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This is an advance summary of a forthcoming article in the Oxford Research Encyclopedia of Physics. Please check back later for the full article. Adiabatic quantum computing (AQC) is a model of computation that uses quantum mechanical processes operating under adiabatic conditions. As a form of universal quantum computation, AQC employs the principles of superposition, tunneling, and entanglement that manifest in quantum physical systems. The AQC model of quantum computing is distinguished using dynamical evolution that is slow with respect to the time and energy scales of the underlying physical systems. This adiabatic condition enforces the promise that the quantum computational state will remain well defined and controllable, thus enabling the development of new algorithmic principles. Several notable algorithms developed within the AQC model include methods for solving unstructured search and combinatorial optimization problems. In an idealized setting, the asymptotic complexity analyses of these algorithms indicate that computational speed ups may be possible relative to state-of-the-art conventional methods. However, the presence of non-ideal conditions, including non-adiabatic dynamics, non-zero temperature, and physical noise complicate the assessment of the potential computational performance. A relaxation of the adiabatic condition is captured in the complementary computational heuristic of quantum annealing, which accommodates physical systems operating at finite-temperature and in open environments. While quantum annealing (QA) provides a more accurate model for the behavior of actual quantum physical systems, the possibility of non-adiabatic effects obscures a clear separation with conventional computing complexity. A series of technological advances in the control of quantum physical systems have enabled experimental realizations of AQC and QA. Prominent examples include demonstrations using superconducting electronics, which encode quantum information in the magnetic flux induced by very weak current operating at cryogenic temperatures. A family of devices specialized for unconstrained optimization problems have been applied to solving a variety of specific domains including logistics, finance, science, and numerical analysis. An accompanying infrastructure has also developed to support these experimental demonstrations and to enable access to a broader community of users. Although AQC is most commonly applied in superconducting technologies, alternative approaches include optically trapped neutral atoms and ion-trapped systems. The significant progress in our understanding of AQC has revealed several open topics that continue to motivate research into this model of quantum computation. Foremost is the development of methods for fault-tolerant operation that will ensure the scalability of AQC for solving large-scale problems. In addition, unequivocal experimental demonstrations are needed that differentiate the computational power of AQC and its variants from conventional computing approaches. This will also require advances in the fabrication and control of quantum physical systems under the adiabatic restrictions.

Quantum annealing solves combinatorial optimization problems by finding the energetic ground states of an embedded Hamiltonian. However, quantum annealing dynamics under the embedded Hamiltonian may violate the principles of adiabatic evolution and generate excitations that correspond to errors in the computed solution. Here we empirically benchmark the probability of chain breaks and identify sweet spots for solving a suite of embedded Hamiltonians. We further correlate the physical location of chain breaks in the quantum annealing hardware with the underlying embedding technique and use these localized rates in a tailored post-processing strategies. Our results demonstrate how to use characterization of the quantum annealing hardware to tune the embedded Hamiltonian and remove computational errors.