Quantum simulations of a qubit of space

Abstract

In loop quantum gravity approach to Planck scale physics, quantum geometry is represented by superposition of the so-called spin network states. In the recent literature, a class of spin networks promising from the perspective of quantum simulations of quantum gravitational systems has been studied. In this case, the spin network states are represented by graphs with four-valent nodes, and two dimensional intertwiner Hilbert spaces (qubits of space) attached to them. In this article, construction of quantum circuits for a general intertwiner qubit is presented. The obtained circuits are simulated on 5-qubit (Yorktown) and 15-qubit (Melbourne) IBM superconducting quantum computers, giving satisfactory fidelities. The circuits provide building blocks for quantum simulations of complex spin networks in the future. Furthermore, a class od maximally entangled states of spin networks is introduced. As an example of application, attempts to determine transition amplitudes for a monopole and a dipole spin networks with the use of superconducting quantum processor are made.

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

“…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. However, while quantum simulations aim to use speedup offered by quantum computers, severe technical limitations will necessitate a clever pre-processsing of complex inputs.…”

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.…”

Prelude to Simulations of Loop Quantum Gravity on Adiabatic Quantum Computers

“…The above definitions of the basis states for a qubit have recently been considered in the context of universal quantum computations in Refs. Li et al (2019), Mielczarek (2019), Czelusta and Mielczarek (2021). Alternatively, it is convenient to construct our qubit states such that they are eigenvectors of the volume operator [see e.g.…”