Quantum Gravity and Computation

Lucién Hardy

László Gyöngyösi

The theory of quantum gravity is aimed to fuse general relativity with quantum theory into a more fundamental framework.The space of quantum gravity provides both the non-fixed causality of general relativity and the quantum uncertainty of quantum mechanics.In a quantum gravity scenario, the causal structure is indefinite and the processes are causally non-separable.In this work, we provide a model for the information processing structure of quantum gravity.We show that the quantum gravity environment is an information resource-pool from which valuable information can be extracted.We analyze the structure of the quantum gravity space and the entanglement of the space-time geometry.We study the information transfer capabilities of quantum gravity space and define the quantum gravity channel.We reveal that the quantum gravity space acts as a background noise on the local environment states.We characterize the properties of the noise of the quantum gravity space and show that it allows the separate local parties to simulate remote outputs from the local environment state, through the process of remote simulation.We characterize the information transfer of the gravity space and the correlation measure functions of the gravity channel.We investigate the process of stimulated storage for quantum gravity memories, a phenomenon that exploits the information resource-pool property of quantum gravity.The results confirm the perception that the benefits of the quantum gravity space can be exploited in quantum computations, particularly in the development of quantum computers.

H.‐H. von Borzeszkowski, H.‐J. Treder

S. Gudder

Lior Cohen, Anthony J. Brady, Zichang Huang +4 more

The problem of simulating complex quantum processes on classical computers gave rise to the field of quantum simulations. Quantum simulators solve problems, such as Boson sampling, where classical counterparts fail. In another field of physics, the unification of general relativity and quantum theory is one of the greatest challenges of our time. One leading approach is Loop Quantum Gravity (LQG). Here, we connect these two fields and design a linear-optical simulator such that the evolution of the optical quantum gates simulates the spinfoam amplitudes of LQG. It has been shown that computing transition amplitudes in simple quantum field theories falls into the class BQP -- which strongly suggests that computing transition amplitudes of LQG are classically intractable. Therefore, these amplitudes are efficiently computable with universal quantum computers which are, alas, possibly decades away. We propose here an alternative special-purpose linear-optical quantum computer, which can be implemented using current technologies. This machine is capable of efficiently computing these quantities. This work opens a new way to relate quantum gravity to quantum information and will expand our understanding of the theory.

Lior Cohen, Anthony J. Brady, Zichang Huang +4 more

The problem of simulating complex quantum processes on classical computers gave rise to the field of quantum simulations. Quantum simulators solve problems, such as boson sampling, where classical counterparts fail. In another field of physics, the unification of general relativity and quantum theory is one of the greatest challenges of our time. One leading approach is loop quantum gravity (LQG). Here, we connect these two fields and design a linear-optical simulator such that the evolution of the optical quantum gates simulates the spin-foam amplitudes of LQG. It has been shown that computing transition amplitudes in simple quantum field theories falls into the bounded-error quantum polynomial time class, which strongly suggests that computing transition amplitudes of LQG are classically intractable. Therefore, these amplitudes are efficiently computable with universal quantum computers, which are, alas, possibly decades away. We propose here an alternative special-purpose linear-optical quantum computer that can be implemented using current technologies. This machine is capable of efficiently computing these quantities. This work opens a new way to relate quantum gravity to quantum information and will expand our understanding of the theory.