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Quantum computers show potential for achieving computational advantage over classical computers, with many candidate applications in combinatorial optimisation. We present an application level benchmarking framework for near-term quantum…
We prove that quantum computation is polynomially equivalent to classical probabilistic computation with an oracle for estimating the value of simple sums, quadratically signed weight enumerators. The problem of estimating these sums can be…
We propose a novel method for reducing the number of variables in quadratic unconstrained binary optimization problems, using a quantum annealer (or any sampler) to fix the value of a large portion of the variables to values that have a…
Recent advances in quantum computing and the increasing availability of quantum hardware have substantially enhanced the practical relevance of quantum approaches to discrete optimization. Among these, the Quadratic Unconstrained Binary…
Quantum annealing offers a promising paradigm for solving NP-hard combinatorial optimization problems, but its practical application is severely hindered by two challenges: the complex, manual process of translating problem descriptions…
This paper describes an approximate method for global optimization of polynomial programming problems with bounded variables. The method uses a reformulation and linearization technique to transform the original polynomial optimization…
Constraints make hard optimization problems even harder to solve on quantum devices because they are implemented with large energy penalties and additional qubit overhead. The parity mapping, which has been introduced as an alternative to…
An effective formalism for quantum constrained systems is presented which allows manageable derivations of solutions and observables, including a treatment of physical reality conditions without requiring full knowledge of the physical…
Quantum algorithms have begun to surpass classical ones in several computation fields, yet practical application remains challenging due to hardware and software limitations. Here, we introduce a quantum algorithm that quadratically…
We present a hybrid classical-quantum framework based on the Frank-Wolfe algorithm, Q-FW, for solving quadratic, linearly-constrained, binary optimization problems on quantum annealers (QA). The computational premise of quantum computers…
In this paper, we solve a maximization problem where the objective function is quadratic and the constraints set is the reachable values set of a stable discrete-time affine system. This problem is equivalent to solve an infinite number of…
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…
The Quadratic Unconstrained Binary Optimization (QUBO) model has gained prominence in recent years with the discovery that it unifies a rich variety of combinatorial optimization problems. By its association with the Ising problem in…
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…
Quantum and quantum-inspired optimisation algorithms are designed to solve problems represented in binary, quadratic and unconstrained form. Combinatorial optimisation problems are therefore often formulated as Quadratic Unconstrained…
Quantum algorithms can be analyzed in a query model to compute Boolean functions where input is given in a black box and the aim is to compute function value for arbitrary input using as few queries as possible. We concentrate on quantum…
Streamlining constraints (or streamliners, for short) narrow the search space, enhancing the speed and feasibility of solving complex constraint satisfaction problems. Traditionally, streamliners were crafted manually or generated through…
Quantum computing offers significant potential for solving NP-hard combinatorial (optimization) problems that are beyond the reach of classical computers. One way to tap into this potential is by reformulating combinatorial problems as a…
Quantum optimization is the most mature quantum computing technology to date, providing a promising approach towards efficiently solving complex combinatorial problems. Methods such as adiabatic quantum computing (AQC) have been employed in…
This paper provides necessary and sufficient conditions for constructing a universal quantum computer over continuous variables. As an example, it is shown how a universal quantum computer for the amplitudes of the electromagnetic field…