defined by geometrically local checks on a two-dimensional lattice of quantum bits (qubits), making them particularly well suited for fault-tolerant quantum information processing. Here, we…
Quantum annealing is a computational approach designed to leverage quantum fluctuations for solving large-scale classical optimization problems. Although incorporating standard transverse field (TF) terms in the annealing process can help…
Variational quantum algorithms (VQAs) have the potential of utilizing near-term quantum machines to gain certain computational advantages over classical methods. Nevertheless, modern VQAs suffer from cumbersome computational overhead,…
Topological Data Analysis (TDA) offers a suite of computational tools that provide quantified shape features in high dimensional data that can be used by modern statistical and predictive machine learning (ML) models. In particular,…
Matrix representations of quantum operators are computationally complete but often obscure the structural topology of information flow within a quantum circuit \cite{nielsen2000}. In this paper, we introduce a generalized graph-theoretic…
Quantum computation is a promising emerging technology, and by utilizing the principles of quantum mechanics, it is expected to achieve faster computations than classical computers for specific problems. There are two distinct architectures…
Quantum computers are designed to outperform standard computers by running quantum algorithms. Areas in which quantum algorithms can be applied include cryptography, search and optimisation, simulation of quantum systems, and solving large…
We discuss classical and quantum algorithms for solvability testing and finding integer solutions x,y of equations of the form af^x + bg^y = c over finite fields GF(q). A quantum algorithm with time complexity q^(3/8) (log q)^O(1) is…
Quantum computing is a promising paradigm based on quantum theory for performing fast computations. Quantum algorithms are expected to surpass their classical counterparts in terms of computational complexity for certain tasks, including…
Quantum computing has been a prominent research area for decades, inspiring transformative fields such as quantum simulation, quantum teleportation, and quantum machine learning (QML), which are undergoing rapid development. Within QML,…
We consider classical and quantum algorithms which have a duality property: roughly, either the algorithm provides some nontrivial improvement over random or there exist many solutions which are significantly worse than random. This enables…
This is continuation of the approach to performing quantum algorithms using geometric structures which was presented by Aerts and Czachor. We solve the Simon's problem which, next to the Shor's alghorithm, is a representative of a quantum…