Finding the global minimum of a potential energy surface is a fundamental challenge in materials science, with applications ranging from protein folding to cluster physics and, more broadly, to systems in which the number of (meta)stable configurations grows prohibitively large. In recent decades, quantum annealing (QA) has emerged as a promising global optimization strategy, exploiting quantum fluctuations in contrast to the thermal fluctuations that drive its classical counterpart. Here, we introduce a novel implementation of QA based on path-integral molecular dynamics, an efficient and well-established framework for sampling the quantum nuclear density without the need to manipulate many-body wavefunctions explicitly. While retaining the flexibility and simplicity of molecular dynamics simulations, this quantum-annealing protocol delivers strong performance across a wide range of atomic systems, simulated by either empirical force fields or machine-learning interatomic potentials. The method can be used either as a global optimizer of the potential-energy surface, or as a quantum-informed structure-search strategy in which nuclear quantum effects are included directly in the optimization workflow -- a feature particularly relevant for materials such as high-pressure hydrides.
Finding the global minimum of a potential energy surface is a fundamental challenge in materials science, with applications ranging from protein folding to cluster physics and, more broadly, to systems in which the number of (meta)stable configurations grows prohibitively large. In recent decades, quantum annealing (QA) has emerged as a promising global optimization strategy, exploiting quantum fluctuations in contrast to the thermal fluctuations that drive its classical counterpart. Here, we introduce a novel implementation of QA based on path-integral molecular dynamics, an efficient and well-established framework for sampling the quantum nuclear density without the need to manipulate many-body wavefunctions explicitly. While retaining the flexibility and simplicity of molecular dynamics simulations, this quantum-annealing protocol delivers strong performance across a wide range of atomic systems, simulated by either empirical force fields or machine-learning interatomic potentials. The method can be used either as a global optimizer of the potential-energy surface, or as a quantum-informed structure-search strategy in which nuclear quantum effects are included directly in the optimization workflow -- a feature particularly relevant for materials such as high-pressure hydrides.
Finding the global minimum in a rugged potential landscape is a computationally hard task, often equivalent to relevant optimization problems. Annealing strategies, either classical or quantum, explore the configuration space by evolving the system under the influence of thermal or quantum fluctuations. The thermal annealing dynamics can rapidly freeze the system into a low-energy configuration, and it can be simulated well on a classical computer, but it easily gets stuck in local minima. Quantum annealing, on the other hand, can be guaranteed to find the true ground state and can be implemented in modern quantum simulators; however, quantum adiabatic schemes become prohibitively slow in the presence of quasidegeneracies. Here, we propose a strategy which combines ideas from simulated annealing and quantum annealing. In such a hybrid algorithm, the outcome of a quantum simulator is processed on a classical device. While the quantum simulator explores the configuration space by repeatedly applying quantum fluctuations and performing projective measurements, the classical computer evaluates each configuration and enforces a lowering of the energy. We have simulated this algorithm for small instances of the random energy model, showing that it potentially outperforms both simulated thermal annealing and adiabatic quantum annealing. It becomes most efficient for problems involving many quasidegenerate ground states.
Quantum annealing is a computational paradigm in which optimisation problems are encoded in the energy landscape of an interacting quantum system and explored through its dynamical evolution. By continuously transforming an initial Hamiltonian into one whose ground state represents the solution, the system navigates complex energy landscapes through a combination of quantum fluctuations, tunnelling processes, and dissipative dynamics. Quantum annealing is primarily designed for discrete optimisation and sampling tasks and provides a physically motivated heuristic for exploring rugged landscapes that arise across science and engineering. Modern quantum annealers realise programmable spin systems with thousands of qubits, making them among the largest controllable quantum devices currently available. Beyond optimisation, they also serve as experimental platforms for studying non-equilibrium many-body quantum dynamics in regimes that are challenging to access classically. In this review we introduce the principles of quantum annealing, describe the main hardware platforms and algorithmic techniques, and analyse the roles of tunnelling, spectral gaps, and open-system effects in determining performance. We survey applications ranging from optimisation and machine learning to quantum simulation and many-body physics, and discuss the central challenges of benchmarking, scaling, and control. These developments position quantum annealing at the interface of optimisation, stochastic sampling, and programmable quantum dynamics.
Structural rearrangements play a central role in the organization and function of complex biomolecular systems. In principle, Molecular Dynamics (MD) simulations enable us to investigate these thermally activated processes with an atomic level of resolution. In practice, an exponentially large fraction of computational resources must be invested to simulate thermal fluctuations in metastable states. Path sampling methods focus the computational power on sampling the rare transitions between states. One of their outstanding limitations is to efficiently generate paths that visit significantly different regions of the conformational space. To overcome this issue, we introduce a new algorithm for MD simulations that integrates machine learning and quantum computing. First, using functional integral methods, we derive a rigorous low-resolution spatially coarse-grained representation of the system's dynamics, based on a small set of molecular configurations explored with machine learning. Then, we use a quantum annealer to sample the transition paths of this low-resolution theory. We provide a proof-of-concept application by simulating a benchmark conformational transition with all-atom resolution on the D-Wave quantum computer. By exploiting the unique features of quantum annealing, we generate uncorrelated trajectories at every iteration, thus addressing one of the challenges of path sampling. Once larger quantum machines will be available, the interplay between quantum and classical resources may emerge as a new paradigm of high-performance scientific computing. In this work, we provide a platform to implement this integrated scheme in the field of molecular simulations.
Quantum annealing is a computational paradigm in which optimisation problems are mapped onto the energy landscape of an interacting quantum system and explored through its dynamical evolution. By continuously transforming a simple initial Hamiltonian into one whose ground state encodes the solution, the system traverses a complex landscape via a combination of quantum fluctuations, tunnelling processes, and dissipative dynamics. Unlike gate-based quantum computing, quantum annealing is a specialised and near-term approach aimed primarily at discrete optimisation and sampling tasks. While it is not expected to provide polynomial-time solutions to NP-hard problems in the worst case, it offers a physically motivated heuristic for navigating rugged energy landscapes that arise across science and engineering. Modern quantum annealers realise programmable spin systems with thousands of qubits, placing them among the largest controllable quantum devices currently available. As a result, their significance extends beyond optimisation: they also function as experimental platforms for studying non-equilibrium many-body quantum dynamics in regimes that are difficult to access using classical simulation. In this review we present an accessible introduction to the principles of quantum annealing, describe the main hardware platforms and algorithmic techniques, and analyse how tunnelling, spectral gaps, and open-system effects shape computational performance. We survey applications ranging from optimisation and machine learning to quantum simulation and many-body physics, and discuss the central challenges in benchmarking, scaling, and control. These perspectives position quantum annealing as a distinctive framework at the interface of optimisation, stochastic sampling, and programmable quantum dynamics, with a role that is complementary to both classical algorithms and gate-based quantum computing.
The details of an efficient global optimization approach, quantum thermal annealing with renormalization (QTAR) (Y. H. Lee and B. J. Berne, J. Phys. Chem. A, in press (2000)) are presented in this paper. This method is based on the application of the Migdal-Kadanoff method for decimating Trotter time slices in the staging and primitive algorithms for sampling path integrals using Monte Carlo methods. In a nutshell, one starts in a strong quantum regime where the number of Trotter beads representing each quantum particle and the value of Planck's constant are large, thereby allowing for efficient tunneling through the barriers of a rough energy landscape typical in the folding of proteins, and anneals the system methodically to the classical limit where the values of the aforementioned quantities are 1 and 0, respectively. Global optimization of the system is achieved through the iterative use of such quantum-to-classical annealing cycles. The QTAR algorithm applied to a highly frustrated BLN model protein with 46 residues more efficiently locates the global energy minimum than established methods like simulated annealing.
Abstract The details of an efficient global optimization approach, quantum thermal annealing with renormalization (QTAR) (Y. H. Lee and B. J. Berne, J. Phys. Chem. A, in press (2000)) are presented in this paper. This method is based on the application of the Migdal‐Kadanoff method for decimating Trotter time slices in the staging and primitive algorithms for sampling path integrals using Monte Carlo methods. In a nutshell, one starts in a strong quantum regime where the number of Trotter beads representing each quantum particle and the value of Planck's constant are large, thereby allowing for efficient tunneling through the barriers of a rough energy landscape typical in the folding of proteins, and anneals the system methodically to the classical limit where the values of the aforementioned quantities are 1 and 0, respectively. Global optimization of the system is achieved through the iterative use of such quantum‐to‐classical annealing cycles. The QTAR algorithm applied to a highly frustrated BLN model protein with 46 residues more efficiently locates the global energy minimum than established methods like simulated annealing.