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The LogQ algorithm encodes Quadratic Unconstrained Binary Optimization (QUBO) problems, which are often encountered in the industry (portfolio optimization, fleet optimization, charging stations, etc.). It was developed within the framework…
The paradigm behind digital quantum computing inherits the idea of using binary information processing. Nature in fact gives much more rich structures of physical objects that can be used for encoding information, which is especially…
Solving combinatorial optimization problems using variational quantum algorithms (VQAs) has emerged as a promising research direction. Since the introduction of the Quantum Approximate Optimization Algorithm (QAOA), numerous variants have…
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…
It was pointed out in [JSW+25] that widely-studied optimization problems such as D-regular max-k-XORSAT can be reduced to decoding of LDPC codes, using quantum algorithms related to Regev's reduction. LDPC codes have very good decoders,…
We introduce a method for solving combinatorial optimization problems on digital quantum computers, where we incorporate auxiliary counterdiabatic (CD) terms into the adiabatic Hamiltonian, while integrating bias terms derived from an…
The variational quantum eigensolver (VQE) is an algorithm for finding the ground states of a given Hamiltonian. Its application to binary-formulated combinatorial optimization (CO) has been widely studied in recent years. However, typical…
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…
Encoding combinatorial optimization problems into physically meaningful Hamiltonians with tractable energy landscapes forms the foundation of quantum optimization. Numerous works have studied such efficient encodings for the class of…
Solving linear ordinary differential equations (ODE) is one of the most promising applications for quantum computers to demonstrate exponential advantages. The challenge of designing a quantum ODE algorithm is how to embed non-unitary…
Variational Quantum Algorithm (VQA) is a hybrid algorithm for noisy quantum devices. However, statistical fluctuations and physical noise degrade the solution quality, so it is difficult to maintain applicability for large-scale problems.…
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…
Qubit-based variational quantum algorithms have undergone rapid development in recent years but still face several challenges. In this context, we propose a symmetry-enhanced digitized counterdiabatic quantum algorithm utilizing qudits…
MaxCut is a canonical NP-hard combinatorial optimization problem in graph theory with broad applications ranging from physics to bioinformatics. Although variational quantum algorithms offer promising new approaches that may eventually…
In this work, we present a Gauss-Newton based quantum algorithm (GNQA) for combinatorial optimization problems that, under optimal conditions, rapidly converges towards one of the optimal solutions without being trapped in local minima or…
A specialized algorithm for quadratic optimization (QO, or, formerly, QP) with disjoint linear constraints is presented. In the considered class of problems, a subset of variables are subject to linear equality constraints, while variables…
Quantum optimization holds promise for addressing classically intractable combinatorial problems, yet a standardized framework for benchmarking its performance, particularly in terms of solution quality, computational speed, and scalability…
Quantum approximate optimization algorithm (QAOA) has shown promise in solving combinatorial optimization problems by providing quantum speedup on near-term gate-based quantum computing systems. However, QAOA faces challenges for…
The discretized Poisson equation matrix (DPEM) in 1D has been shown to require an exponentially large number of terms when decomposed in the Pauli basis when solving numerical linear algebra problems on a quantum computer. Additionally,…
The growing demand for solving large-scale, data-intensive linear and conic optimization problems, particularly in applications such as artificial intelligence and machine learning, has highlighted the limitations of classical interior…