Physicists have made a groundbreaking advancement in understanding one of science’s most profound mysteries—what lies at the core of black holes. In a pioneering study published in PRX Quantum, a team led by Enrico Rinaldi has utilized quantum computing and machine learning to simulate the quantum structure believed to exist within black holes. By leveraging the holographic principle, the researchers have explored a mathematical framework known as a matrix model, paving a new path to comprehend gravity itself—without ever crossing the event horizon.
The announcement comes as scientists continue to grapple with the challenge of unifying the theories of general relativity and quantum field theory. Each excels in its domain—relativity in explaining gravity and the universe’s large-scale structure, and quantum theory in governing subatomic particles. However, they appear fundamentally incompatible. The study, conducted by researchers from the University of Michigan, RIKEN, and Keio University, employs holographic duality—a radical notion suggesting that gravity in three dimensions can be mapped to a quantum system without gravity in just two dimensions.
Bridging Space-Time and Quantum Matter
“In Einstein’s General Relativity, space-time exists but there are no particles,” Rinaldi explains. “In the Standard Model, particles exist, but there’s no gravity.” This dichotomy has long puzzled physicists and stalled efforts to develop a quantum theory of gravity. The matrix models explored in this study are mathematical constructs designed to merge these conflicting perspectives into a cohesive framework.
By focusing on simplified versions of these models—versions that still retain essential features of black holes—the researchers were able to test algorithms on both quantum circuits and classical neural networks. Their objective: to find the ground state, the configuration of minimum energy, which may encode the very blueprint of space-time itself.
The violation of the singlet constraint αE0| ˆ G2 α|E0 as a function of the cutoff for various couplings λ = g2 N = 0.2, 0.5, 1.0, and 2.0 for the SU(2) bosonic model. Even (E) and odd (O) values are plotted with different colors in logarithmic scale. The other parameters are m2 = 1 and c = 0.
Mapping the Quantum Terrain With Matrix Models
Matrix models are central to string theory, where fundamental particles are described not as points, but as tiny vibrating strings. In this framework, black holes can be modeled as dense collections of such strings, and their behavior is encoded in enormous numerical arrays—matrices. However, solving these models directly is extremely challenging, particularly when it comes to identifying their ground state. That’s where computational innovation becomes crucial.
“It’s really important to understand what this ground state looks like, because then you can create things from it,” Rinaldi says. “So for a material, knowing the ground state is like knowing, for example, if it’s a conductor, or if it’s a superconductor, 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.”
Using a bosonic matrix model with two or three matrix variables, the researchers simulated low-energy states using quantum gates on qubit systems. Due to the limited capacity of current quantum hardware—just dozens of qubits—they kept the simulations modest in scale but rich in structure. Their results demonstrate the feasibility of using quantum variational methods to approximate the matrix model’s wavefunction—a significant step in realizing quantum simulations of gravitational systems.
Quantum Circuits as Music Sheets of the Universe
The process of programming a quantum circuit can be likened to composing a symphony. Each qubit corresponds to a wire, and quantum gates act like musical notes, modifying the system’s state in structured steps. But unlike a traditional score, the “music” of a quantum algorithm evolves unpredictably, requiring optimization to hit the right notes.
“You can read them as music, going from left to right,” the author adds. “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.”
This poetic analogy reflects the challenge of using quantum algorithms to find an accurate ground state—essentially composing a piece of code that behaves like the inside of a black hole. The researchers implemented variational quantum eigensolvers (VQEs) to minimize energy and used loss functions sensitive to both energy and symmetry constraints. Despite limited quantum hardware, they were able to benchmark their results against exact diagonalization methods and neural networks, achieving impressive alignment.
As the field of quantum computing continues to evolve, the implications of this study could be far-reaching. By potentially unlocking the secrets of black holes, scientists may inch closer to a unified theory of physics, bridging the gap between the cosmos’s grand scale and the minute world of quantum particles. The future of this research lies in advancing quantum hardware capabilities, which could lead to even more profound discoveries about the universe’s most enigmatic phenomena.
