Efficient large-scale quantum optimization via counterdiabatic ansatz

András Czégel

Jialiang Tang, Xi Chen, Zhi-Yuan Wei

Counterdiabatic (CD) driving enables efficient quantum state preparation, but it requires implementing highly nonlocal adiabatic gauge potentials (AGP) that are impractical to compute and realize in large many-body systems. We introduce a \textit{weighted nested-commutator} (WNC) ansatz to approximate AGP using local operators. The WNC ansatz generalizes the standard nested-commutator ansatz by assigning independent variational weights to commutators of local Hamiltonian terms, thereby enlarging the variational space while preserving a fixed operator range. We show that the WNC ansatz can be efficiently optimized using a local optimization scheme. Moreover, it systematically outperforms the nested-commutator ansatz in preparing one-dimensional matrix product states (MPS) and the ground state of a nonintegrable quantum Ising model. We then numerically demonstrate that CD driving based on the WNC ansatz significantly accelerates the preparation of 1D MPS for system sizes up to $N = 1000$ qubits, as well as the two-dimensional Affleck-Kennedy-Lieb-Tasaki state on a hexagonal lattice with up to $N = 3 \times 10$ sites.

Jie Liu, Xin Wang

Quantum approximate optimization algorithm (QAOA) is one of the fundamental variational quantum algorithms, while a version of QAOA that includes counterdiabatic driving, termed digitized counterdiabatic QAOA (DC-QAOA), is generally considered to outperform QAOA for all system sizes when the circuit depth for the two algorithms are held equal. Nevertheless, DC-QAOA introduces more cnot gates per layer, so the overall circuit complexity is a tradeoff between the number of cnot gates per layer and the circuit depth and must be carefully assessed. In this paper, we conduct a comprehensive comparison of DC-QAOA and QAOA on maxcut problem with the total number of cnot gates held equal, and we focus on one implementation of counterdiabatic terms using nested commutators in DC-QAOA, termed as DC-QAOA(NC). We have found that DC-QAOA(NC) reduces the overall circuit complexity as compared to QAOA only for sufficiently large problems, and for maxcut problem the number of qubits must exceed 16 for DC-QAOA(NC) to outperform QAOA. Additionally, we benchmark DC-QAOA(NC) against QAOA on the Sherrington-Kirkpatrick model under realistic noise conditions, finding that DC-QAOA(NC) exhibits significantly improved robustness compared to QAOA, maintaining higher fidelity as the problem size scales. Notably, in a direct comparison between one-layer DC-QAOA(NC) and three-layer QAOA where both use the same number of cnot gates, we identify an exponential performance advantage for DC-QAOA(NC), further signifying its suitability for large-scale quantum optimization tasks. We have further shown that this advantage can be understood from the effective dimensions introduced by the counterdiabatic driving terms. Moreover, based on our finding that the optimal parameters generated by DC-QAOA(NC) strongly concentrate in the parameter space, we have devised an instance-sequential training method for DC-QAOA(NC) circuits, which, compared to traditional methods, offers performance improvement while using even fewer quantum resources. Our findings provide a more comprehensive understanding of the advantages of DC-QAOA circuits and an efficient training method based on their generalizability.

Amira Abbas, Andris Ambainis, Brandon Augustino +43 more

Joaquín Molina, Herbert Díaz-Moraga, Dardo Goyeneche +1 more

Variational quantum algorithms based on qudits have attracted significant attention in recent years. However, as in their qubit-based counterparts, challenges such as barren plateaus and the design of efficient ansatz remain major obstacles. In this work, we propose to address these issues through a qudit implementation of the ADAPT-VQE algorithm, which constructs the ansatz iteratively. Specifically, we introduce an operator pool inspired by adiabatic evolution enhanced with counterdiabatic driving for ansatz construction and employ it to solve Max 3-Cut. We show that the warm-start strategy inherent to ADAPT-VQE, together with an ansatz construction based on counterdiabatic operators, achieves higher accuracy and lower native gates implementation than approaches on fixed ansatz. Furthermore, we show that, in qudit-based quantum computing, ADAPT-VQE with a counterdiabatic operator pool can navigate rough optimization landscapes with local traps through the burrowing mechanism, suggesting robustness against barren plateau effects and providing a scalable framework for variational quantum algorithms with qudits.

Pranav Chandarana, Pablo Suárez Vieites, Narendra N. Hegade +3 more

Abstract The use of variational quantum algorithms for optimization tasks has emerged as a crucial application for the current noisy intermediate-scale quantum computers. However, these algorithms face significant difficulties in finding suitable ansatz and appropriate initial parameters. In this paper, we employ meta-learning using recurrent neural networks to address these issues for the recently proposed digitized-counterdiabatic quantum approximate optimization algorithm (QAOA). By combining meta-learning and counterdiabaticity, we find suitable variational parameters and reduce the number of optimization iterations required. We demonstrate the effectiveness of our approach by applying it to the MaxCut problem and the Sherrington–Kirkpatrick model. Our method offers a short-depth circuit ansatz with optimal initial parameters, thus improving the performance of the state-of-the-art QAOA.