Vikram Khipple Mulligan, Hans Melo, Haley I. Merritt, Stewart Slocum, Brian D. Weitzner, Andrew M. Watkins, P. Douglas Renfrew, Craig Pelissier, Paramjit S. Arora, Richard Bonneau
Abstract Although a wide variety of quantum computers are currently being developed, actual computational results have been largely restricted to contrived, artificial tasks. Finding ways to apply quantum computers to useful, real-world computational tasks remains an active research area. Here we describe our mapping of the protein design problem to the D-Wave quantum annealer. We present a system whereby Rosetta, a state-of-the-art protein design software suite, interfaces with the D-Wave quantum processing unit to find amino acid side chain identities and conformations to stabilize a fixed protein backbone. Our approach, which we call the QPacker , uses a large side-chain rotamer library and the full Rosetta energy function, and in no way reduces the design task to a simpler format. We demonstrate that quantum annealer-based design can be applied to complex real-world design tasks, producing designed molecules comparable to those produced by widely adopted classical design approaches. We also show through large-scale classical folding simulations that the results produced on the quantum annealer can inform wet-lab experiments. For design tasks that scale exponentially on classical computers, the QPacker achieves nearly constant runtime performance over the range of problem sizes that could be tested. We anticipate better than classical performance scaling as quantum computers mature.
Abstract Although a wide variety of quantum computers are currently being developed, actual computational results have been largely restricted to contrived, artificial tasks. Finding ways to apply quantum computers to useful, real-world computational tasks remains an active research area. Here we describe our mapping of the protein design problem to the D-Wave quantum annealer. We present a system whereby Rosetta, a state-of-the-art protein design software suite, interfaces with the D-Wave quantum processing unit to find amino acid side chain identities and conformations to stabilize a fixed protein backbone. Our approach, which we call the QPacker , uses a large side-chain rotamer library and the full Rosetta energy function, and in no way reduces the design task to a simpler format. We demonstrate that quantum annealer-based design can be applied to complex real-world design tasks, producing designed molecules comparable to those produced by widely adopted classical design approaches. We also show through large-scale classical folding simulations that the results produced on the quantum annealer can inform wet-lab experiments. For design tasks that scale exponentially on classical computers, the QPacker achieves nearly constant runtime performance over the range of problem sizes that could be tested. We anticipate better than classical performance scaling as quantum computers mature.
Modelling and predicting protein configurations is crucial for advancing drug discovery, enabling the design of treatments for life-threatening diseases. A critical aspect of this challenge is rotamer optimisation - the determination of optimal side-chain conformations given a fixed protein backbone. This problem, involving the internal degrees of freedom of amino acid side-chains, significantly influences the protein's overall structure and function. In this work, we develop a resource-efficient optimisation algorithm to compute the ground state energy of protein structures, with a focus on side-chain configuration. We formulate the rotamer optimisation problem as a Quadratic Unconstrained Binary Optimisation problem and map it to an Ising model, enabling efficient quantum encoding. Building on this formulation, we propose a quantum algorithm based on the Quantum Approximate Optimisation Algorithm to explore the conformational space and identify low-energy configurations. To benchmark our approach, we conduct a classical study using custom-built libraries tailored for structural characterisation and energy optimisation. Our quantum method demonstrates a reduction in computational cost compared to classical simulated annealing techniques, offering a scalable and promising framework for protein structure optimisation in the quantum era.
Quantum annealing has shown promise for finding solutions to difficult optimization problems, including protein folding. Recently, we used the D-Wave Advantage quantum annealer to explore the folding problem in a coarse-grained lattice model, the HP model, in which amino acids are classified into two broad groups: hydrophobic (H) and polar (P). Using a set of 22 HP sequences with up to 64 amino acids, we demonstrated the fast and consistent identification of the correct HP model ground states using the D-Wave hybrid quantum-classical solver. An equally relevant biophysical challenge, called the protein design problem, is the inverse of the above, where the task is to predict protein sequences that fold to a given structure. Here, we approach the design problem by a two-step procedure implemented and executed on a D-Wave machine. In the first step, we perform a pure sequence-space search by varying the type of amino acid at each sequence position, and seek sequences which minimize the HP-model energy of the target structure. After mapping this task onto an Ising spin-glass representation, we employ a hybrid quantum-classical solver to deliver energy-optimal sequences for structures with 30–64 amino acids, with a 100% success rate. In the second step, we filter the optimized sequences from the first step according to their ability to fold to the intended structure. In addition, we try solving the sequence optimization problem using only the quantum processing unit (QPU), which confines us to sizes ≤20 , due to exponentially decreasing success rates. To shed light on the pure QPU results, we investigate the effects of control errors caused by an imperfect implementation of the intended Hamiltonian on the QPU, by numerically analyzing the Schrödinger equation. We find that the simulated success rates in the presence of control noise semiquantitatively reproduce the modest pure QPU results for larger chains. Published by the American Physical Society 2024
Using a simple lattice model with a 2 letter amino acid alphabet (H: hydrophobic and P: polar), we have explored the important biophysical problems of protein folding and protein design. Our formulation of these problems features a simple algebraic form for the Hamiltonian irrespective of the system size and composition. Since exact results are available from for lattice HP chains up to a size of 30, we were able to thoroughly validate our approach. The D-Wave advantage quantum annealer successfully identifies the ground state of the HP model protein chain in 100% of cases. For a few longer protein chains with up to 64 amino acids, where exact enumerations were not available but extensive Monte Carlo studies exist, the D-Wave hybrid annealer found the correct ground states within minutes, once again with a 100% success rate. Applying the same technique to the protein design problem, we found novel HP protein sequences with the same ground state as the largest systems we studied for folding. In contrast to the sequences used for folding, some of our newly found sequences had unique rather than degenerate ground states.
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.
Protein folding -- the problem of predicting the spatial structure of a protein given its sequence of amino-acids -- has attracted considerable research effort in biochemistry in recent decades. In this work, we explore the potential of quantum computing to solve a simplified version of protein folding. More precisely, we numerically investigate the performance of a variational quantum algorithm, the Quantum Approximate Optimization Algorithm (QAOA), in sampling low-energy conformations of short peptides. We start by benchmarking the algorithm on an even simpler problem: sampling self-avoiding walks, which is a necessary condition for a valid protein conformation. Motivated by promising results achieved by QAOA on this problem, we then apply the algorithm to a more complete version of protein folding, including a simplified physical potential. In this case, based on numerical simulations on 20 qubits, we find less promising results: deep quantum circuits are required to achieve accurate results, and the performance of QAOA can be matched by random sampling up to a small overhead. Overall, these results cast serious doubt on the ability of QAOA to address the protein folding problem in the near term, even in an extremely simplified setting. We believe that the approach and conclusions presented in this work could offer valuable methodological insights on how to systematically evaluate variational quantum optimization algorithms on real-world problems beyond protein folding.
Lattice models have been used extensively over the past thirty years to examine the principles of protein folding and design. These models can be used to determine the conformation of the lowest energy fold out of a large number of possible conformations. However, due to the size of the conformational space, new algorithms are required for folding longer proteins sequences. Preliminary work was performed by Babbush et al. (2012) to fold a small peptide on a planar lattice using a quantum annealing device. We extend this work by providing improved Ising-type Hamiltonian encodings for the problem of finding the lowest energy conformation of a lattice protein. We demonstrate a decrease in quantum circuit complexity from quadratic to quasilinear in certain cases. Additionally, we generalize to three spatial dimensions in order to obtain results with higher correlation to the actual atomistic 3D structure of the protein and outline our heuristic approach for splitting large problem instances into smaller subproblems that can be directly solved with the current D-Wave 2000Q architecture. To the best of our knowledge, this work sets a new record for lattice protein folding on a quantum annealer by folding Chignolin (10 residues) on a planar lattice and Trp-Cage (8 residues) on a cubic lattice.