Images on the Blackhole captured through Quantum Computing Simulation Methods.

Our entire universe, according to scientists, is a holographic projection of particles. And given that the black hole is considered an enormous particle (contains a massive mass), it can actually warp an entire space-time. Enrico Rinaldi, a Tokyo-based research scientist from the University of Michigan Department of Physics, introduced the use of Holographic Duality in formulating a solution that can describe the gravity of the black hole. The simulations depict the reality wherein the gravitational qualities emerge from the simulations, and the simulation methods blend with each side of the curved space-time.

Holographic duality is a mathematical conjecture that links particle theories and interactions with gravity theory. This conjecture implies that the theories of gravity and particles are mathematically equivalent: whatever happens in the theory of gravity also happens in the theory of particles, and vice versa.

Both theories explain various dimensions, but they differ by one in the number of dimensions they describe. So, for example, gravity exists in three dimensions inside the geometry of a black hole, but particle physics lives in two dimensions on its surface—a flat disk. The three-dimensional gravity of the black hole connects mathematically to the two-dimensional particles dancing above it. As a result, a black hole exists in three dimensions, yet we see it through particle projections.

Rinaldi and his co-authors were able to examine ways how to probe holographic duality using quantum computing and deep learning to find the lowest energy state of mathematical problems called quantum matrix models.

 Connecting the two different theories is a longstanding issue in physics—something people have been trying to do since the last century.

Enrico Rinaldi, a research scientist in the U-M Department of Physics

Particle theory is represented in the quantum matrix models. Because holographic duality implies that what happens mathematically in a system representing particle theory will also affect a system representing gravity, solving such a quantum matrix model could provide gravity information.

The matrix models are numbers that represent objects in string theory, which is a framework in which one-dimensional strings represent particles in particle theory. Researchers are aiming to determine the precise arrangement of particles in the system that represents the system’s lowest energy state, called the ground state when they solve matrix models like these. Nothing happens to the system in its natural condition unless you add anything to it that causes it to be perturbed.

We hope that by understanding the properties of this particle theory through the numerical experiments, we understand something about gravity. Unfortunately it’s still not easy to solve the particle theories. And that’s where the computers can help us.

Enrico Rinaldi, a research scientist in the U-M Department of Physics

So for a material, knowing the ground state is like knowing, for example, if it’s a conductor, or if it’s a super conductor, or if it’s really strong, or if it’s weak. But finding this ground state among all the possible states is quite a difficult task. That’s why we are using these numerical methods.

If you read it as music, you’re basically transforming the qubits from the beginning into something new each step. But you don’t know which operations you should do as you go along, which notes to play. The shaking process will tweak all these gates to make them take the correct form such that at the end of the entire process, you reach the ground state. So you have all this music, and if you play it right, at the end, you have the ground state.

Enrico Rinaldi, a research scientist in the U-M Department of Physics

The numbers in the matrix models can be thought of as grains of sand, according to Rinaldi. The model’s ground condition is when the sand is level. However, if the sand has ripples, then it is essential to find a means to smooth it out. To find a solution, the researchers turned to quantum circuits. The quantum circuits are represented as wires in this manner, and each qubit, or quantum information bit, represents a wire. Gates, which are quantum operations defining how the information will move down the wires, are placed on top of the cables.

The researchers in Rinaldi’s work define the quantum wave function, which is a mathematical description of the quantum state of their matrix model. Then they utilize a unique neural network to determine the matrix’s wave function with the least amount of energy—its ground state. To obtain the matrix model’s ground state, the neural network’s numbers go through an iterative “optimization” process, tapping the bucket of sand until 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. 

We have shown how to get the full information about the ground state using these new emerging technologies, quantum computers and deep learning.

Because these matrices are one possible representation for a special type of black hole, if we know how the matrices are arranged and what their properties are, we can know, for example, what a black hole looks like on the inside. What is on the event horizon for a black hole? Where does it come from? Answering these questions would be a step towards realizing a quantum theory of gravity.

Enrico Rinaldi, a research scientist in the U-M Department of Physics

The findings, according to Rinaldi, set a high bar for future work on quantum and machine learning algorithms that can be used to examine quantum gravity using the concept of holographic duality.

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