Abstract Recently, digitized-counterdiabatic (CD) quantum approximate optimization algorithm (QAOA) has been proposed to make QAOA converge to the solution of an optimization problem in fewer steps, inspired by Trotterized CD driving in continuous-time quantum annealing. In this paper, we critically revisit this approach by focusing on the paradigmatic weighted and unweighted one-dimensional MaxCut problem. We study two variants of QAOA with first and second-order CD corrections. Our results show that, indeed, higher order CD corrections allow for a quicker convergence to the exact solution of the problem at hand by increasing the complexity of the variational cost function. Remarkably, however, the total number of free parameters needed to achieve this result is independent of the particular QAOA variant analyzed for the problems considered.
Abstract Recently, digitized-counterdiabatic (CD) quantum approximate optimization algorithm (QAOA) has been proposed to make QAOA converge to the solution of an optimization problem in fewer steps, inspired by Trotterized CD driving in continuous-time quantum annealing. In this paper, we critically revisit this approach by focusing on the paradigmatic weighted and unweighted one-dimensional MaxCut problem. We study two variants of QAOA with first and second-order CD corrections. Our results show that, indeed, higher order CD corrections allow for a quicker convergence to the exact solution of the problem at hand by increasing the complexity of the variational cost function. Remarkably, however, the total number of free parameters needed to achieve this result is independent of the particular QAOA variant analyzed for the problems considered.
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.
Abstract The bin packing problem (BPP), a classical NP-hard combinatorial optimization challenge, has emerged as a promising application for quantum computing. In this work, we tackle the one-dimensional BPP (1dBPP) using a digitized counterdiabatic quantum approximate optimization algorithm (DC-QAOA) that incorporates counterdiabatic (CD) driving to achieve a 40% higher feasibility ratio than standard QAOA, while reducing quantum resource requirements. We investigate three ansatz schemes -DC-QAOA, CD-inspired ansatz, and CD-mixer ansatz - each integrating CD terms with distinct combinations of cost and mixer Hamiltonians, resulting in different DC-QAOA variants. Numerical simulations demonstrate that these DC-QAOA variants maintain solution accuracy with less than 5% variance across varying iteration numbers, circuit depths, and Hamiltonian step sizes. Moreover, they require approximately 7 to 8 times fewer measurements to achieve comparable precision under the same parameter variations. Experimental validation on a 10-item 1dBPP instance using IBM quantum computers shows the CD-mixer ansatz achieves five times more feasibility solutions and greater robustness against NISQ noise. Collectively, these results establish DC-QAOA as a resource-efficient framework for combinatorial optimization on near-term quantum devices.
The quantum approximate optimization algorithm (QAOA) is a near-term hybrid algorithm intended to solve combinatorial optimization problems, such as MaxCut. QAOA can be made to mimic an adiabatic schedule, and in the p → ∞ limit the final state is an exact maximal eigenstate in accordance with the adiabatic theorem. In this work, the connection between QAOA and adiabaticity is made explicit by inspecting the regime of p large but finite. By connecting QAOA to counterdiabatic (CD) evolution, we construct CD-QAOA angles which mimic a counterdiabatic schedule by matching Trotter "error" terms to approximate adiabatic gauge potentials which suppress diabatic excitations arising from finite ramp speed. In our construction, these "error" terms are helpful, not detrimental, to QAOA. Using this matching to link QAOA with quantum adiabatic algorithms (QAA), we show that the approximation ratio converges to one at least as 1 − C ( p ) ∼ 1 / p μ . We show that transfer of parameters between graphs, and interpolating angles for p + 1 given p are both natural byproducts of CD-QAOA matching. Optimization of CD-QAOA angles is equivalent to optimizing a continuous adiabatic schedule. Finally, we show that, using a property of variational adiabatic gauge potentials, QAOA is at least counterdiabatic, not just adiabatic, and has better performance than finite time adiabatic evolution. We demonstrate the method on three examples: a 2 level system, an Ising chain, and the MaxCut problem.
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.
Recently, digitized-counterdiabatic (CD) corrections to the quantum approximate optimization algorithm (QAOA) have been proposed, yielding faster convergence within the desired accuracy than standard QAOA. In this manuscript, we apply this approach to a fully connected spin model with random couplings. We show that the performances of the algorithm are related to the spectral properties of the instances analyzed. In particular, the larger the gap between the ground state and the first excited states, the better the convergence to the exact solution.
The Quantum Approximate Optimization Algorithm (QAOA), whose design is underpinned by the adiabatic theorem, is one of the leading variational quantum algorithms for preparing the ground states of gauge theories. A recently proposed variant, DC-QAOA, incorporates counterdiabatic driving to accelerate the adiabatic process, reducing both circuit depth and runtime. In this work, we present a systematic analysis, from both theoretical and computational perspectives, of DC-QAOA and related counterdiabatic variants for preparing the ground state of the Schwinger model, the paradigmatic (1+1)-dimensional lattice gauge theory. Benchmarking these methods against standard QAOA, we show that counterdiabatic driving improves ground-state preparation while lowering circuit depth requirements. Our results establish counterdiabatic protocols as a practical route towards efficient quantum simulation of gauge theories.