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.
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.
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 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.
We introduce a method for solving combinatorial optimization problems on digital quantum computers, where we incorporate auxiliary counterdiabatic (CD) terms into the adiabatic Hamiltonian, while integrating bias terms derived from an iterative digitized counterdiabatic quantum algorithm. We call this protocol bias-field digitized counterdiabatic quantum optimization (BF-DCQO). Designed to effectively tackle large-scale combinatorial optimization problems, BF-DCQO demonstrates resilience against the limitations posed by the restricted coherence times of current quantum processors and shows clear enhancement even in the presence of noise. Additionally, our purely quantum approach eliminates the dependency on classical optimization required in hybrid classical-quantum schemes, thereby circumventing the trainability issues often associated with variational quantum algorithms. Through the analysis of an all-to-all connected general Ising spin-glass problem, we exhibit a polynomial scaling enhancement in ground-state success probability compared to traditional DCQO and finite-time adiabatic quantum optimization methods. Furthermore, it achieves scaling improvements in ground-state success probabilities, increasing by up to two orders of magnitude, and offers an average 1.3 × better approximation ratio than the quantum approximate optimization algorithm for the problem sizes studied. We validate these findings through experimental implementations on both trapped-ion quantum computers and superconducting processors, tackling a maximum weighted independent set problem with 36 qubits and a spin glass on a heavy-hexagonal lattice with 100 qubits, respectively. These results mark a significant advancement in gate-based quantum computing, employing a fully quantum algorithmic approach.
XY mixer are a type of mixing Hamiltonians used in the quantum alternating operator ansatzs (QAOA) framework for solving combinatorial optimization problems where the feasible subspace consists of states with the same Hamming weight. In this paper, we propose an extension of the XY-mixer ansatzes to solve optimization problems that do not adhere to this specific subspace structure. For problems, such as maximal independent set, one can employ positive semidefinite programming and a greedy algorithm to obtain upper and lower bounds for the optimal solution, then utilize the XY-mixer ansatzes in the separated subspaces between the upper and lower bounds to address the problem at hand. Additionally, we find suitable counterdiabatic (CD) driving terms that complement the XY-mixer ansatzes. These driving terms accelerate the QAOA evolution towards the target state and also confine the evolution within the subspace. By combining XY-mixer ansatzes with counterdiabatic driving (XY-CD mixers), we present a generalized QAOA-based scheme for finding higher-quality approximate solutions to combinatorial problems.
The quantum approximate optimization algorithm (QAOA) has proved to be an effective classical-quantum algorithm serving multiple purposes, from solving combinatorial optimization problems to finding the ground state of many-body quantum systems. Since the QAOA is an Ansatz-dependent algorithm, there is always a need to design Ans\"atze for better optimization. To this end, we propose a digitized version of the QAOA enhanced via the use of shortcuts to adiabaticity. Specifically, we use a counterdiabatic (CD) driving term to design a better Ansatz, along with the Hamiltonian and mixing terms, enhancing the global performance. We apply our digitized-CD QAOA to Ising models, classical optimization problems, and the P-spin model, demonstrating that it outperforms the standard QAOA in all cases we study.
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.