A physicist at the University of Michigan is utilizing quantum computing and machine learning for a better understanding of the concept known as holographic duality.
Holographic duality is mathematical speculation connecting particle theories and their interactions with gravity theory. This hypothesis implies that the theories of gravity and particles are mathematically identical: what occurs mathematically in the theory of gravity occurs mathematically in the theory of particles, and conversely.
Both theories describe various dimensions, but the number of dimensions described by each differs by one. Gravity, for example, is prevailing in three dimensions inside the shape of a black hole, whereas particle theory is prevailing in two dimensions, on its surface—a flat disc.
Consider the black hole, which warps space-time due to its enormous mass. The gravity of the black hole, prevailing in three dimensions, mathematically connects to the particles dancing overhead, prevailing in two dimensions. As a result, a black hole prevails in a three-dimensional space, but we are viewing it as a projection through particles.
According to some scientists, our whole universe is a holographic projection of particles, leading to a dependable quantum theory of gravity.
There are no particles in Einstein’s General Theory of Relativity; there is only space-time and in the Standard Model of particle physics, there is no gravity, only particles,” said Enrico Rinaldi, a research scientist in the University of Michigan’s Department of Physics. Associating the two different theories is a long-lasting complication in physics—something people have been attempting to do for over a century.
Rinaldi and his co-authors investigate the way for probing holographic duality by utilizing quantum computing and deep learning for detecting the lowest energy state of mathematical problems known as quantum matrix models in a study published in the journal PRX Quantum.
Particle theory is represented by these quantum matrix models. Because holographic duality implies that whatever is occurring mathematically in a system representing particle theory will similarly influence a system representing gravity. Disclosing details regarding gravity is possible when such a quantum matrix model is solved.
Rinaldi and his colleagues utilized two matrix models that are quite simple to be solved by traditional methods but contain all the properties of more complicated matrix models that are used for describing black holes via holographic duality.
Rinaldi who is Tokyo-based and presented by Theoretical Quantum Physics Laboratory at RIKEN stated that we anticipate that by understanding the attributes of this particle theory via numerical experiments, we will understand something regarding gravity. However, it is unfortunate that there is still difficulty in solving the particle theories and this is the place where the aid of computers is required.
These matrix models are blocks of numbers representing objects in string theory – a framework in which one-dimensional strings represent particles in particle theory. When researchers are solving such matrix models, they are looking for a specific configuration of particles in the system representing the system’s lowest energy state, known as the ground state. Nothing happens to the system in its ground state unless something is added for perturbing it.
Rinaldi explained that it is critical to understand the way this ground state looks so that things can be created from it. Knowing the ground state of a material is equivalent to knowing whether it is a conductor, a superconductor, extremely strong, or extremely weak. However, locating this ground state among all possible states is a tedious task. That is the reason for employing such numerical methods.
Rinaldi compares the numbers in the matrix models to grains of sand. The model’s ground state can be considered when the sand is even. However, if there are ripples in the sand, one must find a way to smoothen them. For solving this, the researchers turned to quantum circuits initially. The quantum circuits are denoted by wires in this method, and each qubit, or a bit of quantum particulars, is a wire. Above the wires are gates, which are quantum operations that govern how information travels through the wires.
Rinaldi explained that we can read them like music, from left to right. If we read it as music, we are essentially transforming the qubits from the start into something new at every step. However, we don’t know which operations are to be performed or which notes to be played as we progress. The shaking process will alter all of these gates for making them take the correct shape, resulting in the ground state at the end of the process. So, we have all this music, and if played correctly, we will end up with the ground state.
The researchers wanted to compare this quantum circuit method to a deep learning method. Deep learning is a type of machine learning that employs a neural network approach—a set of algorithms that attempts to discover relationships in data like how the human brain operates.
By feeding thousands of images of faces, neural networks are used for designing facial recognition software, from which they draw specific landmarks of the face for recognizing individual images or generating new faces of people who don’t exist.
In Rinaldi’s study, the researchers define the quantum wave function, which is a mathematical description of the quantum state of their matrix model.
Then a specialized neural network is employed for determining the wave function of the matrix in its ground state – the lowest possible energy. The neural network’s numbers go through an iterative optimization process for finding the matrix model’s ground state, tapping the bucket of sand to level all of its grains.
The researchers identified the ground state of both matrix models they investigated using both approaches, but the quantum circuits are restricted by a tiny number of qubits. Current quantum hardware has the capability of handling a few dozens of qubits: the addition of lines to a music sheet becomes costly, and the more lines added, the less accurately the music can be played.
Rinaldi explained that other commonly used methods will be able to determine the energy of the ground state but not the complete structure of the wave function. The method for obtaining complete information about the ground state was demonstrated by utilizing quantum computers and deep learning – new emerging technologies.
Since these matrices are one feasible representation for a specific type of black hole, if the arrangement of matrices is known along with their properties, we can know the way a black hole looks on the interior. What is the source of the event horizon for a black hole? Answer to such questions would be a significant step towards the realization of a quantum theory of gravity.
According to Rinaldi, the findings provide an important benchmark for future work on quantum and ML (Machine Learning) algorithms that researchers can utilize for studying quantum gravity using the concept of holographic duality.
Rinaldi’s co-authors are:
- Xizhi Han at Stanford University
- Mohammad Hassan at City College of New York
- Yuan Feng at Pasadena City College
- Franco Nori at U-M and RIKEN
- Michael McGuigan at Brookhaven National Laboratory
- Masanori Hanada at University of Surrey
