Suppressing unwanted transitions out of the instantaneous ground state is a major challenge in unitary adiabatic quantum computation. A recent approach consists in building counterdiabatic potentials approximated using variational strategies. In this Letter, we extend this variational approach to Lindbladian dynamics, having as a goal the suppression of diabatic transitions between pairs of Jordan blocks in quantum annealing. We show that, surprisingly, unitary counterdiabatic ans\atze are successful for dissipative dynamics as well, allowing for easier experimental implementations compared to Lindbladian ans\atze involving dissipation. Our approach not only guarantees improvements of open-system adiabaticity but also enhances the success probability of quantum annealing.Suppressing unwanted transitions out of the instantaneous ground state is a major challenge in unitary adiabatic quantum computation. A recent approach consists in building counterdiabatic potentials approximated using variational strategies. In this Letter, we extend this variational approach to Lindbladian dynamics, having as a goal the suppression of diabatic transitions between pairs of Jordan blocks in quantum annealing. We show that, surprisingly, unitary counterdiabatic ans\atze are successful for dissipative dynamics as well, allowing for easier experimental implementations compared to Lindbladian ans\atze involving dissipation. Our approach not only guarantees improvements of open-system adiabaticity but also enhances the success probability of quantum annealing.

Sep 27, 20211 citation

Optimizing counterdiabaticity by variational quantum circuits

Dan Sun, Pranav Chandarana, Zi‐Hua Xin +1 more

Using counterdiabatic (CD) driving-aiming at suppression of diabatic transition-in digitized adiabatic evolution has garnered immense interest in quantum protocols and algorithms. However, improving the approximate CD terms with a nested commutator ansatz is a challenging task. In this work, we propose a technique of finding optimal coefficients of the CD terms using a variational quantum circuit. By classical optimization routines, the parameters of this circuit are optimized to provide the coefficients corresponding to the CD terms. Then their improved performance is exemplified in Greenberger-Horne-Zeilinger state preparation on the nearest-neighbour Ising model. Finally, we also show the advantage over the usual quantum approximation optimization algorithm, in terms of fidelity with bounded time. This article is part of the theme issue 'Shortcuts to adiabaticity: theoretical, experimental and interdisciplinary perspectives'.Using counterdiabatic (CD) driving-aiming at suppression of diabatic transition-in digitized adiabatic evolution has garnered immense interest in quantum protocols and algorithms. However, improving the approximate CD terms with a nested commutator ansatz is a challenging task. In this work, we propose a technique of finding optimal coefficients of the CD terms using a variational quantum circuit. By classical optimization routines, the parameters of this circuit are optimized to provide the coefficients corresponding to the CD terms. Then their improved performance is exemplified in Greenberger-Horne-Zeilinger state preparation on the nearest-neighbour Ising model. Finally, we also show the advantage over the usual quantum approximation optimization algorithm, in terms of fidelity with bounded time. This article is part of the theme issue 'Shortcuts to adiabaticity: theoretical, experimental and interdisciplinary perspectives'.

arXiv:2208.02087Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering SciencesNov 6, 202216 citations

Counterdiabatic driving in the quantum annealing of the p -spin model: A variational approach

G. Passarelli, V. Cataudella, Rosario Fazio +1 more

In this paper, the issue of reducing the time-to-solution in adiabatic quantum computation is addressed. The authors apply a variational principle to derive approximations of the counterdiabatic driving operator as a shortcut to adiabaticity. Two different ansatzes are discussed for the ferromagnetic $p$ -spin model and its generalizations, including short-range interactions and random couplings. Numerical simulations show good performances, almost independently of the system size, up to hundreds of qubitsIn this paper, the issue of reducing the time-to-solution in adiabatic quantum computation is addressed. The authors apply a variational principle to derive approximations of the counterdiabatic driving operator as a shortcut to adiabaticity. Two different ansatzes are discussed for the ferromagnetic $p$-spin model and its generalizations, including short-range interactions and random couplings. Numerical simulations show good performances, almost independently of the system size, up to hundreds of qubits

arXiv:1912.09711Physical Review ResearchMar 9, 202065 citations

Genetic optimization of quantum annealing

Pratibha Raghupati Hegde, Gianluca Passarelli, Annarita Scocco +1 more

The study of optimal control of quantum annealing by modulating the pace of evolution and by introducing a counterdiabatic potential has gained significant attention in recent times. In this work, we present a numerical approach based on genetic algorithms to improve the performance of quantum annealing, which evades the Landau-Zener transitions to navigate to the ground state of the final Hamiltonian with high probability. We optimize the annealing schedules starting from the polynomial ansatz by treating their coefficients as chromosomes of the genetic algorithm. We also explore shortcuts to adiabaticity by computing a practically feasible $k$ -local optimal driving operator, showing that even for $k=1$ we achieve substantial improvement of the fidelity over the standard annealing solution. With these genetically optimized annealing schedules and/or optimal driving operators, we are able to perform quantum annealing in relatively short timescales and with higher fidelity compared to traditional approaches.The study of optimal control of quantum annealing by modulating the pace of evolution and by introducing a counterdiabatic potential has gained significant attention in recent times. In this work, we present a numerical approach based on genetic algorithms to improve the performance of quantum annealing, which evades the Landau-Zener transitions to navigate to the ground state of the final Hamiltonian with high probability. We optimize the annealing schedules starting from the polynomial ansatz by treating their coefficients as chromosomes of the genetic algorithm. We also explore shortcuts to adiabaticity by computing a practically feasible $k$-local optimal driving operator, showing that even for $k=1$ we achieve substantial improvement of the fidelity over the standard annealing solution. With these genetically optimized annealing schedules and/or optimal driving operators, we are able to perform quantum annealing in relatively short timescales and with higher fidelity compared to traditional approaches.

arXiv:2108.03185Physical Review AJan 26, 202236 citations

Minimizing irreversible losses in quantum systems by local counterdiabatic driving

Dries Sels, Anatoli Polkovnikov

42:365303] as a means to make fast changes in the Hamiltonian without exciting transitions. Such driving in principle allows one to realize arbitrarily fast annealing protocols or implement fast dissipationless driving, circumventing standard adiabatic limitations requiring infinitesimally slow rates. These ideas were tested and used both experimentally and theoretically in small systems, but in larger chaotic systems, it is known that exact counterdiabatic protocols do not exist. In this work, we develop a simple variational approach allowing one to find the best possible counterdiabatic protocols given physical constraints, like locality. These protocols are easy to derive and implement both experimentally and numerically. We show that, using these approximate protocols, one can drastically suppress heating and increase fidelity of quantum annealing protocols in complex many-particle systems. In the fast limit, these protocols provide an effective dual description of adiabatic dynamics, where the coupling constant plays the role of time and the counterdiabatic term plays the role of the Hamiltonian.42:365303] as a means to make fast changes in the Hamiltonian without exciting transitions. Such driving in principle allows one to realize arbitrarily fast annealing protocols or implement fast dissipationless driving, circumventing standard adiabatic limitations requiring infinitesimally slow rates. These ideas were tested and used both experimentally and theoretically in small systems, but in larger chaotic systems, it is known that exact counterdiabatic protocols do not exist. In this work, we develop a simple variational approach allowing one to find the best possible counterdiabatic protocols given physical constraints, like locality. These protocols are easy to derive and implement both experimentally and numerically. We show that, using these approximate protocols, one can drastically suppress heating and increase fidelity of quantum annealing protocols in complex many-particle systems. In the fast limit, these protocols provide an effective dual description of adiabatic dynamics, where the coupling constant plays the role of time and the counterdiabatic term plays the role of the Hamiltonian.

arXiv:1607.05687Proceedings of the National Academy of SciencesMay 1, 2017269 citations

Geometrical scheduling of adiabatic control without information of energy spectra

Yuta Shingu, Takuya Hatomura

Adiabatic control is a fundamental technique for manipulating quantum systems, guided by the quantum adiabatic theorem, which ensures suppressed nonadiabatic transitions under slow parameter variations. Quantum annealing, a heuristic algorithm leveraging adiabatic control, seeks the ground states of Ising spin glass models and has drawn attention for addressing combinatorial optimization problems. However, exponentially small energy gaps in such models often necessitate impractically long runtime to satisfy the adiabatic condition. Despite this limitation, improving the quality of approximate solutions remains crucial for practical applications. The quantum adiabatic brachistochrone provides a method to enhance adiabaticity by minimizing an action representing nonadiabaticity via the variational principle. While effective, its implementation requires detailed energy spectra, complicating its use in quantum annealing. Shortcuts to adiabaticity by counterdiabatic driving offer alternative approaches for accelerating adiabatic processes. However, the theory of shortcuts to adiabaticity often faces challenges such as nonlocal control requirements, high computational cost, and trade-offs between speed and energy efficiency. In this work, we propose a novel quantum adiabatic brachistochrone protocol tailored for quantum annealing that eliminates the need for energy spectrum information. Our approach builds on advancements in counterdiabatic driving to design efficient parameter schedules. We demonstrate the effectiveness of our method through numerical simulations on the transverse-field Ising chain and axial next-nearest neighbor Ising models.Adiabatic control is a fundamental technique for manipulating quantum systems, guided by the quantum adiabatic theorem, which ensures suppressed nonadiabatic transitions under slow parameter variations. Quantum annealing, a heuristic algorithm leveraging adiabatic control, seeks the ground states of Ising spin glass models and has drawn attention for addressing combinatorial optimization problems. However, exponentially small energy gaps in such models often necessitate impractically long runtime to satisfy the adiabatic condition. Despite this limitation, improving the quality of approximate solutions remains crucial for practical applications. The quantum adiabatic brachistochrone provides a method to enhance adiabaticity by minimizing an action representing nonadiabaticity via the variational principle. While effective, its implementation requires detailed energy spectra, complicating its use in quantum annealing. Shortcuts to adiabaticity by counterdiabatic driving offer alternative approaches for accelerating adiabatic processes. However, the theory of shortcuts to adiabaticity often faces challenges such as nonlocal control requirements, high computational cost, and trade-offs between speed and energy efficiency. In this work, we propose a novel quantum adiabatic brachistochrone protocol tailored for quantum annealing that eliminates the need for energy spectrum information. Our approach builds on advancements in counterdiabatic driving to design efficient parameter schedules. We demonstrate the effectiveness of our method through numerical simulations on the transverse-field Ising chain and axial next-nearest neighbor Ising models.

arXiv:2501.11846Physical Review AJul 16, 20253 citations

p

-spin model and its generalizations, including short-range interactions and random couplings. Numerical simulations show good performances, almost independently of the system size, up to hundreds of qubits

k

-local optimal driving operator, showing that even for

k=1

we achieve substantial improvement of the fidelity over the standard annealing solution. With these genetically optimized annealing schedules and/or optimal driving operators, we are able to perform quantum annealing in relatively short timescales and with higher fidelity compared to traditional approaches.