Simulating a universe down to the Planck length and time for discretization is an incredibly complex task that goes beyond the capabilities of current technology, including a billion qubit computer. While quantum computing has the potential to solve certain problems more efficiently than classical computers, simulating an entire universe at such a fine-grained level remains far beyond our current understanding and technological capabilities.
There are several reasons why simulating a universe with that level of detail is highly challenging:
Scale: A universe with a Planck length and time discretization would involve an astronomical number of individual units, making it computationally infeasible to simulate all of them accurately. Even with a billion qubits, the number of qubits required to simulate such a universe would likely be orders of magnitude higher.
Complexity: Simulating a universe involves modeling not just the behavior of individual particles, but also their interactions, forces, and the emergent properties that arise from those interactions. The computational complexity of such a simulation grows exponentially with the number of particles, making it extremely demanding even for advanced computing systems.
Uncertainty: Quantum systems are inherently probabilistic, and the inherent uncertainty at the quantum level introduces additional challenges for accurate simulation. Achieving high-fidelity simulations that account for the full quantum behavior of particles is a significant obstacle.
Physical Constraints: Building a billion qubit computer is a formidable engineering task in itself, and current quantum technologies are still in their infancy. Even if a billion qubit computer were available, there would be practical limitations in terms of qubit coherence times, error rates, and the ability to implement the required quantum gates accurately.
It's important to note that simulating a universe at such a level of detail may also be philosophically and conceptually complex, as it raises questions about the nature of reality and the limitations of scientific inquiry.
In summary, while the idea of simulating a universe at the Planck scale is intriguing, it remains beyond our current technological and scientific capabilities. It's an area of ongoing research and exploration, but significant advancements and breakthroughs would be required to reach that level of simulation.