Computational multiqubit tunnelling in programmable quantum annealers
Sergio Boixo, Vadim Smelyanskiy, Alireza Shabani, Sergei V. Isakov, M. I. Dykman, Vasil S. Denchev, M. H. S. Amin, Anatoly Yu. Smirnov, Masoud Mohseni, Hartmut Neven
Quantum tunnelling is a phenomenon in which a quantum state traverses energy barriers higher than the energy of the state itself. Quantum tunnelling has been hypothesized as an advantageous physical resource for optimization in quantum annealing. However, computational multiqubit tunnelling has not yet been observed, and a theory of co-tunnelling under high- and low-frequency noises is lacking. Here we show that 8-qubit tunnelling plays a computational role in a currently available programmable quantum annealer. We devise a probe for tunnelling, a computational primitive where classical paths are trapped in a false minimum. In support of the design of quantum annealers we develop a nonperturbative theory of open quantum dynamics under realistic noise characteristics. This theory accurately predicts the rate of many-body dissipative quantum tunnelling subject to the polaron effect. Furthermore, we experimentally demonstrate that quantum tunnelling outperforms thermal hopping along classical paths for problems with up to 200 qubits containing the computational primitive.
Quantum tunnelling is a phenomenon in which a quantum state traverses energy barriers higher than the energy of the state itself. Quantum tunnelling has been hypothesized as an advantageous physical resource for optimization in quantum annealing. However, computational multiqubit tunnelling has not yet been observed, and a theory of co-tunnelling under high- and low-frequency noises is lacking. Here we show that 8-qubit tunnelling plays a computational role in a currently available programmable quantum annealer. We devise a probe for tunnelling, a computational primitive where classical paths are trapped in a false minimum. In support of the design of quantum annealers we develop a nonperturbative theory of open quantum dynamics under realistic noise characteristics. This theory accurately predicts the rate of many-body dissipative quantum tunnelling subject to the polaron effect. Furthermore, we experimentally demonstrate that quantum tunnelling outperforms thermal hopping along classical paths for problems with up to 200 qubits containing the computational primitive.
Quantum tunneling is a phenomenon in which a quantum state traverses energy barriers above the energy of the state itself. Tunneling has been hypothesized as an advantageous physical resource for optimization. Here we present the first experimental evidence of a computational role of multiqubit quantum tunneling in the evolution of a programmable quantum annealer. We develop a theoretical model based on a NIBA Quantum Master Equation to describe the multiqubit dissipative tunneling effects under the complex noise characteristics of such quantum devices. We start by considering a computational primitive, an optimization problem consisting of just one global and one false minimum. The quantum evolutions enable tunneling to the global minimum while the corresponding classical paths are trapped in a false minimum. In our study the non-convex potentials are realized by frustrated networks of qubit clusters with strong intra-cluster coupling. We show that the collective effect of the quantum environment is suppressed in the "critical" phase during the evolution where quantum tunneling "decides" the right path to solution. In a later stage dissipation facilitates the multiqubit tunneling leading to the solution state. The predictions of the model accurately describe the experimental data from the D-Wave Two quantum annealer at NASA Ames. In our computational primitive the temperature dependence of the probability of success in the quantum model is opposite to that of the classical paths with thermal hopping. Specifically, we provide an analysis of an optimization problem with sixteen qubits, demonstrating eight qubit tunneling that increases success probabilities. Furthermore, we report results for larger problems with up to 200 qubits that contain the primitive as subproblems.
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.
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.
Quantum annealing has emerged as a promising approach for solving NP-hard optimization problems, leveraging quantum phenomena such as quantum tunneling to navigate complex energy landscapes. However, the extent to which quantum tunneling contributes to performance enhancements compared to classical methods remains unclear. In this work, we present a comprehensive investigation combining experimental analysis, theoretical modeling, and algorithmic development to characterize when and why quantum annealing provides computational advantages.
We introduce a novel methodology for generating synthetic Quadratic Unconstrained Binary Optimization (QUBO) problems with controlled gradient variance, enabling systematic investigation of landscape characteristics that favor quantum approaches. Our experimental evaluation encompasses four canonical NP-hard problems: Graph Partitioning, Max Cut, Number Partitioning, and Set Cover. Using D-Wave's Advantage2 quantum annealer with 4,400+ qubits, we compare quantum annealing against classical solvers including simulated annealing, stochastic gradient descent, and commercial optimization software.
Our results demonstrate that quantum annealing shows measurable advantages when energy landscapes exhibit high gradient variance (>0.3), suggesting that quantum tunneling effects are most beneficial for rugged optimization landscapes. We provide a theoretical justification for this empirical observation through a WKB-approximation-based model connecting gradient variance to barrier width and tunneling probability. This model achieves R2=0.90 correlation with experimental data and yields quantitative predictions for quantum advantage thresholds.
Critical decision-making issues in science, engineering, and industry are based on combinatorial optimization; however, its application is inherently limited by the NP-hard nature of the problem. A specialized paradigm of analogue quantum computing, quantum annealing (QA), has been proposed to solve these problems by encoding optimization problems into physical energy landscapes and solving them by quantum tunnelling systematically through exploration of solution space. This is a critical review that summarizes the current applications of quantum annealing to combinatorial optimization and includes a theoretical background, hardware designs, algorithm implementation strategies, encoding and embedding schemes, protocols to benchmark quantum annealing, areas of implementation, and links with the quantum algorithms implementation with gate-based hardware and classical solvers. We develop a unified framework, relating adiabatic quantum dynamics, Ising and QUBO models, stoquastic and non-stoquastic Hamiltonians, and diabatic transitions to modern flux-qubit annealers (Chimera, Pegasus, Zephyr topologies), and emergent architectures (Lechner-Hauke-Zoller systems, Rydberg atom platforms), and hybrids of quantum and classical computation. Through our analysis, we find that overhead in embedding and encoding is the largest determinant of the scalability and performance (this is not just the number of qubits). Minor embeddings also usually have a physical qubit count per logical variable of between 5 and 12 qubits, which limits effective problem capacity by 80-92% and, due to chain-breaking errors, compromises the quality of solutions.