Analysis: Hagar's "The NISQ Trap"

Paper: "The NISQ Trap: Eight Years of Demonstrations the Hardware Was Built to Lose" Author: Amit Hagar, Department of History and Philosophy of Science and Medicine, Indiana University, Bloomington arXiv: 2607.07530v3 (submitted July 2026) Subject: Quantum Physics (quant-ph)

The Passage

The following excerpt is reproduced from the paper because it states, in a single paragraph, one of the sharpest distinctions in the entire quantum advantage debate — the difference between a hardware demonstration and a computational one:

Second, the role of demonstration in the field requires reconsideration. A demonstration that a hardware can run a circuit, and that the circuit produces an observable matching a known answer, is a demonstration of competent diagnostic engineering. The press cycle of the past several years has conflated such results with computational advantage, and the conflation has been productive of funding without being productive of the matter of fact under investigation. Distinguishing the two locates the engineering within a programme whose ultimate test is the construction of machines capable of running circuits the simulability theorems do not reach.

— Hagar, arXiv:2607.07530

What the Paper Argues

Hagar's central claim: with a single clear exception, every NISQ-era flagship "quantum advantage" demonstration has, within eighteen months of its announcement, been classically reproduced, shown to rest on classically tractable structure, or closed by a simulability theorem.

The paper covers eight years of announcements — random circuit sampling, BosonSampling, and related sampling-based supremacy claims — and argues that this is not a string of bad luck but a structural pattern. NISQ hardware can only maintain sufficient fidelity in a narrow region of circuit-space, and that same region — low effective depth, strong algebraic structure, geometric locality — is precisely the region where classical algorithms compress and simulate efficiently. The hardware and the classical simulator are, in Hagar's phrase, "responding to the same property of the circuit." The regime a NISQ device can survive is, almost by construction, the regime a classical computer can already handle.

Hagar frames the NISQ era itself as a 1998 retreat from the unmet conditions of the 1996 fault-tolerance threshold theorems — an interim research program adopted while error rates remained too high for full error correction. Eight years later, he argues, the retreat has produced a closed loop rather than a path forward.

The Six Theoretical Results (2024–2026)

The paper's argument rests on six specific results published between 2024 and April 2026, each showing that noisy circuits in a particular regime admit efficient classical simulation:

Result	Contribution
Mele et al. (2024)	Under standard local-noise models above a constant rate, any quantum circuit's noisy output converges to that of a circuit of only logarithmic effective depth
Nelson, Rajakumar & Gullans (2025)	Tightens these bounds under the geometric locality constraints present in superconducting and trapped-ion architectures
Zhang et al. (2025)	Shows classical simulability of noisy circuits in quasi-polynomial time under approximate Markovianity
Upreti et al. (2025)	Shows non-Gaussianity in bosonic (photonic) circuits accelerates classical attack once realistic noise is present
Oh et al. (2024)	Shows classical simulability of constant-depth linear-optical circuits with noise, via percolation methods
Lee et al. (2025)	Shows classical simulation is enabled by exponential decay of correlations in noisy random circuits

The unifying claim is not that any one result kills any one experiment — it is that the same physical features that let a noisy device run reliably are, across every hardware modality tried so far, the same features a classical algorithm can exploit.

Demonstration vs. Advantage: Why the Distinction Matters

The quoted passage draws a line this course returns to repeatedly: running hardware successfully is not the same as beating a classical computer at something that matters.

A circuit that produces "an observable matching a known answer" tells you the qubits, gates, and readout electronics work — that is real, valuable engineering. It does not, by itself, tell you that no classical computer could have produced the same answer faster. Hagar's complaint is that the press cycle has treated the first kind of success as though it were automatically evidence of the second, and that this conflation has been "productive of funding without being productive of the matter of fact under investigation" — a formulation Fermi would appreciate: the incentive structure has decoupled from the empirical question it is nominally funded to answer.

The One Exception: Google's Quantum Echoes / OTOC Experiment

Hagar explicitly identifies Google's 2025 Quantum Echoes (OTOC) result — analyzed in this book's Google Quantum Echoes Paper Analysis — as "the one demonstration of the period that stands neither reproduced nor closed by theorem." But he does not treat it as a clean win for the advantage claim either. He notes that the reported observable depended on a global rescaling factor obtained through error mitigation, that classical validity was checked only up to 40 qubits while the advantage claim was made at 65, and that classical heuristics discussed in the paper's own supplementary material complicate the headline result. This lines up closely with the caveats already identified in this book's independent review of that paper — the extrapolation past the verified 40-qubit boundary is the same gap both analyses flag.

The Pushback: Scott Aaronson's Response

Scott Aaronson responded to Hagar's preprint on his blog, Shtetl-Optimized, in a post titled "NISQ and quantum supremacy did not fail." His argument is narrower than a wholesale rejection of Hagar's thesis, and worth separating into its parts:

He agrees the thesis Hagar defends — that NISQ-era quantum supremacy has "failed" — is "surprisingly widely shared," and treats the paper as worth engaging seriously rather than dismissing.
He argues that sampling-based demonstrations specifically — Random Circuit Sampling and BosonSampling — passed a threshold roughly two years before Hagar's preprint after which, absent a further classical breakthrough, they clearly exceed what any existing classical computer can simulate.
He directly disputes one of Hagar's supporting citations: an October 2025 paper on classical simulation of noisy random circuits. Aaronson argues that algorithm still requires time exponential in circuit depth, and that simulating the deep, roughly 100-qubit random circuits Google and Quantinuum have since run experimentally remains, in his assessment, "pretty hopeless" for current classical methods.

The disagreement, in other words, is not about whether the diagnostic-engineering-versus-advantage distinction is real — both sides accept it — but about whether the specific classical results Hagar cites actually close the gap for the specific deep random-circuit experiments run most recently. That is an empirically resolvable dispute, not a philosophical one, and it is likely to keep moving in both directions as new classical algorithms and new hardware runs are published.

Relevance to This Course

Hagar's paper matters to this book for a reason distinct from Palmer's or Dyakonov's arguments: it is not a claim about a hard physical ceiling on qubit count, and it is not an argument that quantum mechanics itself needs revision. It is a historiographic and epistemological claim about how a field has interpreted its own results — made by a historian and philosopher of science rather than a physicist, which is itself worth noting when weighing the argument.

The core mechanism Hagar identifies — that the noise regime a device can survive and the regime a classical algorithm can compress are not independent, but are shaped by the same circuit properties — gives a structural explanation for a pattern this book documents elsewhere: quantum advantage claims that get walked back by improved classical algorithms within roughly a year or two (see the 2019 random circuit sampling episode discussed in the Google Quantum Echoes Paper Analysis). If Hagar is right, that pattern is not coincidence or bad luck across a series of unrelated announcements — it is close to a structural feature of running quantum algorithms on unprotected hardware.

The burden-of-proof framing in Hagar's conclusion is worth stating plainly for investors and policymakers: after roughly thirty announced "advantage-class" results without one that has held up beyond eighteen months (Google's OTOC result being the still-contested exception), the burden falls on NISQ proponents to produce a result that survives contact with the next simulability theorem — not on skeptics to prove none can.

Credibility Assessment

Overall rating: 7 / 10 — A well-sourced structural argument, contested at the margins by working complexity theorists.

Strengths:

Draws on six specific, citable 2024–2026 theoretical results rather than general skepticism, making the central claim falsifiable in principle.
Correctly identifies and names a conflation — hardware demonstration versus computational advantage — that recurs throughout this book's case studies.
Engages directly and specifically with the strongest counterexample (Google's OTOC result) rather than ignoring it.
Prompted a substantive, specific rebuttal from Scott Aaronson, one of the field's most rigorous voices — a sign the argument was taken seriously rather than dismissed.

Weaknesses:

Authored by a philosopher of science rather than a complexity theorist; Aaronson's rebuttal suggests at least one supporting citation (the October 2025 simulation result) may be read too strongly.
The "eighteen months" pattern, while striking, is drawn retrospectively from a small number of flagship announcements — a pattern of this size is suggestive rather than statistically decisive.
As with any argument in an actively moving field, both the classical-simulation results and the hardware results it rests on are subject to revision within the same eighteen-month window the paper itself highlights.

The paper does not need to be the final word to be useful. It supplies precise vocabulary — "diagnostic engineering" versus "computational advantage" — for a distinction investors and journalists routinely collapse, and it does so with citations specific enough that the claim can be checked rather than merely asserted.