Investigating the potential for a limited quantum speedup on protein lattice problems (2004.01118v2)

Abstract: Protein folding is a central challenge in computational biology, with important applications in molecular biology, drug discovery and catalyst design. As a hard combinatorial optimisation problem, it has been studied as a potential target problem for quantum annealing. Although several experimental implementations have been discussed in the literature, the computational scaling of these approaches has not been elucidated. In this article, we present a numerical study of quantum annealing applied to a large number of small peptide folding problems, aiming to infer useful insights for near-term applications. We present two conclusions: that even naive quantum annealing, when applied to protein lattice folding, has the potential to outperform classical approaches, and that careful engineering of the Hamiltonians and schedules involved can deliver notable relative improvements for this problem. Overall, our results suggest that quantum algorithms may well offer improvements for problems in the protein folding and structure prediction realm.

• The paper demonstrates that quantum annealing can achieve a limited speedup on NP-hard protein lattice folding challenges through optimized simulation techniques.
• It utilizes a large dataset of 29,503 peptide sequences and employs Krylov-Schur numerical diagonalization to analyze spectral gaps and time-to-solution metrics.
• The findings indicate quantum annealing’s potential to complement classical methods in protein folding, opening pathways for hybrid biological optimization strategies.

Investigating the Potential for Quantum Speedup in Protein Folding on Lattice Models

The paper "Investigating the potential for a limited quantum speedup on protein lattice problems" addresses a significant challenge in computational biology, specifically the problem of protein folding and its computational complexity. By exploring quantum annealing as a means to solve protein lattice folding problems, the authors aim to provide insights into the advantages and limitations of quantum approaches in this domain, focusing on the potential for a limited quantum speedup.

Technical Context and Methodology

Protein folding is an NP-hard combinatorial optimization problem, which means that solving it is computationally intense and scales poorly with the size of the problem. Traditional methods like those based on classical computational heuristics may not provide satisfactory solutions within reasonable timeframes for larger proteins. Quantum annealing, a form of quantum computation, has been suggested as a viable alternative for certain NP-hard problems due to its inherent parallelism and potential efficiency in finding global minima of complex energy landscapes represented by Hamiltonians.

The paper in question employed quantum annealing simulations to evaluate its efficiency compared to classical methods. A large dataset comprising 29,503 small peptide sequences was utilized, each representing unique global energy minima. Through techniques like numerical diagonalization of Hamiltonians using Krylov-Schur methods and simulations of unitary evolution, the spectral gaps and time-to-solutions (TTS) for these lattice folding problems were investigated. The quantum annealing process was optimized by adjusting parameters like annealing time and leveraging stoquastic and non-stoquastic catalyst Hamiltonians.

Results and Analysis

The paper found that although some instances exhibited exponential decay of the minimum spectral gap — a theoretical measure limiting quantum annealing performance — this did not always translate to significantly longer runtimes due to optimized shorter runs that achieve a sizeably high probability of obtaining the correct solution. In fact, unlike theoretical expectations which suggest a $\Delta^{-2}$ runtime scaling, the actual performance was significantly milder. The optimized TTS showed scalability with the size of the protein lattice.

The less severe scaling observed suggests that quantum annealing, while not providing a polynomial-time solution, might still offer practical benefits over classical approaches for current problem sizes of interest in biology, which are inherently limited to a few hundred residues due to biophysical constraints. The introduction of tailored trajectories and engineering of Hamiltonians demonstrated significant improvements in performance compared to naive implementations, suggesting that careful parameter tuning is crucial.

Implications and Speculations

The results indicate that quantum annealing might not only be a step towards handling lattice protein folding problems more efficiently but could also complement classical methods by offering starting points that are closer to the global minimum, facilitating more effective hybrid classical-quantum techniques in computational biology. This could have profound implications for areas like drug discovery and biochemical research, where understanding protein structures is fundamental.

The ability of quantum methods to handle even modest-sized optimization problems more effectively than classical simulated annealing, as shown in the paper, opens pathways for their immediate application within current technological constraints. As hardware continues to evolve towards more sophisticated quantum annealers and quantum error correction becomes feasible, the field of practically solvable problem sizes could expand.

Future advancements could potentially focus on hybrid models that exploit the benefits of quantum approaches for generating initial solutions or narrowing down search spaces that classical methods can refine further. The next steps could also involve exploring more complex models beyond lattice approximations, integrating real-world biochemical constraints into the quantum computational paradigm.

In conclusion, while the paper underscores the challenges of achieving quantum speedup, it provides valuable insights into the practical application of quantum annealing for protein folding and suggests promising avenues for research and development in the intersection of quantum computing and computational biology.