Adiabatic Quantum Computing and Quantum Annealing

Abstract

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.

A Review of Machine Learning Classification Using Quantum Annealing for Real-World Applications

“…Quantum annealing is a heuristic search algorithm for finding the lowest energy state by traversing over the solution landscape [19]. The lowest energy state is achieved through the evolution of a time-dependent Hamiltonian.…”

“…The solution returned by the quantum annealing process may not end up in the ground state because of the influences of external energy sources [19]. Hence, in practice, the probability of the system staying in a low energy state might be low for certain problems.…”

Kuantum Uyarlamalı Genetik Algoritmalar için Çözüm Kalitesini Artıracak Yeni Bir Yaklaşım

“…Yani aralarındaki mesafe ne olursa olsun birbirinden etkilenen parçacıkların olduğunu ifade etmektedir [19]. Bu daha çok adyabetik (adiabatic) kuantum bilgisayarlarda karşımıza çıkan bir kavramdır [20].…”

Review of Sublinear Modeling in Probabilistic Graphical Models by Statistical Mechanical Informatics and Statistical Machine Learning Theory

“…(10. 24) In the case of a continuous state space = (−∞, +∞), the posterior and prior probabilistic models correspond to Gaussian graphical models, and the statistical trajectory in Eqs. (10.23) and (10.24) can be exactly computed by means of the multi-dimensional Gaussian integral formula [30].…”

“…However, it is well known that many applicable formulations in data sciences as well as computational sciences can be reduced to combinatorial problems with some constraint conditions which can be regarded as an Ising Model in statistical mechanical informatics [18,19]. Moreover, much interest has focused on applying quantum annealing as a novel high-speed optimization technology to massive optimization problems [20][21][22][23][24].…”