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.
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.
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 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.
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.
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.
- A study published in the international journal npj Quantum Information (Nature Portfolio) presents a resource-efficient quantum algorithm framework based on the Variational Quantum Eigensolver (VQE) for peptide and protein folding. - By translating protein folding into a tetrahedral lattice model and combining Conditional Value-at-Risk (CVaR) VQE with a classical evolutionary algorithm, the number of required qubits was drastically reduced. - It successfully folded a 7-amino acid neuropeptide using only 9 qubits on actual IBM 20-qubit quantum hardware, demonstrating its practical potential for next-generation drug discovery in the NISQ (Noisy Intermediate-Scale Quantum) era. [Quantum Biology Society] The protein folding problem, which involves predicting the three-dimensional structure of proteins and peptides from their primary amino acid sequence, plays a central role in various applications such as chemistry, biology, and medicine. However, as the sequence lengthens, the number of possible structures to explore explodes exponentially, making it difficult for classical computers to handle its intrinsic NP-hard complexity. Recently, a new quantum algorithm that can efficiently solve this long-standing challenge even on noisy intermediate-scale quantum (NISQ) computers has been developed, drawing the attention of the academic community. The paper titled "Resource-efficient quantum algorithm for protein folding," published in the international journal npj Quantum Information, presents an innovative computing framework for the discovery of next-generation peptide drugs. The research team of Anton Robert and Ivano Tavernelli from IBM Quantum, IBM Research - Zurich in Switzerland successfully led this groundbreaking study. ■ The Meeting of Lattice Models and Qubit Optimization Until now, attempts to introduce quantum computing to protein folding have required an unattainably high number of qubits that current, near-term quantum hardware cannot handle. To solve this, the research team converted protein folding into a tetrahedral lattice model. This model can efficiently depict the growth of a polymer chain while maintaining chemically plausible bond angles. In particular, they adopted a method of adding penalty terms to the Hamiltonian to prevent unphysical amino acid overlaps (e.g., beads occupying the same lattice site). Through this, they succeeded in drastically reducing the number of qubits required for calculation while suppressing the complexity of the algorithm to the level of O(N⁴). ■ Demonstration of Folding on Actual Quantum Hardware This algorithm maximized efficiency by combining CVaR-VQE, a variation of the Variational Quantum Eigensolver (VQE), with a classical Differential Evolution optimizer. Applying this technique, the researchers simulated the folding of the 10-amino acid Angiotensin peptide using only 22 qubits, successfully finding the most stable energy state (native fold). Furthermore, they successfully demonstrated the folding of a 7-amino acid neuropeptide (APRLRFY) using only 9 qubits on IBM's 20-qubit quantum computer hardware. This study is a groundbreaking achievement proving that the protein folding problem, which previously required massive computing resources, can be successfully solved even in a noisy real quantum processor environment. It is expected to bring tremendous innovation to next-generation /de novo/ drug design and disease treatment research utilizing quantum computing in the future.
Abstract Predicting the three-dimensional structure of a protein from its primary sequence of amino acids is known as the protein folding problem. Due to the central role of proteins’ structures in chemistry, biology and medicine applications, this subject has been intensively studied for over half a century. Although classical algorithms provide practical solutions for the sampling of the conformation space of small proteins, they cannot tackle the intrinsic NP-hard complexity of the problem, even when reduced to the simplest Hydrophobic-Polar model. On the other hand, while fault-tolerant quantum computers are beyond reach for state-of-the-art quantum technologies, there is evidence that quantum algorithms can be successfully used in noisy state-of-the-art quantum computers to accelerate energy optimization in frustrated systems. In this work, we present a model Hamiltonian with O(N4) O ( N 4 ) scaling and a corresponding quantum variational algorithm for the folding of a polymer chain with N monomers on a lattice. The model reflects many physico-chemical properties of the protein, reducing the gap between coarse-grained representations and mere lattice models. In addition, we use a robust and versatile optimization scheme, bringing together variational quantum algorithms specifically adapted to classical cost functions and evolutionary strategies to simulate the folding of the 10 amino acid Angiotensin on 22 qubits. The same method is also successfully applied to the study of the folding of a 7 amino acid neuropeptide using 9 qubits on an IBM 20-qubit quantum computer. Bringing together recent advances in building gate-based quantum computers with noise-tolerant hybrid quantum-classical algorithms, this work paves the way towards accessible and relevant scientific experiments on real quantum processors.