Chalmers and Lund University test quantum protein folding

Researchers from Chalmers University of Technology and Lund University are testing the limits of current quantum hardware by applying variational quantum algorithms to protein design. Their work focuses on optimizing sequences to minimize energy in a target structure, the first of these two steps, rather than attempting full protein folding computations on noisy intermediate-scale quantum (NISQ) devices.

The team compared problem-informed quantum circuits with the hardware-efficient ansatz, achieving a significant success probability (≥0.2) in most instances when running the latter on quantum hardware at Jülich Supercomputing Centre with parameters from simulations. This approach acknowledges the constraints of existing technology while exploring practical applications for quantum computing in biomolecular design.

Variational Quantum Algorithms for Lattice Protein Design

This work diverges from full protein folding computations by concentrating on the sequence optimization task, a less computationally intensive process suitable for current quantum hardware limitations. The team’s investigation centers on noisy intermediate-scale quantum (NISQ) devices, moving beyond theoretical simulations to practical implementation. The approach splits the protein design problem into two distinct phases; the first, addressed in this study, focuses on energy minimization, while the second verifies whether the resulting sequences achieve the intended structure.

Classical simulations of quantum circuits and, in select instances, tests on quantum hardware are being used to assess the utility of VQAs. The researchers report they are unaware of prior publications exploring these specific quantum circuits applied to protein design challenges. A key parameter in their VQA implementation is the maximization of, adjusted through variational parameters denoted as θ = (β₁, …, βₚ, γ₁, …, γₚ).

Comparisons between two distinct quantum circuit construction methods are central to the study: problem-informed circuits and the hardware-efficient ansatz. The quantum approximate optimization algorithm (QAOA) and its variants form the basis of the problem-informed approach, while the hardware-efficient ansatz uses problem-agnostic circuits. Initial noiseless simulations revealed that a carefully selected mixer within the problem-informed circuits achieved success probabilities exceeding 0.95 across all tested instances. However, performance dropped drastically when noise was introduced, a common challenge with NISQ devices.

The hardware-efficient ansatz demonstrated improved performance in noisy simulations compared to its problem-informed counterpart. A significant success probability (≥0.2) was obtained in most instances.

This suggests a potential pathway for using existing quantum technology despite its limitations, and highlights the importance of circuit design compatible with hardware constraints. “For large p and suitably chosen parameters θ, QAOA can be seen as a discrete version of the analog quantum annealing method,” the paper states, referencing a connection to existing protein design techniques.

QAOA Performance in Noisy and Noise-Free Simulations

Despite strong performance in ideal conditions, standard variants of the quantum approximate optimization algorithm (QAOA) struggle with the realities of current quantum hardware due to the substantial circuit depths they require. Simulations reveal that even the best QAOA variants fall short when noise is introduced, hindering practical application on noisy intermediate-scale quantum (NISQ) devices. This limitation prompted investigation into alternative approaches, specifically the hardware-efficient ansatz (HEA), and its ability to maintain performance amidst noise.

The research team found that HEA circuits, particularly single-layer versions, demonstrated superior results in noisy simulations compared to all QAOA variants tested. When deployed on IBM’s Torino quantum device, two-layer HEA circuits achieved a success probability of at least 0.2 for most instances studied, even with problem sizes up to N = 29. The team also explored transferring parameters between similar problem instances, a technique that further improved HEA performance in noisy environments.

The simulations considered five QAOA variants and problem instances with N ≤ 16, all using 15 layers, with initial variational parameters set to π. The observed success with HEA contrasts with the difficulties encountered with larger problem instances, those exceeding N = 16, which proved challenging to solve even with the single-layer HEA in the presence of noise. Experiments using parameters derived from noiseless simulations generally yielded higher success rates on the hardware.

This suggests that imperfectly optimized parameters may contribute to the poorer performance observed in noisy simulations, and that careful parameter selection remains important for maximizing the potential of these algorithms. “Both HEAs, and especially the single-layer one, perform better than any of the QAOAs studied,” the study reports, emphasizing the relative robustness of the hardware-efficient approach.

Hardware-Efficient Ansatz for NISQ Device Compatibility

Hardware-efficient circuits demonstrated resilience on a quantum device at Jülich Supercomputing Centre, achieving a success probability of ≥0.2 in most instances tested, a notable outcome given the limitations of current quantum hardware. Unlike problem-informed circuits, which rely on encoding specific to the optimization task, these circuits prioritize compatibility with the physical constraints of NISQ devices, offering a different strategy for mitigating noise. The research team focused on single- and two-layer implementations of the hardware-efficient ansatz.

Classical optimization of these parameters remains a computationally hard problem, yet using parameters pre-determined from simulations proved effective in transferring performance to the physical hardware. Specifically, simulations yielding high success probabilities translated to significant success rates when deployed on the quantum hardware, suggesting the potential for a viable workflow even with imperfect optimization. The team observed that parameters from noiseless simulations generally yielded higher success rates on the hardware.

The team chose problem instances with N ≤ 16 for simulations and chose instances such that the sequence optimization problem has a unique solution for HP chains with lengths N ≤ 30. “Their higher noise tolerance motivated us to conduct hardware experiments with the HEAs,” the study reports, highlighting a deliberate shift towards prioritizing practical implementation over theoretical complexity.

This focus on shallower circuits, coupled with parameter transfer from simulations, represents a pragmatic approach to using quantum computing within the constraints of current technology, offering a pathway toward solving complex optimization problems despite the challenges of noise and limited qubit counts.

Sequence Optimization as a Protein Design Step

Focusing solely on minimizing energy within a target structure represents a strategic simplification of the broader protein design challenge, allowing researchers to assess quantum algorithms without the computational demands of full folding simulations. The work detailed in this paper examines protein design by initially concentrating on sequence optimization, a step preceding the verification of whether generated sequences actually fold correctly.

This approach acknowledges current limitations in quantum computing power and prioritizes a more tractable aspect of a complex biological problem. Researchers chose problem instances with N ≤ 16 where a unique solution exists and is known to fold to the target structure, streamlining evaluation of variational quantum algorithms (VQAs).

This investigation uses a simplified, yet relevant, coarse-grained HP model, retaining qualitative insights applicable to more complex phenomena like liquid-liquid phase separation in disordered proteins and protein evolution modeling. The researchers specifically sought to minimize E(C_t,s), the energy of a target structure C_t given a sequence s, rather than tackling the full folding computation, a decision driven by resource constraints. A key aspect of their work involves assessing defined as the number of sequences that fold into a specific target structure, a characteristic linked to mutation tolerance observed in natural proteins.

By selecting the most designable structure for each chain length N, the team created a controlled environment for evaluating the effectiveness of VQAs and identifying challenges to their broader application. “Our choice of simplified yet non-trivial problems with a priori known exact solutions helps us evaluate the effectiveness of nascent computational techniques such as VQAs and identify the inherent challenges impeding their wider applicability,” the paper states, highlighting the deliberate construction of test cases to isolate and address specific algorithmic hurdles. The paper details the methodology and results in subsequent sections, outlining the structure of their investigation from problem formulation to numerical and experimental findings.

HP Model Simplifications for Resource-Efficient Testing

The energy minimization process central to protein design relies on calculating a contact matrix, detailing interactions between beads within a lattice structure, a method essential for assessing potential protein configurations. This matrix, denoted as w_ij, indicates whether two beads are in contact, represented by a value of 1, or not, represented by 0, forming the basis for evaluating the stability of a given protein sequence.

Researchers used this HP model, focusing on hydrophobic and polar beads, to establish a quantifiable energy landscape for protein folding simulations. Variational quantum algorithms were evaluated through both classical simulations and, notably, experiments conducted at Jülich Supercomputing Centre, allowing for direct comparison between theoretical predictions and real-world performance. The team’s methodology focused on deterministic training schemes, defining success by the probability of reaching the ground state in the final quantum state, a metric used to gauge the algorithm’s effectiveness.

Success probability, a key performance indicator, was assessed across a range of quantum circuit layers, from one to fifteen. Simulations revealed a significant drop in success probability when noise, mirroring the characteristics of the quantum hardware, was introduced, prompting investigation into the impact of reducing the number of layers.

This exploration aimed to determine if a shallower circuit architecture could mitigate the detrimental effects of noise and maintain a reasonable level of performance, a critical consideration for near-term quantum applications. The results showed that, while noiseless simulations yielded high success probabilities, the introduction of realistic noise significantly degraded performance, highlighting the challenges of implementing quantum algorithms on current hardware.

Challenges of Parameter Optimization in Variational Circuits

Parameter optimization presents a significant hurdle for variational quantum algorithms, limiting their practical success on current noisy intermediate-scale quantum (NISQ) devices despite using parameterized quantum circuits and iterative classical computations to find solutions. Effective initialization heuristics and strategies to mitigate noise-induced errors are important, yet the optimization of circuit parameters remains a critical bottleneck, particularly due to the occurrence of barren plateaus and poor convergence in high-dimensional parameter landscapes.

Transfer learning techniques, including parameter donation between related problem instances, have emerged as potential solutions to accelerate convergence and enhance robustness, especially relevant given the constraints of limited coherence times and gate fidelities. Researchers explored parameter transfer, attempting to reuse optimized parameters from smaller instances to guide optimization, but this did not yield notable improvements despite significant overlap between low-energy regions of different parameter landscapes.

This suggests circuit depth, rather than initial parameter selection, is the dominant limiting factor in achieving high success rates. To address this, the team recast the protein design problem into a Quadratic Unconstrained Binary Optimization (QUBO) form, introducing a penalty term to prevent trivial solutions involving homopolymer sequences of hydrophobic beads.

“These strategies are especially relevant in the context of current quantum hardware,” the paper states, emphasizing the need to account for the limitations of existing technology. To circumvent the need for deep circuits, researchers also considered the hardware-efficient ansatz, a problem-agnostic approach with shallower circuits, offering a potential pathway to improved performance in the face of noise and hardware constraints.

D-Wave Quantum Annealers and Lattice Protein Folding

Unlike previous explorations of quantum approaches to protein folding, this work focuses specifically on the initial step of sequence optimization, identifying amino acid sequences that minimize energy within a target structure, a less computationally demanding task suited to current quantum hardware. The team’s investigation uses classical simulations of quantum circuits and, in selected cases, tests on quantum hardware to assess performance under realistic conditions. Initial results with the quantum approximate optimization algorithm (QAOA) revealed a trade-off between circuit performance and depth; an XY-mixer yielded strong results in simulations but required more quantum operations.

This highlights a critical challenge for near-term quantum computing, where the accumulation of errors limits the feasibility of deep circuits. Researchers found that QAOA’s performance drops drastically under noise, prompting a shift in focus toward hardware-efficient ansatzes, problem-agnostic circuits designed to better align with the constraints of existing quantum processors.

While problem-informed circuits initially showed promise in noiseless simulations, a significant success probability (≥0.2) was obtained in most instances when running the problem-agnostic circuits with parameters derived from simulations. This suggests that shallower circuits, even if less tailored to the specific problem, can be more robust and practical for implementation on noisy intermediate-scale quantum devices.

Transfer Learning Strategies for QAOA Convergence

Transfer learning strategies offer a pathway to improved convergence for variational quantum algorithms facing the realities of current hardware. Researchers used parameter donation within quantum approximate optimization algorithm (QAOA) circuits to accelerate optimization. Initial tests focused on five QAOA variants applied to protein sequence optimization problems with known solutions. The team’s methodology included a deterministic iterative procedure for parameter optimization, starting with angles initialized to π. The researchers specifically examined problem instances with N ≤ 16 elements, seeking to establish a baseline for performance evaluation.

While the initial parameter selection yielded good results in noiseless simulations, the study demonstrated that performance degraded under realistic conditions. To address this, the team explored alternative optimization techniques, recognizing that the presence of noise necessitates a careful balance between circuit size and expressivity. The work highlights the importance of adapting algorithms to the capabilities of existing technology, rather than solely focusing on theoretical improvements in ideal conditions, and provides a foundation for further investigation into robust quantum optimization methods.

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