aqora

Learning adiabatic quantum algorithms for solving optimization problems

Davide Pastorello, Enrico Blanzieri

An adiabatic quantum algorithm is essentially given by three elements: An initial Hamiltonian with known ground state, a problem Hamiltonian whose ground state corresponds to the solution of the given problem and an evolution schedule such that the adiabatic condition is satisfied. A correct choice of these elements is crucial for an efficient adiabatic quantum computation. In this paper we propose a hybrid quantum-classical algorithm to solve optimization problems with an adiabatic machine assuming restrictions on the class of available problem Hamiltonians. The scheme is based on repeated calls to the quantum machine into a classical iterative structure. In particular we present a technique to learn the encoding of a given optimization problem into a problem Hamiltonian and we prove the convergence of the algorithm. Moreover the output of the proposed algorithm can be used to learn efficient adiabatic algorithms from examples.An adiabatic quantum algorithm is essentially given by three elements: An initial Hamiltonian with known ground state, a problem Hamiltonian whose ground state corresponds to the solution of the given problem and an evolution schedule such that the adiabatic condition is satisfied. A correct choice of these elements is crucial for an efficient adiabatic quantum computation. In this paper we propose a hybrid quantum-classical algorithm to solve optimization problems with an adiabatic machine assuming restrictions on the class of available problem Hamiltonians. The scheme is based on repeated calls to the quantum machine into a classical iterative structure. In particular we present a technique to learn the encoding of a given optimization problem into a problem Hamiltonian and we prove the convergence of the algorithm. Moreover the output of the proposed algorithm can be used to learn efficient adiabatic algorithms from examples.

arXiv:1909.06870Sep 15, 20191 citation

Adiabatic Training for Variational Quantum Algorithms

Ernesto Acosta, Carlos Cano, Guillermo Botella +1 more

arXiv:2410.18618Lecture notes in computer scienceJan 1, 20251 citation

Optimizing adiabatic quantum pathways via a learning algorithm

Xiaodong Yang, Ran Liu, Jun Li +1 more

Designing proper time-dependent control fields for slowly varying the system to the ground state that encodes the problem solution is crucial for adiabatic quantum computation. However, inevitable perturbations in real applications demand us to accelerate the evolution so that the adiabatic errors can be prevented from accumulation. Here, by treating this trade-off task as a multiobjective optimization problem, we propose a gradient-free learning algorithm with pulse smoothing technique to search optimal adiabatic quantum pathways and apply it to the Landau-Zener Hamiltonian and Grover search Hamiltonian. Numerical comparisons with a linear schedule, local adiabatic theorem induced schedule, and gradient-based algorithm searched schedule reveal that the proposed method can achieve significant performance improvements in terms of the adiabatic time and the instantaneous ground-state population maintenance. The proposed method can be used to solve more complex and real adiabatic quantum computation problems.Designing proper time-dependent control fields for slowly varying the system to the ground state that encodes the problem solution is crucial for adiabatic quantum computation. However, inevitable perturbations in real applications demand us to accelerate the evolution so that the adiabatic errors can be prevented from accumulation. Here, by treating this trade-off task as a multiobjective optimization problem, we propose a gradient-free learning algorithm with pulse smoothing technique to search optimal adiabatic quantum pathways and apply it to the Landau-Zener Hamiltonian and Grover search Hamiltonian. Numerical comparisons with a linear schedule, local adiabatic theorem induced schedule, and gradient-based algorithm searched schedule reveal that the proposed method can achieve significant performance improvements in terms of the adiabatic time and the instantaneous ground-state population maintenance. The proposed method can be used to solve more complex and real adiabatic quantum computation problems.

arXiv:2006.15300Physical Review AJul 16, 202010 citations

Quantum Algorithms for Optimization Problems

Dilnoz Muhamediyeva, Rustam Raximov, Shavkat Urokov

Lecture notes in computer scienceJul 29, 20250 citations

Learning quantum operator by quantum adiabatic computation

Ding Liu, Minghu Jiang

In this article, we introduce the quantum adiabatic computation to the research field of quantum operator learning. Compared with existing conventional optimization approaches, the adiabatic algorithm ensures to reach the global optimal solution, and thus avoids the local minimum problem. The performance of the experiments on two tasks indicates the feasibility and potentiality of this novel method. We firmly believe that the quantum adiabatic computation can be applied to other tasks of machine learning.In this article, we introduce the quantum adiabatic computation to the research field of quantum operator learning. Compared with existing conventional optimization approaches, the adiabatic algorithm ensures to reach the global optimal solution, and thus avoids the local minimum problem. The performance of the experiments on two tasks indicates the feasibility and potentiality of this novel method. We firmly believe that the quantum adiabatic computation can be applied to other tasks of machine learning.

Oct 1, 20141 citation

Speedup in adiabatic evolution based quantum algorithms

Jie Sun, Songfeng Lu, Fang Liu

Science China Physics Mechanics and AstronomyJul 19, 201221 citations

Learning adiabatic quantum algorithms over optimization problems

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