Related papers: Quantum speedup for combinatorial optimization wit…
Adiabatic quantum optimization offers a new method for solving hard optimization problems. In this paper we calculate median adiabatic times (in seconds) determined by the minimum gap during the adiabatic quantum optimization for an NP-hard…
While it seems possible that quantum computers may allow for algorithms offering a computational speed-up over classical algorithms for some problems, the issue is poorly understood. We explore this computational speed-up by investigating…
We propose a quantum Monte Carlo (QMC) algorithm for non-equilibrium dynamics in a system with a parameter varying as a function of time. The method is based on successive applications of an evolving Hamiltonian to an initial state and…
One of the major application areas of interest for both near-term and fault-tolerant quantum computers is the optimization of classical objective functions. In this work, we develop intuitive constructions for a large class of these…
The quantum adiabatic algorithm is a Hamiltonian based quantum algorithm designed to find the minimum of a classical cost function whose domain has size N. We show that poor choices for the Hamiltonian can guarantee that the algorithm will…
The quantum approximate optimisation algorithm was proposed as a heuristic method for solving combinatorial optimisation problems on near-term quantum computers and may be among the first algorithms to perform useful computations in the…
We introduce the idea of using adiabatic rotation to generate superpositions of a large class of quantum states. For quantum computing this is an interesting alternative to the well-studied "straight line" adiabatic evolution. In ways that…
We develop a quantum-classical hybrid algorithm for function optimization that is particularly useful in the training of neural networks since it makes use of particular aspects of high-dimensional energy landscapes. Due to a recent…
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…
We present a new approach to study the thermodynamic properties of $d$-dimensional classical systems by reducing the problem to the computation of ground state properties of a $d$-dimensional quantum model. This classical-to-quantum mapping…
We analyze the complexity of the quantum optimization algorithm based on adiabatic evolution for the set partition problem. We introduce a cost function defined on a logarithmic scale of the partition residues so that the total number of…
We propose a hybrid classical-quantum digitized-counterdiabatic algorithm to tackle the protein folding problem on a tetrahedral lattice. Digitized-counterdiabatic quantum computing is a paradigm developed to compress quantum algorithms via…
To date, research in quantum computation promises potential for outperforming classical heuristics in combinatorial optimization. However, when aiming at provable optimality, one has to rely on classical exact methods like integer…
Quantum computers may achieve speedups over their classical counterparts for solving linear algebra problems. However, in some cases -- such as for low-rank matrices -- dequantized algorithms demonstrate that there cannot be an exponential…
Topological invariants of a dataset, such as the number of holes that survive from one length scale to another (persistent Betti numbers) can be used to analyze and classify data in machine learning applications. We present an improved…
The maximal clique problem, to find the maximally sized clique in a given graph, is classically an NP-complete computational problem, which has potential applications ranging from electrical engineering, computational chemistry,…
The advent of quantum algorithms has initiated a discourse on the potential for quantum speedups for optimization problems. However, several factors still hinder a practical realization of the potential benefits. These include the lack of…
We present a quantum algorithm for approximating maximum independent sets of a graph based on quantum non-Abelian adiabatic mixing in the sub-Hilbert space of degenerate ground states, which generates quantum annealing in a secondary…
Emerging quantum processors provide an opportunity to explore new approaches for solving traditional problems in the post Moore's law supercomputing era. However, the limited number of qubits makes it infeasible to tackle massive real-world…
Quantum annealing (QA) has the potential to significantly improve solution quality and reduce time complexity in solving combinatorial optimization problems compared to classical optimization methods. However, due to the limited number of…