A specialized laboratory is required for such a quantum computer. Not only does it need laser-generated (radiated) random numbers, but it also requires a quantum computer with a specific type of qubit optimized for Shor's algorithm, high-efficiency power supplies, sub-zero cooling, and a fully controlled environment.

However, laser-generated random numbers are not directly tied to the security of ECDSA or most other cryptographic algorithms. Random number generation is a separate component of cryptography, essential for key generation and other cryptographic operations.

For example:
https://arxiv.org/pdf/2302.06639.pdf
This paper discusses related concepts.

Current IBM Quantum systems—and other publicly available quantum computers—do not possess the necessary hardware (such as arithmetic circuits) for "126+ logical qubits with error correction" (e.g., "Cat Qubits").

If someone were to achieve this, the scientific community would immediately recognize who accomplished it—and they would know exactly where those researchers are located. 

Until then, most claims about such capabilities are just effective marketing by quantum computing providers.