outer space

With information from the University of Michigan – 02/18/2022

The simulation methods the team used combine with every aspect of the curved spacetime to represent the fact that the properties of gravity come from the simulations.

[Imagem: Enrico Rinaldi/Umich/RIKEN/A. Silvestri]

**3D duality**

What if everything around us was just a hologram?

The problem might be – and a team of physicists from Japan and the US are using quantum computing and machine learning to better understand the idea, which is called 3D binary – or simply the holographic universe.

3D duality is a mathematical conjecture linking theories of particles and their interactions, known as the Standard Model of physics, with Einstein’s theory of gravity. This conjecture suggests that gravitational theory and particle theory are mathematically equivalent: what happens mathematically in gravitational theory happens in particle theory and vice versa.

The two theories describe different dimensions, but the number of dimensions they describe varies with only one difference. So in the form of a black hole, for example, gravity exists in three dimensions, while the theory of particles exists in two dimensions, on its surface – a flat disk.

To visualize this, think again about the black hole, which envelops spacetime due to its enormous mass. The gravity of a black hole, present in three dimensions, is mathematically related to the particles that dance above it, in two dimensions. Therefore, a black hole exists in three-dimensional space, but we see it as a projection through particles.

Some scientists hypothesize that the entire universe follows the same principle, being a three-dimensional projection of particles, and this may lead to a fixed quantum theory of gravity.

“In Einstein’s theory of general relativity, there are no particles – there is only spacetime. And in the Standard Model of particle physics, there is no gravity, there are only particles,” explains Enrico Rinaldi, from the University of Michigan, USA. “Connecting the two different theories is an age-old question in physics – something people have been trying to do since the last century.”

**In search of reality**

Since there are no powerful enough supercomputers to simulate all of this, Rinaldi and his colleagues are evaluating how to investigate 3D duality using quantum computers and deep learning to solve mathematical problems, primarily involving finding a low-energy state of systems called a quantum matrix.

Quantum matrix models are representations of particle theory. Since the 3D duality implies that what happens mathematically in a system that represents particle theory will similarly affect a system that represents gravity, solving the quantum matrix model can reveal information about gravity.

The team used two matrix models that are simple enough to be solved using traditional methods, but have all the properties of the more complex matrix models used to describe black holes in 2D.

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

You can think of the numbers in the matrix models as grains of sand, Rinaldi compares. When the sand is level, this is the basic state of the form. But if there are ripples in the sand, you need to find a way to level it. For example, put sand in a bucket and hit it.

“It’s really important to understand what that base state is like, because then you can create things out of it,” Rinaldi explained. “So, for a given substance, knowing the base state is like knowing, say, whether it is a conductor, or whether it is a superconductor, or whether it is really strong or weak. But finding this base state among all possible states is A very difficult task. That is why we use these numerical methods.”

**Quantum circles**

To do this, the researchers first looked at quantum circuits. In this method, quantum circuits are represented by wires, and each qubit, or piece of quantum information, is a wire. On top of the wires are logic gates, which are quantum processes that dictate how information passes through the wires.

“You can read it as music, from left to right,” Rinaldi explains. “If you read this as music, you’re basically converting qubits into something new with each step. But you don’t know what operations you should be doing as you go along, what notes you should play. Animating process [como no balde de areia] We will modify all these logic gates to make them take the correct shape, so that at the end of the whole process they reach the base state. So you have all this music, and if you play it right, you eventually get the base state.”

**deep learning**

Then the researchers wanted to compare the use of the quantum circuit method with the method of deep learning. Deep learning is a type of artificial intelligence that uses a neural network approach, a series of algorithms that try to find relationships in data, similar to how the human brain works.

Neural networks are used to design facial recognition software, feeding thousands of images of faces – from which they draw specific facial features to recognize individual images or create new faces of nonexistent people.

First of all, the team defined the mathematical description of the quantum state of their matrix model, called a quantum wave function. Then they used a special neural network to find the wavefunction of the matrix with the lowest possible energy – its ground state. The neural network numbers go through an iterative “optimization” process to find the base state of the matrix model, as if hitting the sand bucket so that all the grains are flat.

**3D black hole**

Both approaches found the base case for both examined matrix models.

“Other methods that people commonly use can find ground state energy, but not the entire wave function structure. We show you how to get all the ground state information using these new emerging technologies, quantum computers and deep learning.”

However, quantum circuits have been limited by the small number of available qubits. Current quantum devices can handle only a few dozen qubits: adding lines to your score or grains of sand to your bucket gets expensive, and the more you add, the less accurate your music playback.

But what do these results tell us about the hologram inside the black hole?

“Because these matrices are a potential representation of a special kind of black hole, if we know how the matrices are organized and what their properties are, we can know, for example, what the black hole inside looks like? Where is the black hole? Where?” Rinaldi said. The questions would be a step towards developing a quantum theory of gravity.

**index:**

condition: *Matrix model simulation using quantum computing, deep learning, and lattice Monte Carlo*

Authors: Enrico Rinaldi, Ziggy Han, Mohamed Hassan, Yuan Feng, Franco Nuri, Michael McGuigan, Masanori Hanada

Magazine: PRX Quantum

Volume: 3, 010324

DOI: 10.1103/PRXQuantum.3.010324

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