Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2006.15300 · Physical Review A

Optimizing adiabatic quantum pathways via a learning algorithm

Xiaodong Yang, Ran Liu, Jun Li, Xinhua Peng

Published Jul 16, 2020• 10 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.102.012614

Related papers

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.

arXiv:1909.06870•Sep 15, 2019•1 citation

Quantum adiabatic algorithm design using reinforcement learning

Jian Hui Lin, Zhong Yuan Lai, Xiaopeng Li

Quantum algorithm design plays a crucial role in exploiting the computational advantage of quantum devices. Here we develop a deep-reinforcement-learning based approach for quantum adiabatic algorithm design. Our approach is generically applicable to a class of problems with solution hard-to-find but easy-to-verify, e.g., searching and NP-complete problems. We benchmark this approach in Grover-search and 3-SAT problems, and find that the adiabatic algorithm obtained by our RL approach leads to significant improvement in the resultant success probability. In application to Grover search, our RL design automatically produces an adiabatic quantum algorithm that has the quadratic speedup. We find for all our studied cases that quantitatively the RL-designed algorithm has a better performance compared to the analytically constructed nonlinear Hamiltonian path when the encoding Hamiltonian is solvable, and that this RL-design approach remains applicable even when the nonlinear Hamiltonian path is not analytically available. In 3-SAT we find RL design has fascinating transferability---the adiabatic algorithm obtained by training on a specific choice of clause number leads to better performance consistently over the linear algorithm on different clause numbers. These findings suggest the applicability of reinforcement learning for automated quantum adiabatic algorithm design. Further considering the established complexity equivalence of circuit and adiabatic quantum algorithms, we expect the RL-designed adiabatic algorithm to inspire novel circuit algorithms as well. Our approach is potentially applicable to different quantum hardware from trapped ions and optical lattices to superconducting-qubit devices.

arXiv:1812.10797•Physical Review A•May 18, 2020•39 citations

Using Optimal Control Theory to Improve Adiabatic Quantum Trajectories.

Constantin Brif

Motivation• In adiabatic quantum computation (AQC), the system is kept in the instantaneous ground state |φ 0 (t) of a slowly varying Hamiltonian H(t), which provides inherent protection against dephasing and relaxation in the energy eigenstate basis.• However, this protection does not guarantee full fault tolerance, since there still exist some types of noise, which can drive undesirable transitions out of the ground state.• Therefore, it would be desirable to try decreasing the accumulation of errors by performing a computation in a shorter time.However, how to reconcile faster evolution with the requirement of adiabaticity?• Our approach: (1) consider Hamiltonians containing multiple control functions and (2) use quantum optimal control theory (QOCT) to find control sets which achieve the target state with a high fidelity while simultaneously maximizing the degree of adiabaticity.• Exploring properties of optimal adiabatic trajectories in few-qubit model systems elucidates the dynamic mechanisms which suppress unwanted excitations from the ground state.

•Feb 28, 2019•0 citations

Exploring adiabatic quantum trajectories via optimal control

Constantin Brif, Matthew D Grace, Mohan Sarovar +1 more

Adiabatic quantum computation employs a slow change of a time-dependent control function (or functions) to interpolate between an initial and final Hamiltonian, which helps to keep the system in the instantaneous ground state. When the evolution time is finite, the degree of adiabaticity (quantified in this work as the average ground-state population during evolution) depends on the particulars of a dynamic trajectory associated with a given set of control functions. We use quantum optimal control theory with a composite objective functional to numerically search for controls that achieve the target final state with a high fidelity while simultaneously maximizing the degree of adiabaticity. Exploring the properties of optimal adiabatic trajectories in model systems elucidates the dynamic mechanisms that suppress unwanted excitations from the ground state. Specifically, we discover that the use of multiple control functions makes it possible to access a rich set of dynamic trajectories, some of which attain a significantly improved performance (in terms of both fidelity and adiabaticity) through the increase of the energy gap during most of the evolution time.

arXiv:1310.3443•New Journal of Physics•Jun 24, 2014•35 citations

Pulse optimization in adiabatic quantum computation and control

Daniel Turyansky, Yehonatan Zolti, Y. Cohen +1 more

We present a robust pulse optimization method for adiabatic population transfer and adiabatic quantum computation. The approach relies on identifying control pulses that keep the evolving quantum system close to its instantaneous ground state. By combining advanced gradient-free optimization tools with specialized cost functions for adiabatic control, it achieves both efficiency and robustness. To demonstrate its generality, we apply the method to three examples involving both atomic and superconducting qubits. We test different optimization cost functions and discretization bases, showing that the approach outperforms ensemble optimization. Finally, to verify its performance on real quantum hardware, we implement digitized adiabatic qubit control using the optimized pulses on the IBM quantum cloud.

arXiv:2507.09770•Physical Review Research•Feb 2, 2026•0 citations

Exploring adiabatic quantum trajectories via optimal control

Constantin Brif, Matthew Grace, Mohan Sarovar +1 more

Abstract. Adiabatic quantum computation employs a slow change of a time-dependent control function (or functions) to interpolate between an initial and final Hamiltonian, which helps to keep the system in the instantaneous ground state. When the evolution time is finite, the degree of adiabaticity (quantified in this work as the average ground-state population during evolution) depends on the particulars of a dynamic trajectory associated with a given set of control functions. We use quantum optimal control theory with a composite objective functional to numerically search for controls that achieve the target final state with a high fidelity while simultaneously maximizing the degree of adiabaticity. Exploring properties of optimal adiabatic trajectories in model systems elucidates the dynamic mechanisms that suppress unwanted excitations from the ground state. Specifically, we discover that the use of multiple control functions makes it possible to access a rich set of dynamic trajectories, some of which attain a significantly improved performance (in terms of both fidelity and adiabaticity) through the increase of the energy gap during most of the evolution time. Submitted to: New J. Phys. † Author to whom any correspondence should be addressed. ar

•Aug 14, 2016•16 citations
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.
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.
Quantum algorithm design plays a crucial role in exploiting the computational advantage of quantum devices. Here we develop a deep-reinforcement-learning based approach for quantum adiabatic algorithm design. Our approach is generically applicable to a class of problems with solution hard-to-find but easy-to-verify, e.g., searching and NP-complete problems. We benchmark this approach in Grover-search and 3-SAT problems, and find that the adiabatic algorithm obtained by our RL approach leads to significant improvement in the resultant success probability. In application to Grover search, our RL design automatically produces an adiabatic quantum algorithm that has the quadratic speedup. We find for all our studied cases that quantitatively the RL-designed algorithm has a better performance compared to the analytically constructed nonlinear Hamiltonian path when the encoding Hamiltonian is solvable, and that this RL-design approach remains applicable even when the nonlinear Hamiltonian path is not analytically available. In 3-SAT we find RL design has fascinating transferability---the adiabatic algorithm obtained by training on a specific choice of clause number leads to better performance consistently over the linear algorithm on different clause numbers. These findings suggest the applicability of reinforcement learning for automated quantum adiabatic algorithm design. Further considering the established complexity equivalence of circuit and adiabatic quantum algorithms, we expect the RL-designed adiabatic algorithm to inspire novel circuit algorithms as well. Our approach is potentially applicable to different quantum hardware from trapped ions and optical lattices to superconducting-qubit devices.
Motivation• In adiabatic quantum computation (AQC), the system is kept in the instantaneous ground state |φ 0 (t) of a slowly varying Hamiltonian H(t), which provides inherent protection against dephasing and relaxation in the energy eigenstate basis.• However, this protection does not guarantee full fault tolerance, since there still exist some types of noise, which can drive undesirable transitions out of the ground state.• Therefore, it would be desirable to try decreasing the accumulation of errors by performing a computation in a shorter time.However, how to reconcile faster evolution with the requirement of adiabaticity?• Our approach: (1) consider Hamiltonians containing multiple control functions and (2) use quantum optimal control theory (QOCT) to find control sets which achieve the target state with a high fidelity while simultaneously maximizing the degree of adiabaticity.• Exploring properties of optimal adiabatic trajectories in few-qubit model systems elucidates the dynamic mechanisms which suppress unwanted excitations from the ground state.
Adiabatic quantum computation employs a slow change of a time-dependent control function (or functions) to interpolate between an initial and final Hamiltonian, which helps to keep the system in the instantaneous ground state. When the evolution time is finite, the degree of adiabaticity (quantified in this work as the average ground-state population during evolution) depends on the particulars of a dynamic trajectory associated with a given set of control functions. We use quantum optimal control theory with a composite objective functional to numerically search for controls that achieve the target final state with a high fidelity while simultaneously maximizing the degree of adiabaticity. Exploring the properties of optimal adiabatic trajectories in model systems elucidates the dynamic mechanisms that suppress unwanted excitations from the ground state. Specifically, we discover that the use of multiple control functions makes it possible to access a rich set of dynamic trajectories, some of which attain a significantly improved performance (in terms of both fidelity and adiabaticity) through the increase of the energy gap during most of the evolution time.
We present a robust pulse optimization method for adiabatic population transfer and adiabatic quantum computation. The approach relies on identifying control pulses that keep the evolving quantum system close to its instantaneous ground state. By combining advanced gradient-free optimization tools with specialized cost functions for adiabatic control, it achieves both efficiency and robustness. To demonstrate its generality, we apply the method to three examples involving both atomic and superconducting qubits. We test different optimization cost functions and discretization bases, showing that the approach outperforms ensemble optimization. Finally, to verify its performance on real quantum hardware, we implement digitized adiabatic qubit control using the optimized pulses on the IBM quantum cloud.
Abstract. Adiabatic quantum computation employs a slow change of a time-dependent control function (or functions) to interpolate between an initial and final Hamiltonian, which helps to keep the system in the instantaneous ground state. When the evolution time is finite, the degree of adiabaticity (quantified in this work as the average ground-state population during evolution) depends on the particulars of a dynamic trajectory associated with a given set of control functions. We use quantum optimal control theory with a composite objective functional to numerically search for controls that achieve the target final state with a high fidelity while simultaneously maximizing the degree of adiabaticity. Exploring properties of optimal adiabatic trajectories in model systems elucidates the dynamic mechanisms that suppress unwanted excitations from the ground state. Specifically, we discover that the use of multiple control functions makes it possible to access a rich set of dynamic trajectories, some of which attain a significantly improved performance (in terms of both fidelity and adiabaticity) through the increase of the energy gap during most of the evolution time. Submitted to: New J. Phys. † Author to whom any correspondence should be addressed. ar