Ambient unitaries don't enable shallow group designs
Why quantum shortcuts can't fake random unitaries
Quantum computers need to generate random quantum operations for testing and calibration, but a new proof shows that shallow circuits—the speediest option—fundamentally cannot do this job for several important classes of operations. Even when you allow extra helper qubits and operations beyond the target group, the mathematical obstacle remains: you need circuit depth that grows with system size, not shrinks.
Quantum engineers use random unitary sampling to benchmark hardware and validate quantum algorithms. This result means those benchmarking protocols will require substantially deeper circuits than researchers hoped, adding significant overhead to the time and resources needed to verify that quantum computers are working correctly.