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Although quantum computing holds promise for solving Combinatorial Optimization Problems (COPs), the limited qubit capacity of NISQ hardware makes large-scale instances intractable. Conventional methods attempt to bridge this gap through…
Quantum Max Cut (QMC) problem for systems of qubits is an example of a 2-local Hamiltonian problem, and a prominent paradigm in computational complexity theory. This paper investigates the algebraic structure of a higher-dimensional analog…
Distributed functional scalar quantization (DFSQ) theory provides optimality conditions and predicts performance of data acquisition systems in which a computation on acquired data is desired. We address two limitations of previous works:…
MaxCut is a key NP-Hard combinatorial optimization graph problem with extensive theoretical and industrial applications, including the Ising model and chip design. While quantum computing offers new solutions for such combinatorial…
The characterization of quantum dynamics is a fundamental and central task in quantum mechanics. This task is typically addressed by quantum process tomography (QPT). Here we present an alternative "direct characterization of quantum…
We introduce a quantum algorithm that produces approximate solutions for combinatorial optimization problems. The algorithm depends on a positive integer p and the quality of the approximation improves as p is increased. The quantum circuit…
Consider the following distributed optimization scenario. A worker has access to training data that it uses to compute the gradients while a server decides when to stop iterative computation based on its target accuracy or delay…
Variational quantum algorithms, such as the Recursive Quantum Approximate Optimization Algorithm (RQAOA), have become increasingly popular, offering promising avenues for employing Noisy Intermediate-Scale Quantum devices to address…
We consider a version of the nearest-codeword problem on finite fields $\mathbb{F}_q$ using the Manhattan distance, an analog of the Hamming metric for non-binary alphabets. Similarly to other lattice related problems, this problem is…
The weighted MAX k-CUT problem consists of finding a k-partition of a given weighted undirected graph G(V,E) such that the sum of the weights of the crossing edges is maximized. The problem is of particular interest as it has a multitude of…
In recent years, parameterized quantum circuits have become a major tool to design quantum algorithms for optimization problems. The challenge in fully taking advantage of a given family of parameterized circuits lies in finding a good set…
The relative power of quantum algorithms, using an adaptive access to quantum devices, versus classical post-processing methods that rely only on an initial quantum data set, remains the subject of active debate. Here, we present evidence…
We discuss the advantages of using the approximate quantum Fourier transform (AQFT) in algorithms which involve periodicity estimations. We analyse quantum networks performing AQFT in the presence of decoherence and show that extensive…
Quantum computing is emerging as a new computing resource that could be superior to conventional computing for certain classes of optimization problems. However, in principle, most existing approaches to quantum optimization are intended to…
Quantum kernel methods (QKMs) have emerged as a prominent framework for supervised quantum machine learning. Unlike variational quantum algorithms, which rely on gradient-based optimisation and may suffer from issues such as barren…
Quantum Approximate Optimization Algorithm (QAOA) is a quantum-classical hybrid algorithm proposed with the goal of approximately solving combinatorial optimization problems such as the MAX-CUT problem. It has been considered a potential…
The LogQ algorithm encodes Quadratic Unconstrained Binary Optimization (QUBO) problems with exponentially fewer qubits than the Quantum Approximate Optimization Algorithm (QAOA). The advantages of conventional LogQ are accompanied by a…
The union-find decoder is a leading algorithmic approach to the correction of quantum errors on the surface code, achieving code thresholds comparable to minimum-weight perfect matching (MWPM) with amortised computational time scaling…
The current noisy intermediate-scale quantum (NISQ) era is characterized by substantial errors and noise, which limit the practical feasibility of deep, many-qubit circuits. To address these constraints, quantum circuit cutting has emerged…
The Noisy Intermediate-Scale Quantum (NISQ) era of technology in which we currently find ourselves is defined by non-universality, susceptibility to errors and noise, and a search for useful applications. While demonstrations of practical…