February 3, 2023

# Black Hole, Quantum Computing and Holographic Duality

A physicist at University of Michigan is using quantum computing and machine learning to better understand the idea that everything around us could be just a hologram, the famous so-called holographic duality.

Holographic duality is a mathematical conjecture that connects theories of particles and their interactions with the theory of gravity. This conjecture suggests that the theory of gravity and the theory of particles are mathematically equivalent: what happens mathematically in the theory of gravity happens in the theory of particles, and vice versa.

Both theories describe different dimensions, but the number of dimensions they describe differs by one. So inside the shape of a black hole, for example, gravity exists in three dimensions while a particle theory exists in two dimensions, on its surface—a flat disk.

To envision this, think again of the black hole, which warps space-time because of its immense mass. The gravity of the black hole, which exists in three dimensions, connects mathematically to the particles dancing above it, in two dimensions. Therefore, a black hole exists in a three dimensional space, but we see it as projected through particles.

Some scientists theorize our entire universe is a holographic projection of particles, and this could lead to a consistent quantum theory of gravity.

The team has examined how to probe holographic duality using quantum computing and deep learning to find the lowest energy state of mathematical problems called quantum matrix models.

These quantum matrix models are representations of particle theory. Because holographic duality suggests that what happens, mathematically, in a system that represents particle theory will similarly affect a system that represents gravity, solving such a quantum matrix model could reveal information about gravity.

For the study, the team used two matrix models simple enough to be solved using traditional methods, but which have all of the features of more complicated matrix models used to describe black holes through the holographic duality.

These matrix models are blocks of numbers that represent objects in string theory, which is a framework in which particles in particle theory are represented by one-dimensional strings. When researchers solve matrix models like these, they are trying to find the specific configuration of particles in the system that represent the system’s lowest energy state, called the ground state. In the ground state, nothing happens to the system unless you add something to it that perturbs it.

The researchers have defined the mathematical description of the quantum state of their matrix model, called the quantum wave function. Then they use a special neural network in order to find the wave function of the matrix with the lowest possible energy—its ground state. The numbers of the neural network run through an iterative “optimization” process to find the matrix model’s ground state, tapping the bucket of sand so all of its grains are leveled.

In both approaches, the researchers were able to find the ground state of both matrix models they examined, but the quantum circuits are limited by a small number of qubits. (SciTechDaily)

The study has been published in the journal PRX Quantum.