QUANTUM-INFO-SUPREMACY PAPER

“Demonstrating an unconditional separation between quantum and classical information resources”

arXiv:2509.07255v1 (Sept 2025)

TL;DR – PICK YOUR PERSONA

EXPERT (complexity / quantum-info theorist) “First unconditional, noise-robust experimental separation between n qubits and ≥ 2^{n−o(n)} classical bits for a well-defined communication task (Distributed XEB). 12-qubit trapped-ion device already forces ≥ 62 classical bits; proven via new concentration bounds for Clifford-ensemble DXHOG. Separation survives realistic gate fidelities (≈ 99.94 % two-qubit) without assuming cryptographic or average-case hardness conjectures.”

PRACTITIONER (NISQ hardware / algorithms engineer) “You can benchmark today’s machine with a 12-qubit, 86-layer variational circuit plus random Clifford measurement. If the sample-mean linear cross-entropy (FXEB) exceeds ≈ 0.36, your hardware is provably using more Hilbert-space “information” than any 61-bit classical memory could mimic. Quantinuum H1-1 reached FXEB = 0.427 ± 0.013, clearing the bar by 5 σ.”

GENERAL PUBLIC “Scientists ran a 12-puzzle game on a quantum computer that can’t be played as well by any conventional computer unless that computer memorises at least 500–3 000 ordinary bits of data. The quantum win is guaranteed by maths, not marketing.”

SKEPTIC (anti-hype blogger) “No, this is not about breaking RSA or replacing laptops. It’s a carefully engineered communication-complexity stunt: prepare a pseudo-random 12-qubit state, apply a random Clifford, measure. Classical simulation needs ≥ 62-bit memory—hardly cosmic, but unconditionally proven and already outside the qubit count. The ‘loopholes’ (setting-independence, leakage) are openly listed.”

DECISION-MAKER (funding / policy) “A new, audit-friendly milestone: ‘quantum-information supremacy’. Achievable on mid-scale, commercially available hardware; no need for full error-correction. Provides a concrete, theory-backed metric to gate further R&D investment or procurement.”

WHY SHOULD ANYONE CARE?

• Real-world pain-point: Convincing evidence that near-term quantum devices genuinely tap exponential Hilbert-space resources—critical for justifying continued capital inflow into NISQ platforms.
• Counter-intuitive take: Even noisy 12-qubit states can encode more “distributed correlation” than the best noiseless classical algorithm allowed to store ≤ 61 bits.

WHY THIS TIME IT'S DIFFERENT

The short version: every earlier “quantum-advantage” claim was conditional (“no efficient classical algorithm is known”).

This paper is unconditional (“no efficient classical algorithm can ever exist for this task, proven under standard complexity assumptions”).

Why the 2019-and-later rebuttals don’t apply here

Take-away:

Earlier experiments said “we can’t find a fast classical algorithm.” This one says “a classical algorithm must pay an exponential memory cost, proven; we’ve already crossed that threshold on today’s hardware.”

That is why the “but classical spoofing…” headlines from 2019–2024 do not automatically kill this claim.

JARGON → ENGLISH

Paper says Think of it as Concrete picture “Distributed Linear Cross-Entropy Heavy-Output Generation (ε-DXHOG)” A cooperative game where Alice (state) & Bob (measurement) try to output the likely bit-strings of Bob’s experiment. Two friends separately receive a scrambled lock and a key-shape; they win if their joint guess opens the lock on the first try more often than random. “One-way communication complexity” How many bits must travel from Alice to Bob for him to finish the task. How long a text message must be so your friend can pick the matching emoji. “Haar-random state” A maximally unstructured quantum state—every direction in Hilbert space is equally likely. A perfectly shaken snow-globe: no preferred orientation. “Clifford measurement” A measurement basis that can be reached with only easy gates (H, S, CNOT). Doing arithmetic with only +1, –1, and 0—still surprisingly powerful. “Quantum-information supremacy” Strictly fewer qubits than provably required classical bits. Fitting a library into a suitcase.

WHAT EXACTLY DID THEY DO?

1. Theoretical innovation

• Defined ε-DXHOG: achieve FXEB ≥ ε on average over (Haar state, Clifford measurement).
• Proved Theorem 1: Any classical one-way protocol needs m ≥ min{ Ω(ε² 2ⁿ), Ω(ε² n⁻ᶜ√ⁿ) } bits (explicit constants in Supp. G). – For n = 12, ε = 0.362 → m ≥ 62.
• Showed matching upper bound: m ≈ ε² n ln2 · 2ⁿ bits suffice (random-sphere vector library). Gap ≤ 6× at n = 12.

2. Experimental recipe

a. Hardware: Quantinuum H1-1, 20 ions, 12 active qubits, all-to-all connectivity. b. Alice (state prep): – Variational brickwork, depth 86, 86 ZZ(θ) entanglers, angles optimised offline under a gate-counting noise model. – Predicted fidelity 0.464; median partial-entangler angle θ ≈ 0.213π → 5.9 × 10⁻⁴ two-qubit error. c. Bob (measurement): – Sample random 12-qubit Clifford via Algorithm 1 (X–H–S–CZ–H), Θ(n²) = 144 gates, mid-circuit classical control. d. Randomness: Hardware QRNG continuously re-seeded; one-time pads for measurement basis to avoid pseudo-random spoofing. e. Data: 10 000 independent shots → F̂XEB = 0.427 ± 0.013.

RESULTS IN NUMBERS

• Observed FXEB: 0.427 (13)
• 5-σ conservative ε: 0.362
• Provable classical RAM cut-off: ≥ 62 bits (population mean).
• Classical RAM ceiling (existence): ≤ 382 bits.
• Gate fidelity required for ≥ 2n-bit separation at n = 26: ≤ 2.5 × 10⁻³ (extrapolated).

CAN I REPLICATE OR DEPLOY?

Implementation checklist

✅ Near-term trapped-ion or high-connectivity superconducting device (≥ 99.9 % two-qubit fidelity). ✅ Mid-circuit measurement & classical control (for random Clifford). ✅ True random bit source (QRNG or NIST beacon). ✅ Variational compiler that folds gate & memory error into loss.

UX considerations

• Classical post-processing (FXEB) is trivial; latency dominated by shot count for desired σ.
• Cloud API friendly: state-preparation circuit + measurement spec ≤ few kB per task.

Integration hooks

• Add as nightly “Hilbert-space benchmark” alongside randomized benchmarking.
• Use lower-bound curve (Fig. 4) to translate FXEB into min classical RAM—an audit metric for procurement.

LIMITS & LOOSE BRICKS

• Loophole 1: Measurement basis fixed before state finishes—possible “setting-independence” issue (Bell analogy).
• Loophole 2: No direct leakage & spectator-ion check; sceptic could model 12 qubits + environment as bigger low-entanglement system.
• Finite-n: Separation ~ 2ⁿ/n; needs > 20 qubits for million-bit gap—fidelity must improve commensurately.
• Noise model: Assumes depolarising form; correlated errors could spoof FXEB.
• Classical upper bound: Random-sampling protocol probably not optimal; gap could tighten.

NEXT-DIRECTIONS & SPIN-OFFS

CONFLICT-OF-INTEREST & FUNDING TRANSPARENCY

• Authors include Quantinuum employees (hardware provider); UT Austin team supported by DOE, NSF, IBM fellowship.
• Hardware specs & benchmarking data supplied by Quantinuum; independent group reproduced theoretical bounds.
• No patents filed on the DXHOG task itself; open-source data & code repositories promised.

BOTTOM LINE

This paper supplies the sharpest unconditional yard-stick to date showing that today’s high-fidelity qubits really do occupy an exponentially larger information space than classical bits, short-circuiting perennial “but maybe a smarter algorithm…” objections. It is not a computational-speed claim; it is a memory-compression claim backed by mathematical proof and 10 000 experimental shots. For the ecosystem, it offers a ready-made, audit-ready milestone useful for procurement, investor due-diligence, and road-map planning—provided one keeps the listed loopholes