Enrico Rinaldi, research scientist in the University of Michigan Department of Physics, is using two simulation methods to solve quantum matrix models which can describe what the gravity of a black hole looks like. In this image, a pictorial representation of curved space time connects the two simulation methods. On the bottom, a deep learning method is represented by graphs of points (neural network), while the quantum circuit method on top is represented by lines, squares and circles (qubits and gates). The simulation methods merge with each side of the curved space time to represent the fact that gravity properties come out of the simulations. Rinaldi is based in Tokyo and hosted by the Theoretical Quantum Physics Laboratory at the Cluster for Pioneering Research at RIKEN, Wako. Image credit: Enrico Rinaldi/U-M, RIKEN and A. Silvestri.
Dude, what if everything around us was just … a hologram?
The thing is, it could be-and a University of Michigan physicist is using quantum computing and machine learning to better understand the idea, 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.
"In Einstein's General Relativity theory, there are no particles-there's just space-time. And in the Standard Model of particle physics, there's no gravity, there's just particles," said Enrico Rinaldi, a research scientist in the U-M Department of Physics. "Connecting the two different theories is a longstanding issue in physics-something people have been trying to do since the last century."
In a study published in the journal PRX Quantum, Rinaldi and his co-authors examine 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, Rinaldi and his 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.
"We hope that by understanding the properties of this particle theory through the numerical experiments, we understand something about gravity," said Rinaldi, who is based in Tokyo and hosted by the Theoretical Quantum Physics Laboratory at the Cluster for Pioneering Research at RIKEN, Wako. "Unfortunately it's still not easy to solve the particle theories. And that's where the computers can help us."
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.
"It's really important to understand what this ground state looks like, because then you can create things from it," Rinaldi said. "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."
You can think of the numbers in the matrix models as grains of sand, Rinaldi says. When the sand is level, that's the model's ground state. But if there are ripples in the sand, you have to find a way to level them out. To solve this, the researchers first looked to quantum circuits. In this method, the quantum circuits are represented by wires, and each qubit, or bit of quantum information, is a wire. On top of the wires are gates, which are quantum operations dictating how information will pass along the wires.
