Yes, there is empirical evidence suggesting the possibility of building quantum computers that can solve computationally hard problems. While practical quantum computers are still in development, there have been notable advancements and demonstrations that showcase the potential power of quantum computing.
One significant milestone is the achievement of quantum supremacy, which refers to the point where a quantum computer can perform a specific computational task faster than any known classical computer. In October 2019, Google's research team published a landmark paper in the journal Nature, where they claimed to have achieved quantum supremacy using a 53-qubit quantum processor called Sycamore. They demonstrated that their quantum computer performed a specific task in about 200 seconds, which they estimated would take the most powerful supercomputers thousands of years to complete.
Furthermore, there have been successful applications of quantum computing in specific domains. For instance, quantum computers have shown promise in solving optimization problems, such as the traveling salesman problem and portfolio optimization. Researchers have also made progress in developing quantum algorithms for applications in quantum chemistry simulations, machine learning, and cryptography.
Additionally, quantum computing companies and research institutions are actively working on building more advanced quantum systems with increased qubit counts, improved stability, and error correction capabilities. These advancements aim to address the existing challenges and move closer to the development of practical quantum computers capable of solving complex problems more efficiently than classical computers.
It's important to note that while there is empirical evidence suggesting the potential of quantum computing, there are still significant technical challenges to overcome, such as improving qubit coherence, reducing errors, and scaling up the number of qubits. Continued research, experimentation, and engineering efforts are essential to realizing the full potential of quantum computers.