Quantum Spin Glasses (QSG) is the prototype of disordered systems whose dynamics is affected strongly by quantum effects. Currently, there is not a clear picture of the critical phase of a quantum spin glass in spatial dimension D ≥ 2. We shall specialize in the simplest non-trivial case, namely D=2. As a matter of fact, there are two competing theories and we aim at finding out which is the correct one by providing the answer to four important questions regarding the Quantum Ising spin-glass transition at zero temperature (i.e., L=∞ Trotter’s imaginary-time slices [1]): i)What is the value of the quantum-dynamical z exponent? (the gap scales at the critical point as Δ∼L-z); ii)How should the Finite Size Scaling analysis [2] be carried out when exponent z is unknown? iii)Does exponent z depend on the considered symmetry sector? iv) What are the critical exponents for this universality class [1,2]? These questions are addressed through a combination of exact diagonalization of the Transfer Matrix [1] (for small system sizes, up to L=6) which helps to control the L→∞ limit) and Quantum Monte Carlo (which reaches larger values of L). Beyond pure scientific curiosity, the study is bearer of important technological implications in light of the second quantum revolution, where a detailed understanding of mesoscopic quantum systems can unlock new and potentially game-changing technologies. One of the central questions that our numerical studies aim at answering (the scaling of the spectral gap with respect to the system size) is at the core of the quantum computational complexity of the adiabatic quantum algorithm proposed for some classical optimization problems [3]. Quantum annealers (i.e., devices implementing the Quantum Annealing algorithm), fall in the category of quantum spin glasses. Therefore, our results have immediate technological implications in the exploding field of quantum computing, through the assessment of the theoretical bound to the performance of Quantum Annealers solving instances of hard optimization problems (specifically spin glasses). Indeed, finding the ground state of a spin glass is a prototypical NP-complete problem [4]. Commercial prototypes of Quantum Annealers already exist [5], with a new generation of hardware under development. Our numerical approach pushes algorithms for quantum Ising spin glasses beyond the present limits and led us to develop two novel, highly tuned, multi GPU codes: CQSG and EDQSG.