At present, scientists are studying the gravitational pull of black holes through two simulation methods of quantum computing and deep learning, and solving quantum matrix models that can describe this gravitational force.
What's in the black hole? Is everything that exists around human beings just a holographic projection of particles?
To answer these questions, the team of physicist Enrico Rinaldi of the University of Michigan understands the concept of holographic duality through quantum computing and deep learning. The findings were recently published in the Physics Review X Series - Quantum (PRX Quantum).
Image by Enrico Rinaldi
As in this image, the graph of curved space-time connects two simulation methods, quantum computing and deep learning (deep learning is a machine learning using a neural network approach). In the lower left, the deep learning method is shown in a dot plot (i.e., a neural network), while the quantum circuit method in the upper right is represented by straight lines, squares, and circles corresponding to qubits and qubit gates, respectively. The simulation method merges with each side of curved space-time to indicate that the gravitational study was achieved by simulation.
Holographic duality is a mathematical conjecture that links the theory of particles and their interactions to the theory of gravity. This conjecture suggests that gravity theory and particle theory are mathematically equivalent: what happens in gravity theory also happens in particle theory, and vice versa. The two theories describe different dimensions, with gravity existing in three-dimensional space inside a black hole and particle theory in two-dimensional space.
Image of M87 supermassive black hole under polarized light
To understand this, imagine a black hole. Black holes produce space-time distortions due to massive masses. The gravitational pull of a black hole that exists in three-dimensional space is mathematically linked to particles that exist in two-dimensional space. So, although black holes exist in three-dimensional space, the black holes we see are projected through particles in two-dimensional space.
Some scientists have even speculated that the entire universe is a holographic projection of particles, which could trigger a consistent theory of quantum gravity.
"In Einstein's general theory of relativity, there are no particles, only space-time. In the Standard Model of particle physics, there is no gravitational force, only particles. "Linking these two different theories is a long-standing problem in physics — something that people have been trying to do since the last century." ”
In this study, Rinaldi and his team used quantum computing and deep learning to probe holographic duality to discover the lowest energy states of the quantum matrix model. The team used two matrix models that were simple enough to be solved in traditional ways to describe the more complex matrix model of black holes through holographic duality.
The quantum matrix model represents particle theory. Holographic duality shows that mathematically, what happens in a system that represents particle theory also affects a system that represents gravity. Therefore, solving such a quantum matrix model can reveal information about gravity.
"We want to understand the nature of this particle theory through numerical experiments, and thus learn some information about gravity," Rinaldi said, "unfortunately, solving particle theory is still not easy." And that's where computers can help us. ”
To solve such a matrix model, researchers must first find the specific configuration of the particles in the system that represent the lowest energy state of the system, that is, the ground state.
Rinaldi explains that it is important to understand the ground state, for example, for a material, the ground state means whether it is a conductor or a superconductor, strong electricity or weak current. "You can think of the numbers in a matrix model as grains of sand, and when the sand is horizontal, that's the ground state of the model."
To solve this problem, the researchers first studied quantum circuits. In this method, quantum lines are represented by wires, and each qubit is a wire. At the upper end of the wire is a qubit gate that can be manipulated through the gate to indicate how information is transmitted on the wire.
So how do you find the ground state through a quantum circuit? Rinaldi likens it to music, and in experiments does not know how to manipulate qubits, just as it does not know which notes to play. The vibration process adjusts all the quantum gates, eventually causing them to appear in the correct form, reaching the ground state. Just as by playing many times, you finally find the right note, play it well, and you have a ground state.
Subsequently, the researchers also used deep learning methods as a comparative study. Deep learning is a type of machine learning that uses a neural network approach, a series of algorithms that try to find relationships between data, similar to how the human brain works.
Neural networks are used to design facial recognition software that, by receiving thousands of images of faces, from which neural networks draw features of faces to identify individual images or generate new faces of people who don't exist.
The researchers defined the mathematical description of the matrix model quantum state as a quantum wave function. They then used a special neural network to look for the wave function with the lowest energy, the ground state. The numbers of the neural network find the ground state of the matrix model through an iterative "optimization" process. Just as a bucket of sand is struck, each grain of sand is balanced.
In both methods, the researchers were able to find ground states for both matrix models, but the quantum circuits were limited by the number of qubits. The quantum devices currently applied by the team can only process a few dozen qubits.
"People usually use other methods to find the energy of the ground state, but they can't get the overall structure of the wave function. We've shown how these emerging technologies, namely quantum computers and deep learning, can be used to capture all the information about the ground state. "Since these matrices may represent a special type of black hole, if we know how these matrices are arranged, and their properties, we can know what the interior of a black hole looks like." What's on the surface of a black hole? Where did it come from? Answering these questions would be a step towards realizing the theory of quantum gravity. ”
The team's findings provide an important benchmark for future research into quantum computing and machine learning algorithms, and researchers are able to use holographic duality to study quantum gravity. Rinaldi will work with more scientists to see how these algorithmic results can be extended to larger matrix models and their robustness to the introduction of "noise" or error interference (robustness is the ability of a control system to maintain certain performance under the perturbation of certain parameters).