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Given the fundamental importance of combinatorial optimization across many diverse application domains, there has been widespread interest in the development of unconventional physical computing architectures that can deliver better…
We describe an efficient approximation algorithm for evaluating the ground-state energy of the classical Ising Hamiltonian with linear terms on an arbitrary planar graph. The running time of the algorithm grows linearly with the number of…
Automated per-instance algorithm selection and configuration have shown promising performances for a number of classic optimization problems, including satisfiability, AI planning, and TSP. The techniques often rely on a set of features…
Variational algorithms are promising candidates to be implemented on near-term quantum computers. The variational quantum eigensolver (VQE) is a prominent example, where a parametrized trial state of the quantum mechanical wave function is…
We propose a hybrid quantum-classical algorithm to compute approximate solutions of binary combinatorial problems. We employ a shallow-depth quantum circuit to implement a unitary and Hermitian operator that block-encodes the weighted…
Preparing the ground state of a given Hamiltonian and estimating its ground energy are important but computationally hard tasks. However, given some additional information, these problems can be solved efficiently on a quantum computer. We…
The performance of the quantum approximate optimization algorithm is evaluated by using three different measures: the probability of finding the ground state, the energy expectation value, and a ratio closely related to the approximation…
State-of-the-art quantum algorithms routinely tune dynamically parametrized cost functionals for combinatorics, machine learning, equation-solving, or energy minimization. However, large search complexity often demands many (noisy) quantum…
We describe a reverse integration approach for the exploration of low-dimensional effective potential landscapes. Coarse reverse integration initialized on a ring of coarse states enables efficient "navigation" on the landscape terrain:…
In all but the most trivial optimization problems, the structure of the solutions exhibit complex interdependencies between the input parameters. Decades of research with stochastic search techniques has shown the benefit of explicitly…
For a wide class of Hamiltonians, a novel method to obtain lower and upper bounds for the lowest energy is presented. Unlike perturbative or variational techniques, this method does not involve the computation of any integral (a…
The nonlinear space-fractional problems often allow multiple stationary solutions, which can be much more complicated than the corresponding integer-order problems. In this paper, we systematically compute the solution landscapes of…
Quantum annealing tends to be more difficult as the energy landscape of the problem becomes complicated with many local minima. We have found a transformation for changing the energy landscape that swaps the eigenvalues and paired states…
The prevalence of variational methods in near-term quantum computing makes optimizer choice critical, yet selection is frequently intuition-based. We therefore present a systematic benchmark of eight classical optimization algorithms for…
The Quadratic Unconstrained Binary Optimization (QUBO) problems are NP hard; thus, so far, there are no algorithms to solve them efficiently. There are exact methods like the Branch-and-Bound algorithm for smaller problems, and for larger…
Optimizing the topology of networks is an important challenge across engineering disciplines. In energy systems, network reconfiguration can substantially reduce losses and costs and thus support the energy transition. Unfortunately, many…
The Quantum Approximate Optimisation Algorithm (QAOA) is a hybrid quantum-classical algorithm for solving combinatorial optimisation problems. QAOA encodes solutions into the ground state of a Hamiltonian, approximated by a $p$-level…
We present a classical algorithm to find approximate solutions to instances of quadratic unconstrained binary optimisation. The algorithm can be seen as an analogue of quantum annealing under the restriction of a product state space, where…
When tackling binary optimization problems using quantum algorithms, the conventional Ising representation and Quantum Approximate Optimization Algorithm (QAOA) encounter difficulties in efficiently handling errors for large-scale problems…
We investigate the minimization of Ising Hamiltonians, comparing the performance of gain-based computing paradigms based on the dynamics of semi-classical soft-spin models with quantum annealing. We systematically analyze how the energy…