IBM Research and the University of Chicago posted a paper on 28 July 2026 — Sampling hard circuits with verifiably high fidelity, arXiv:2607.25941 — that pairs a classically hard sampling task with a published lower bound on how faithfully the hard state was prepared. On IBM’s Boston superconducting processor they ran a 64-qubit, depth-73 Clifford circuit doped with 314 T gates, encoded across 76 physical qubits (64 data + 12 ancilla). Syndrome post-selection produced a Clifford reference fidelity F₁ = 0.38(1) and a 95%-confidence lower bound F₂ ≥ 0.349 on the hard doped state. They collected 1,389 post-selected samples in about 14.5 minutes, with effective gate-error measure suppressed roughly 10× after post-selection.
Two days later, on 30 July 2026, IBM’s newsroom framed a related milestone as ~15 minutes, 70 logical qubits, 2,415 logical two-qubit operations, 468 logical T gates, and 10× lower effective logical error. Prefer the arXiv experimental numbers in the body below; flag the press “70 logical” line as a separate framing, not a substitute for the paper’s 64/76 circuit.
This is a certified sampling milestone — not a chemistry, finance, or logistics product. Classical simulators may still improve; the paper says so.
Why it matters
“Quantum advantage” claims have been easy to doubt because the harder the circuit, the harder it is to prove the machine got the right answer. Random circuit sampling (RCS) showed speed; verification often needed strong noise assumptions or classical simulation that stops scaling.
The IBM–UChicago protocol, doped Clifford sampling (DCS), tries to keep both: hardness and a certificate. Start with a deep Clifford circuit whose fidelity you can measure efficiently with direct fidelity estimation (DFE). Encode it in a spacetime code so ancilla syndromes catch faults. Then inject non-Clifford T gates only where they commute with the checks — so the hard state inherits the same error-detection machinery. Measure the Clifford fidelity; bound how much doping can hurt it; publish the lower bound with the samples.
For a stranger, the peg is trust plus wall-clock time in one package: the machine finished in about a quarter of an hour, and the team published a number saying the hard state was prepared with fidelity at least 0.349 at 95% confidence under their stated Pauli-noise assumptions.
Key numbers (arXiv vs IBM PR)
| Quantity | arXiv experiment (prefer) | IBM Newsroom (30 Jul 2026) |
|---|---|---|
| Data / “logical” qubits | 64 data | 70 logical |
| Circuit depth | 73 | (not highlighted as 73) |
| T gates | 314 | 468 logical T |
| Physical qubits | 76 (64+12 ancilla) | (PR focuses on logical counts) |
| Logical two-qubit ops | 2,336 CZ in DCS + 308 syndrome CZ = 2,644 CZ total | 2,415 logical two-qubit ops |
| Clifford fidelity F₁ | 0.38(1) (DFE) | — |
| Hard-state lower bound F₂ | ≥ 0.349 (95% CI) | “remarkably high circuit fidelity” |
| Post-selected samples / runtime | 1,389 in ~14.5 min | ~15 minutes |
| Error suppression after post-selection | ~10× | 10× lower effective logical error |
| Processor | IBM Boston (Heron-family layout) | IBM quantum system |
The arXiv Note added explains an earlier open-boundary version was classically simulated; the present manuscript uses periodic boundary conditions to close that contraction path. If you see older write-ups with 70/468/0.284/16.1 min, treat them as a different instance or press-era framing — not the numbers to put in the lede without a label.
How the certificate works
Figure 1 of the paper is the argument in one diagram. Measure the encoded Clifford state’s fidelity F₁ and its syndrome distribution. Dope with T gates that commute with stabilizers so syndromes stay statistically the same (S₁ ≈ S₂). The only fidelity loss doping can force, under their Pauli model, comes from converting previously “harmless” faults into harmful ones. Monte Carlo over noise strengths and polarizations bounds that loss at 0.010(1) for this instance. Subtracting that upper confidence limit from the lower confidence limit on DFE fidelity yields F₂ ≥ 0.349.
Hardware details that matter for the claim:
- Virtual Z / frame-tracking T gates add essentially no new noise on this platform.
- Pauli twirling pushes noise toward a stochastic Pauli channel.
- Post-selection rate for the Clifford DFE was 3.83(4)×10⁻⁴; readout mitigation raised an estimated “true” Clifford fidelity to 0.55(2) — a separate, higher figure the authors report alongside the conservative bound.
- Validation at low and intermediate T counts (5, 75, and S-gate doping) kept DFE or XEB proxies above the predicted floor; full syndrome histograms matched across doping strategies.
Bill Fefferman’s group at UChicago supplied the complexity side: the ensemble is argued to be hard on average under standard sampling conjectures. The authors scanned tensor-network, stabilizer, and hybrid classical methods and judged this finite instance intractable for current algorithms — while explicitly warning that better classical methods and hardware can change the race.
What this is not
- Not “unbreakable” advantage. The paper’s own outlook expects classical algorithms to improve.
- Not fault-tolerant logical qubits of the kind used in crypto-relevant resource estimates. These are error-detected data qubits in a spacetime code with post-selection overhead — a big step, a different object from a fully corrected logical qubit that runs indefinitely.
- Not a useful end-user application. No molecule, no portfolio, no warehouse routing. The output is samples from a hard distribution plus a fidelity certificate.
- Not the same story as Innsbruck’s ion work, Majorana claims, or photon experiments already on The Good Signal. Different hardware, different protocol.
What to watch
- Quantum Advantage Tracker — IBM says the circuits and results are open; classical groups will keep attacking them (one open-boundary instance already fell; the periodic instance is the live target).
- Whether spacetime codes move from error detection (post-selection) toward error correction at larger volumes without killing the sampling rate.
- Independent reproductions of the F₂ bound under weaker noise assumptions, and device-independent verification ideas the outlook flags as still open.
- Zenodo deposit 10.5281/zenodo.21633064 — the public data trail for anyone auditing the shots.
Fifteen minutes on the quantum side, a published fidelity floor, and an open classical contest: that is the progress signal. The hedge stays in the lede — certified sampling, not a product.
Sources
- Martiel, S. et al. Sampling hard circuits with verifiably high fidelity. arXiv:2607.25941 (28 Jul 2026). https://arxiv.org/abs/2607.25941
- IBM Newsroom, 30 Jul 2026: IBM and The University of Chicago Demonstrate Quantum Advantage… https://newsroom.ibm.com/2026-07-30-ibm-and-the-university-of-chicago-demonstrate-quantum-advantage,-establishing-trusted-quantum-computation-on-logical-circuits
- Experimental data: Zenodo DOI 10.5281/zenodo.21633064
