Random circuit sampling with trusted quantum computations
Demonstrating quantum advantage requires two things: a task that is easy for a quantum computer but hard for a classical computer, and a way to verify the quantum computer's outputs. This is the story of how IBM is advancing quantum error correction to close the gaps in claims of advantage in random circuit sampling — turning a flashy demonstration into a trusted quantum computation.
Arute et al., Nature 574 (2019) · the original "quantum supremacy" demonstration.
Zhao et al., Natl. Sci. Rev. (2025) · classical GPU simulation closes the gap.
Hangleiter, arXiv:2603.09901 · has advantage really been achieved?
Classical hardness
easy
laptop ↔ #P-hard
Closeness to truly random
far
approaches a Haar k-design
Bouland et al., Nature Phys. 15, 159–163 (2019) · computing output probabilities is #P-hard.
Leone et al., PRX Quantum 7, 020321 (2026) · how many T gates make a circuit "random enough."
- ▣Detecting region: the swept-out wires (green) the check can see — bounded by the check itself (the pink line). Errors to the right of it happen after the check and slip through.
- ✕Syndrome: an error inside the region flips the ancilla — a flag. We discard that shot (post-selection).
Ancilla deterministic · shot accepted
Delfosse & Paetznick, arXiv:2304.05943 · spacetime codes of Clifford circuits.
Martiel & Javadi-Abhari, arXiv:2504.15725 · shows how to practically design these codes.
Unencoded circuit fidelity
≈ 0.01
unencoded, same size
Encoded fidelity (minimum)
F > 0.284
Encoded fidelity (average)
0.32 ± 0.01
direct measurement
Pure Clifford state ⇒ fidelity is directly measurable via stabilizer sampling (DFE).
Flammia & Liu, Phys. Rev. Lett. (2011)
Watch as adding T-gates leaves the number of "Id" runs the same, letting us calculate a minimum guaranteed fidelity.
Measured fidelity
>28%
directly & syndrome-estimated
MPS Simulation
1016
centuries to simulate
Stabilizer-based simulation
1017
centuries to simulate
One honest caveat: the verification still trusts the hardware to play fair. An assumption-free demonstration is the next open problem.
Fclifford
=
Id + Harmless
Accept
The lower bound of the doped circuit's fidelity is:
Fclifford
—
Harmless
Accept