Related papers: Hardness-dependent quantum adiabatic schedules for…
Analog quantum algorithms are formulated in terms of Hamiltonians rather than unitary gates and include quantum adiabatic computing, quantum annealing, and the quantum approximate optimization algorithm (QAOA). These algorithms are…
NP-hard problems are not believed to be exactly solvable through general polynomial time algorithms. Hybrid quantum-classical algorithms to address such combinatorial problems have been of great interest in the past few years. Such…
The digital version of adiabatic quantum computing enhanced by counterdiabatic driving, known as digitized counterdiabatic quantum computing, has emerged as a paradigm that opens the door to fast and low-depth algorithms. In this work, we…
Quantum phase estimation (QPE) is a central algorithmic primitive that estimates eigenvalues of a Hamiltonian up to precision $\epsilon$ in Heisenberg-limited time $T=\Theta(1/\epsilon)$. Standard gate-based implementations of QPE require…
We propose and analyze the use of Bayesian optimization techniques to design quantum annealing schedules with minimal user and resource requirements. We showcase our scheme with results for two paradigmatic spin models. We find that…
We analyze the performance of adiabatic quantum computation (AQC) under the effect of decoherence. To this end, we introduce an inherently open-systems approach, based on a recent generalization of the adiabatic approximation. In contrast…
It is believed that the presence of anticrossings with exponentially small gaps between the lowest two energy levels of the system Hamiltonian, can render adiabatic quantum optimization inefficient. Here, we present a simple adiabatic…
Quantum annealing is a continuous-time heuristic quantum algorithm for solving or approximately solving classical optimization problems. The algorithm uses a schedule to interpolate between a driver Hamiltonian with an easy-to-prepare…
The Quantum Approximate Optimization Algorithm (QAOA) exhibits significant potential for tackling combinatorial optimization problems. Despite its promise for near-term quantum devices, a major challenge in applying QAOA lies in the cost of…
We outline an algorithm for the Quantum Counting problem using Adiabatic Quantum Computation (AQC). We show that using local adiabatic evolution, a process in which the adiabatic procedure is performed at a variable rate, the problem is…
We present quantum complexity lower and upper bounds for independent set problems in graphs. In particular, we give quantum algorithms for computing a maximal and a maximum independent set in a graph. We present applications of these…
Adiabatic Quantum Computing (AQC) is an attractive paradigm for solving hard integer polynomial optimization problems. Available hardware restricts the Hamiltonians to be of a structure that allows only pairwise interactions. This requires…
Exploiting the similarity between adiabatic quantum algorithms and quantum phase transitions, we argue that second-order transitions -- typically associated with broken or restored symmetries -- should be advantageous in comparison to…
With progress in quantum technology more sophisticated quantum annealing devices are becoming available. While they offer new possibilities for solving optimization problems, their true potential is still an open question. As the optimal…
This paper concerns quantum heuristics able to extend the domain of quantum computing, defining a promising way in the large number of well-known classical algorithms. Quantum approximate heuristics take advantage of alternation between a…
On neutral atom platforms, preparing specific quantum states is usually achieved by pulse shaping, i.e., by optimizing the time-dependence of the Hamiltonian related to the system. This process can be extremely costly, as it requires…
Adiabatic optimal control schemes are essential for advancing the practical implementation of quantum technologies. However, the vast array of possible adiabatic protocols, combined with their dependence on the particular quantum system and…
We introduce an approach for quantum computing in continuous time based on the Lewis-Riesenfeld dynamic invariants. This approach allows, under certain conditions, for the design of quantum algorithms running on a nonadiabatic regime. We…
In this paper we study the performance of the quantum adiabatic algorithm on random instances of two combinatorial optimization problems, 3-regular 3-XORSAT and 3-regular Max-Cut. The cost functions associated with these two clause-based…
Today, hardware constraints are an important limitation on quantum adiabatic optimization algorithms. Firstly, computational problems must be formulated as quadratic unconstrained binary optimization (QUBO) in the presence of noisy coupling…