The complex matter-field lattice model is a ubiquitous and universal physics model that directly links to many universal spin models. However, finding the ground state of such a model for the most general interactions between the lattice sites is an NP-hard problem. The knowledge of the ground state is crucially essential for the range of applications from quantum annealing to predicting new materials and understanding the behaviour of spin glasses. Here we show how letting the quantised quasi-3D vortex loops pass through the system during the dissipative quench dynamics helps it find its ground state. Such quantized vortices mediated annealing (QVMA) is achieved by introducing and dynamically changing selected couplings between the lattice sites that either affect the local dimensionality of the medium or change the local mobility of the defects. Analysing the performance of QVMA on strongly glassy systems, we demonstrate that QVMA represents a highly efficient mode of physics enhanced computation.
The complex matter-field lattice model is a ubiquitous and universal physics model that directly links to many universal spin models. However, finding the ground state of such a model for the most general interactions between the lattice sites is an NP-hard problem. The knowledge of the ground state is crucially essential for the range of applications from quantum annealing to predicting new materials and understanding the behaviour of spin glasses. Here we show how letting the quantised quasi-3D vortex loops pass through the system during the dissipative quench dynamics helps it find its ground state. Such quantized vortices mediated annealing (QVMA) is achieved by introducing and dynamically changing selected couplings between the lattice sites that either affect the local dimensionality of the medium or change the local mobility of the defects. Analysing the performance of QVMA on strongly glassy systems, we demonstrate that QVMA represents a highly efficient mode of physics enhanced computation.
Population annealing, one of the currently state-of-the-art algorithms for solving spin-glass systems, sometimes finds hard disorder instances for which its equilibration quality at each temperature step is severely damaged. In such cases, therefore, one cannot be sure about having reached the true ground state without vastly increasing the computational resources. In this work, we seek to overcome this problem by proposing a quantum-inspired modification of population annealing. Here we focus on the three-dimensional random plaquette gauge model, whose ground-state energy problem seems to be much harder to solve than that of the standard spin-glass Edwards-Anderson model. In analogy to the toric code, by allowing single bond flips we let the system explore nonphysical states, effectively expanding the configurational space by introducing topological defects that are then annealed through an additional field parameter. The dynamics of these defects allow for the effective realization of nonlocal cluster moves, potentially easing the equilibration process. We study the performance of this method in three-dimensional random plaquette gauge model lattices of various sizes, and we compare it against population annealing. With that we conclude that the newly introduced nonlocal moves are able to improve the equilibration of the lattices, in some cases being superior to a normal population annealing algorithm with a computational resource investment that is 16 times higher.
Spin glasses are disordered magnets with random interactions that are, generally, in conflict with each other. Finding the ground states of spin glasses is not only essential for understanding the nature of disordered magnets and many other physical systems, but also useful to solve a broad array of hard combinatorial optimization problems across multiple disciplines. Despite decades-long efforts, an algorithm with both high accuracy and high efficiency is still lacking. Here we introduce DIRAC - a deep reinforcement learning framework, which can be trained purely on small-scale spin glass instances and then applied to arbitrarily large ones. DIRAC displays better scalability than other methods and can be leveraged to enhance any thermal annealing method. Extensive calculations on 2D, 3D and 4D Edwards-Anderson spin glass instances demonstrate the superior performance of DIRAC over existing methods. The presented framework will help us better understand the nature of the low-temperature spin-glass phase, which is a fundamental challenge in statistical physics. Moreover, the gauge transformation technique adopted in DIRAC builds a deep connection between physics and artificial intelligence. In particular, this opens up a promising avenue for reinforcement learning models to explore in the enormous configuration space, which would be extremely helpful to solve many other hard combinatorial optimization problems.
The promise of efficiently solving classical optimisation problems on quantum computers is tantalizing. As many such problems can be mapped to approximating the ground state of spin-glasses, paradigmatic models for studying many-body localisation, it is natural to ask if some of the intuition coming from quantum statistical mechanics can help guide the construction of novel quantum optimisation algorithms. In this work, we discuss how continuous reverse quantum annealing crossing a many-body localisation transition can be accelerated by considering the density of Landau-Zener crossings as the system is quenched. We provide an interpretation of this behaviour in terms of an effective Fokker-Planck equation for the success probability of the algorithm. This interpretation suggests an improvement in the required annealing time as a function of the system size N, which goes from O(poly(N)) to O(1) for reference states with non-vanishing energy density. We show that the continuous dynamics can be Trotterised with a number of steps that remains modest as system size increases, making it appealing for near-term devices. For the resulting circuit implementation, we provide a quantitative strategy for determining the parameters of the time-dependent Hamiltonian. We compare the performance of our digitised algorithm, which we call FRIO, against that of the QAOA for finding the ground state of spin-glass problems, in particular the SK model. The numerical results suggest that with suitably selected circuit parameters which can be efficiently found using thermalizing dynamics, FRIO almost always outperforms the conventional QAOA ansatz with pre-optimized angles.
Spin glasses are disordered magnets with random interactions that are, generally, in conflict with each other. Finding the ground states of spin glasses is not only essential for the understanding of the nature of disordered magnetic and other physical systems, but also useful to solve a broad array of hard combinatorial optimization problems across multiple disciplines. Despite decades-long efforts, an algorithm with both high accuracy and high efficiency is still lacking. Here we introduce DIRAC - a deep reinforcement learning framework, which can be trained purely on small-scale spin glass instances and then applied to arbitrarily large ones. DIRAC displays better scalability than other methods and can be leveraged to enhance any thermal annealing method. Extensive calculations on 2D, 3D and 4D Edwards-Anderson spin glass instances demonstrate the superior performance of DIRAC over existing methods. As many hard combinatorial optimization problems have Ising spin glass formulations, our results suggest a promising tool in solving these hard problems. Moreover, the presented algorithm will help us better understand the nature of the low-temperature spin-glass phase, which is a fundamental challenge in statistical physics.
We study a quantum annealer where bosons mediate the Ising-type interactions between qubits. We compare the efficiency of ground state preparation for direct and mediated couplings, for which Ising and spin-boson Hamiltonian are employed respectively. This comparison is done numerically for a small frustrated antiferromagnet, with a careful choice of the optimal adiabatic passage that reveals the features of the boson-mediated interactions. Those features can be explained by taking into account what we called excited solutions: states with the same spin correlations as the ground-state but with a larger bosonic occupancy. For similar frequencies of the bosons and qubits, the performance of quantum annealing depends on how excited solutions interchange population with local spin errors. We report an enhancement of quantum annealing thanks to this interchange under certain circumstances.
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.