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We present a sufficient condition for the stability property of extremal graph problems that can be solved via Zykov's symmetrisation. Our criterion is stated in terms of an analytic limit version of the problem. We show that, for example,…
We propose a novel variational method for solving the sub-graph isomorphism problem on a gate-based quantum computer. The method relies (1) on a new representation of the adjacency matrices of the underlying graphs, which requires a number…
Challenging combinatorial optimization problems are ubiquitous in science and engineering. Several quantum methods for optimization have recently been developed, in different settings including both exact and approximate solvers. Addressing…
We give the first polynomial-time algorithms on graphs of bounded maximum induced matching width (mim-width) for problems that are not locally checkable. In particular, we give $n^{\mathcal{O}(w)}$-time algorithms on graphs of mim-width at…
Training machine learning models on classical computers is usually a time and compute intensive process. With Moore's law coming to an end and ever increasing demand for large-scale data analysis using machine learning, we must leverage…
We consider quantum algorithms for the unique sink orientation problem on cubes. This problem is widely considered to be of intermediate computational complexity. This is because there no known polynomial algorithm (classical or quantum)…
The Quantum Approximate Optimization Algorithm (QAOA) requires considered optimization problems to be translated into a compatible format. A popular transformation step in this pipeline involves the quadratization of higher-order binary…
Quantum computing (QC) is expected to solve incredibly difficult problems, including finding optimal solutions to combinatorial optimization problems. However, to date, QC alone is still far to demonstrate this capability except on…
Finding cliques in a graph has several applications for its pattern matching ability. $k$-clique problem, a special case of clique problem, determines whether an arbitrary graph contains a clique of size $k$, has already been addressed in…
In order to achieve speedup over conventional classical computing for finding solution of computationally hard problems, quantum computing was introduced. Quantum algorithms can be simulated in a pseudo quantum environment, but…
The prospect of quantum solutions for complicated optimization problems is contingent on mapping the original problem onto a tractable quantum energy landscape, e.g. an Ising-type Hamiltonian. Subsequently, techniques like adiabatic…
With the development of quantum computing, the use of quantum algorithms to solve combinatorial optimization problems on quantum computers has become a major research focus. The Quadratic Unconstrained Binary Optimization (QUBO) model…
Optimizing objective functions stands to benefit significantly from leveraging quantum computers, promising enhanced solution quality across various application domains in the future. However, harnessing the potential of quantum solvers…
We use Quantum Imaginary Time Evolution (QITE) to solve polynomial unconstrained binary optimization (PUBO) problems. We show that a linear Ansatz yields good results for a wide range of PUBO problems, often outperforming standard classical…
The Operational Fixed Interval Scheduling Problem aims to find an assignment of jobs to machines that maximizes the total weight of the completed jobs. We introduce a new variant of the problem where we consider the additional goal of…
We present a novel quantum optimization-based route compression technique that significantly reduces storage requirements compared to conventional methods. Route optimization systems face critical challenges in efficiently storing selected…
We study a variant of the subgraph isomorphism problem that is of high interest to the quantum computing community. Our results give an algorithm to perform pattern matching in quantum circuits for many patterns simultaneously,…
While current network intrusion detection systems achieve satisfactory accuracy, they often lack explainability. Subgroup Discovery (SD) addresses this by building interpretable rules that characterize feature interactions associated with…
Simon's problem admits an exponential quantum speedup, but current quantum devices support only qubits. This work introduces a general construction for simulating qudit versions of Simon's algorithm on qubit hardware by defining virtual…
The Portfolio Optimization task has long been studied in the Financial Services literature as a procedure to identify the basket of assets that satisfy desired conditions on the expected return and the associated risk. A well-known approach…