Related papers: Optimization by Decoded Quantum Interferometry
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…
Optimization problems in finance, physics and computer science are typically very hard to tackle in classical computing and quantum computing could help speed up computations and provide efficient methods for tackling large problems.…
Quantum computers can execute algorithms that dramatically outperform classical computation. As the best-known example, Shor discovered an efficient quantum algorithm for factoring integers, whereas factoring appears to be difficult for…
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,…
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…
Quantum computing has attracted significant interest in the optimization community because it potentially can solve classes of optimization problems faster than conventional supercomputers. Several researchers proposed quantum computing…
In the era of quantum computing, the emergence of quantum computers and subsequent advancements have led to the development of various quantum algorithms capable of solving linear equations and eigenvalues, surpassing the pace of classical…
We propose a quantum-classical hybrid method for solving large-scale mixed-integer quadratic problems (MIQP). Although extended Benders decomposition is effective for MIQP, its master problem which handles the integer and quadratic…
Quadratic Unconstrained Binary Optimization (QUBO) is a broad class of optimization problems with many practical applications. To solve its hard instances in an exact way, known classical algorithms require exponential time and several…
In this paper, we give quantum algorithms for two fundamental computation problems: solving polynomial systems over finite fields and optimization where the arguments of the objective function and constraints take values from a finite field…
In this paper, we introduce a quantum-enhanced algorithm for simulation-based optimization. Simulation-based optimization seeks to optimize an objective function that is computationally expensive to evaluate exactly, and thus, is…
We consider the problem of optimally decoding a quantum error correction code -- that is to find the optimal recovery procedure given the outcomes of partial "check" measurements on the system. In general, this problem is NP-hard. However,…
Quantum algorithms are getting extremely popular due to their potential to significantly outperform classical algorithms. Yet, applying quantum algorithms to optimization problems meets challenges related to the efficiency of quantum…
Quantum computers can execute algorithms that sometimes dramatically outperform classical computation. Undoubtedly the best-known example of this is Shor's discovery of an efficient quantum algorithm for factoring integers, whereas the same…
This thesis focuses on the intersection of mathematical and computational optimization and quantum information. Main contributions are open-source software code: A hybrid approach mixing "traditional" nonconvex and convex methods can make…
Quantum optimization has emerged as a promising frontier of quantum computing, providing novel numerical approaches to mathematical optimization problems. The main goal of this paper is to facilitate interdisciplinary research between the…
We describe a quantum algorithm based on an interior point method for solving a linear program with $n$ inequality constraints on $d$ variables. The algorithm explicitly returns a feasible solution that is $\varepsilon$-close to optimal,…
Quantum algorithms have the potential to provide exponential speedups over some of the best known classical algorithms. These speedups may enable quantum devices to solve currently intractable problems such as those in the fields of…
The Quantum Approximate Optimization Algorithm (QAOA) has shown promise in solving combinatorial optimization problems by leveraging quantum computational power. We propose a simple approach, the Two-Step QAOA, which aims to improve the…
Quadratically Constrained Quadratic Programs (QCQPs) are an important class of optimization problems with diverse real-world applications. In this work, we propose a variational quantum algorithm for general QCQPs. By encoding the variables…