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arXiv:2506.07866

Protein folding with an all-to-all trapped-ion quantum computer

Sebastián V. Romero, Alejandro Gomez Cadavid, Pavle Nikačević, E. Solano, Narendra N. Hegade, Miguel Angel Lopez-Ruiz, Claudio Girotto, Masako Yamada, Panagiotis Kl. Barkoutsos, Ananth P. Kaushik, Martin Roetteler

Published Jun 9, 2025• 1 citation
arXivHTMLPDF

Abstract

We experimentally demonstrate that the bias-field digitized counterdiabatic quantum optimization (BF-DCQO) algorithm, implemented on IonQ's fully connected trapped-ion quantum processors, offers an efficient approach to solving dense higher-order unconstrained binary optimization (HUBO) problems. Specifically, we tackle protein folding on a tetrahedral lattice for up to 12 amino acids, representing the largest quantum hardware implementations of protein folding problems reported to date. Additionally, we address MAX 4-SAT instances at the computational phase transition and fully connected spin-glass problems using all 36 available qubits. Across all considered cases, our method consistently achieves optimal solutions, highlighting the powerful synergy between non-variational quantum optimization approaches and the intrinsic all-to-all connectivity of trapped-ion architectures. Given the expected scalability of trapped-ion quantum systems, BF-DCQO represents a promising pathway toward practical quantum advantage for dense HUBO problems with significant industrial and scientific relevance.

DOI
10.48550/arxiv.2506.07866

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We experimentally demonstrate that the bias-field digitized counterdiabatic quantum optimization (BF-DCQO) algorithm, implemented on IonQ's fully connected trapped-ion quantum processors, offers an efficient approach to solving dense higher-order unconstrained binary optimization (HUBO) problems. Specifically, we tackle protein folding on a tetrahedral lattice for up to 12 amino acids, representing the largest quantum hardware implementations of protein folding problems reported to date. Additionally, we address MAX 4-SAT instances at the computational phase transition and fully connected spin-glass problems using all 36 available qubits. Across all considered cases, our method consistently achieves optimal solutions, highlighting the powerful synergy between non-variational quantum optimization approaches and the intrinsic all-to-all connectivity of trapped-ion architectures. Given the expected scalability of trapped-ion quantum systems, BF-DCQO represents a promising pathway toward practical quantum advantage for dense HUBO problems with significant industrial and scientific relevance.
We report the largest trapped-ion hardware demonstration of lattice protein-folding optimization to date, using bias-field digitized counterdiabatic quantum optimization (BF-DCQO) on a fully connected 64-qubit Barium development system similar to the forthcoming IonQ Tempo line. Six peptide sequences with 14-16 amino-acid residues are encoded using a coarse-grained tetrahedral lattice model, yielding higher-order spin-glass Hamiltonians with long-range interactions involving up to five-body terms and mapped to 46-61 qubits. The resulting instances are demanding for near-term quantum hardware because low-energy configurations must satisfy backbone-geometry constraints while optimizing dense residue-contact interactions. BF-DCQO uses a non-variational bias-feedback mechanism, where low-energy samples from each round define longitudinal fields that guide subsequent quantum evolutions. Across the studied instances, BF-DCQO shifts raw sampled energy distributions toward lower energies than uniform random sampling, with the strongest improvements appearing in residue-contact variables. To preserve this signal, we introduce a consensus-based post-processing pipeline that combines quantum-learned contact information with feasible backbone geometries. The resulting hybrid workflow reaches the classical reference energy in multiple instances and improves over the corresponding random-seeded pipeline. These results show that BF-DCQO can generate structured samples for dense protein-folding Hamiltonians at previously unexplored trapped-ion scales.
Abstract Combinatorial optimization plays a crucial role in many industrial applications. While classical computing often struggles with complex instances, quantum optimization emerges as a promising alternative. Here, we present an enhanced bias-field digitized counterdiabatic quantum optimization (BF-DCQO) algorithm to address higher-order unconstrained binary optimization (HUBO). We apply BF-DCQO to a HUBO problem featuring three-local terms in the Ising spin-glass model, validated experimentally using 156 qubits on an IBM quantum processor. In the studied instances, our results outperform standard methods such as the quantum approximate optimization algorithm, quantum annealing, simulated annealing, and Tabu search. Furthermore, we provide numerical evidence of the feasibility of a similar HUBO problem on a 433-qubit Osprey-like quantum processor. Finally, we solve denser instances of the MAX 3-SAT problem in an IonQ emulator. Our results show that BF-DCQO offers an effective path for solving large-scale HUBO problems on current and near-term quantum processors.
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.
We present an end-to-end pipeline for large-scale portfolio selection with cardinality constraints and experimentally demonstrate it on trapped-ion quantum processors using hardware-aware decomposition. Building on RMT-based correlation-matrix denoising and community detection, we identify correlated asset groups and introduce a correlation-guided greedy splitting scheme that caps each cluster by the executable qubit budget. Each cluster defines a hardware-embeddable QUBO subproblem that we solve using bias-field digitized counterdiabatic quantum optimization (BF-DCQO), a non-variational method that avoids classical parameter-training loops. We recombine low-energy candidates into global portfolios and enforce feasibility with a two-stage post-processing routine: fast repair followed by a cardinality-preserving swap local search. We benchmark the workflow on a 250-asset universe taken from the S&P 500 and execute subproblems on a 64-qubit Barium development system similar to the forthcoming IonQ Tempo line. We observe that larger executable subproblem sizes reduce decomposition error and systematically improve final objective values and risk-return trade-offs relative to randomized baselines under identical post-processing. Overall, the results establish a hardware-tested route for scaling financial optimization problems, defined by a trade space in which executable problem size and circuit cost are balanced against the resulting solution quality.
Branch-and-bound algorithms effectively solve combinatorial optimization problems, relying on the relaxation of the objective function to obtain tight lower bounds. While this is straightforward for convex objective functions, higher-order formulations pose challenges due to their inherent non-convexity. In this work, we propose branch-and-bound digitized counterdiabatic quantum optimization (BB-DCQO), a quantum algorithm that addresses the relaxation difficulties in higher-order unconstrained binary optimization (HUBO) problems. By employing bias fields as approximate solutions to the relaxed problem, we iteratively enhance the quality of the results compared to the bare bias-field digitized counterdiabatic quantum optimization (BF-DCQO) algorithm. We refer to this enhanced method as BBB-DCQO. In order to benchmark it against simulated annealing (SA), we apply it on sparse HUBO instances with up to 156156156 qubits using tensor network simulations. To explore regimes that are less tractable for classical simulations, we experimentally apply BBB-DCQO to denser problems using up to 100 qubits on IBM quantum hardware. We compare our results with SA and a greedy-tuned quantum annealing baseline. In both simulations and experiments, BBB-DCQO consistently achieved higher-quality solutions with significantly reduced computational overhead, showcasing the effectiveness of integrating counterdiabatic quantum methods into branch-and-bound to address hard non-convex optimization tasks.
We present a quantum feature-selection framework based on a higher-order unconstrained binary optimization (HUBO) formulation that explicitly incorporates multivariate dependencies beyond standard quadratic encodings. In contrast to QUBO-based approaches, the proposed model includes one-, two-, and three-body interaction terms derived from mutual-information measures, enabling the objective function to capture feature relevance, pairwise redundancy, and higher-order statistical structure within a unified energy model. To suppress trivial all-selected solutions, we further include structured linear penalties that promote sparsity while preserving informative variables. The resulting HUBO instances are optimized with digitized counterdiabatic quantum optimization on IonQ Forte and compared against noiseless quantum simulation as well as two classical dimensionality-reduction baselines: SelectKBest based on mutual information and principal component analysis (PCA). We evaluate the proposed workflow on two benchmark classification datasets, namely the Gallstone dataset and the Spambase dataset, and analyze both predictive performance and selected-subset structure. The results show good qualitative agreement between hardware executions and noiseless simulations, supporting the feasibility of implementing higher-order feature-selection Hamiltonians on current trapped-ion processors. In addition, the quantum approach yields competitive classification performance while producing compact and informative feature subsets, highlighting the potential of higher-order quantum optimization for machine-learning preprocessing tasks.