Prelude to Simulations of Loop Quantum Gravity on Adiabatic Quantum Computers

Abstract

The article addresses the possibility of implementing spin network states, used in the loop quantum gravity approach to Planck scale physics on an adiabatic quantum computer. The discussion focuses on applying currently available technologies and analyzes a concrete example of a D-Wave machine. It is introduced a class of simple spin network states which can be implemented on the Chimera graph architecture of the D-Wave quantum processor. However, extension beyond the currently available quantum processor topologies is required to simulate more sophisticated spin network states. This may inspire new generations of adiabatic quantum computers. A possibility of simulating loop quantum gravity is discussed, and a method of solving a graph non-changing scalar (Hamiltonian) constraint with the use of adiabatic quantum computations is proposed. The presented results establish a basis for the future simulations of Planck scale physics, specifically quantum cosmological configurations, on quantum annealers.

Algorithmic approach to cosmological coherent state expectation values in loop quantum gravity

“…In that regard, it is to be observed that LQG also starts to benefit from the field of quantum simulations [51,52]. Platforms based on linear optics [53], nuclear magnetic resonance (NMR) [54], adiabatic methods [55] used e.g. by D-wave machine, or famous IBM devices utilizing superconducting qubits [56] are now being conceptually exploited.…”

On Propagation in Loop Quantum Gravity

“…In fact, our paper suggests a numerical proof of propagation both for Lorentzian and Euclidean GR with gauge group SU(2) by diagonalising the volume operator on four valent vertices numerically, which is feasable since the matrix elements of its fourth power are available analytically [32]. We leave this to future work which may benefit from modern numerical [23][24][25][26] methods and machine learning [27,28] and/or quantum computing [29][30][31] techniques. Finally, in our example, we considered only a tiny subset of solutions as we took only children of "first generation" into account.…”

“…We state in more detail why these features extend to generic arbitrarily large graphs and are extremely likely to the SU(2) case in both Euclidean and Lorentzian signatures. In particular, we encourage the application of numerical methods in LQG [23][24][25][26] perhaps combined with modern machine learning [27,28] or quantum computing [29][30][31] techniques in order to perform an actual SU(2) calculation involving the SU(2) volume operator at least numerically using the explicitly known matrix elements of its fourth power [32] in order to complete the rigorous proof in the SU(2) theory.…”

Quantum speed limit and stability of coherent states in quantum gravity

“…In fact, pinpointing a suitable candidate for semi-classical models will create a crucial fundamental for the years to come: it is predicted that LQG will soon start to enter the realm of quantum simulations [38,39]. Several platforms, for example those utilizing linear optics [40], adiabatic (quantum) computation [41], nuclear magnetic resonance techniques [42] or superconducting qubits [43] are considered. Hence, before the era of quantum simulations in LQG, preparatory work-like in this letter-aiming at making complex objects in LQG computable (by both classical and quantum machines) shall be in focus.…”