Role of quantum fluctuation in inducing ergodicity in the spin glass phase and its effect in quantum annealing.

We review the numerical studies on the critical behaviour of the quantum Sherrington-Kirkpatrick (SK) spin glass model, which indicate that a quantum critical behaviour is observed up to a low but non-zero value of temperature. We revisit the numerical investigations on the spin glass order parameter distributions, which identify a low temperature along with high transverse field spin glass phase where the order parameter distribution becomes a delta function in the thermodynamic limit indicating the restoration of replica symmetry and ergodic nature of the system. In the remaining spin glass phase associated with high temperature and low transverse field, the observed distribution is broad akin to the Parisi order parameter distribution. This essentially indicates the non-ergodic behaviour of the system. We further discuss the annealing dynamics studies on the quantum SK model. Such investigations reveal the system size independence of annealing time when the annealing paths go through the ergodic spin glass region. Interestingly, when such dynamics are performed in the non-ergodic spin glass phase the annealing time becomes an increasing function of the system size. Spin autocorrelation shows faster relaxation in the ergodic spin glass region compared with that found in the non-ergodic spin glass region. This article is part of the theme issue 'Quantum annealing and computation: challenges and perspectives'.

Quantum annealing: an overview.

In this review, after providing the basic physical concept behind quantum annealing (or adiabatic quantum computation), we present an overview of some recent theoretical as well as experimental developments pointing to the issues which are still debated. With a brief discussion on the fundamental ideas of continuous and discontinuous quantum phase transitions, we discuss the Kibble-Zurek scaling of defect generation following a ramping of a quantum many body system across a quantum critical point. In the process, we discuss associated models, both pure and disordered, and shed light on implementations and some recent applications of the quantum annealing protocols. Furthermore, we discuss the effect of environmental coupling on quantum annealing. Some possible ways to speed up the annealing protocol in closed systems are elaborated upon: we especially focus on the recipes to avoid discontinuous quantum phase transitions occurring in some models where energy gaps vanish exponentially with the system size. This article is part of the theme issue 'Quantum annealing and computation: challenges and perspectives'.

Optimizing radiotherapy plans for cancer treatment with Tensor Networks.

We present a novel application of Tensor Network methods in cancer treatment as a potential tool to solve the dose optimization problem in radiotherapy. In particular, the intensity-modulated radiation therapy technique-that allows treating irregular and inhomogeneous tumors while reducing the radiation toxicity on healthy organs-is based on the optimization problem of the beamlets intensities that shall result in a maximal delivery of the therapy dose to cancer while avoiding the organs at risk of being damaged by the radiation. The resulting optimization problem is expressed as a cost function to be optimized. Here, we map the cost function into an Ising-like Hamiltonian, describing a system of long-range interacting qubits. Finally, we solve the dose optimization problem by finding the ground-state of the Hamiltonian using a Tree Tensor Network algorithm. In particular, we present an anatomical scenario exemplifying a prostate cancer treatment. A similar approach can be applied to future hybrid classical-quantum algorithms, paving the way for the use of quantum technologies in future medical treatments.