{"id":"d40afaf5-013a-45a7-8812-4a171abd1c45","arxiv_id":"2605.28964","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":5.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"Quantum protocol identifies primes via Fourier components of entanglement evolution on NISQ devices, using rescaling noise mitigation and a new analytical bound.","lead":"The paper demonstrates identifying prime numbers on IBM quantum processors by linking primality to Fourier components in the time evolution of entanglement in a two-part quantum system. It introduces a rescaling-based noise mitigation technique calibrated on some circuits and extrapolated to others, plus an analytical bound to improve separation of primes and composites.","discovery_kind":"new_application","skeptic_critique":{"model":"grok-4.3","headline":"Global rescaling extrapolation may introduce circuit-dependent bias that erases the claimed prime-composite Fourier separation","rationale":"The reader's weakest assumption correctly isolates the single point where the experimental claim is least secured; the theoretical bound cannot rescue the result if the mitigation step itself is biased. No stronger internal inconsistency appears from the abstract-level description of the construction.","tokens_in":1610,"tokens_out":280,"duration_ms":11051,"concrete_test":"Split the reported circuits into calibration set (numbers ≤ N/2) and held-out set (numbers > N/2); recompute the rescaling factor from the calibration subset only, apply it to the held-out subset, and test whether the prime-composite separation in the target Fourier component remains above the paper's analytical threshold at the same significance level.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The protocol's experimental viability rests on a single global rescaling factor calibrated on a subset of circuits and applied to all others. The analytical bound in the paper assumes this rescaling restores the ideal Fourier-mode distinction derived for the uniform-superposition initial state. If noise (e.g., decoherence or gate errors) scales with circuit depth or with the specific integer under test, the same scalar cannot uniformly correct all instances; the bound then no longer guarantees separation under the actual mitigated data.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript reports an experimental demonstration on IBM quantum processors of a protocol that identifies primes via specific Fourier components extracted from the time evolution of entanglement in a bipartite quantum system initialized in a uniform superposition. It introduces a global rescaling noise-mitigation technique calibrated on a subset of circuits and extrapolated to others, and derives a new analytical bound on the Fourier modes that is claimed to enhance prime-composite separation under moderate noise.","tokens_in":1705,"tokens_out":445,"duration_ms":30639,"significance":"If the central experimental claims and the validity of the global-rescaling extrapolation hold, the work would constitute a concrete NISQ demonstration linking quantum entanglement dynamics to a number-theoretic task, together with a mitigation method whose analytical support could be of broader interest.","major_comments":[{"comment":"The global rescaling factor is calibrated on a subset of circuits and extrapolated; the analytical bound (derived for the ideal uniform-superposition case) is then invoked to guarantee separation. No data, error bars, or circuit-depth dependence are supplied to show that the same scalar restores the claimed Fourier-mode distinction across different integers and depths. This assumption is load-bearing for the experimental claim.","section":"Noise-mitigation technique and experimental results sections"},{"comment":"The abstract states that the bound 'enhances separation under moderate experimental deviations,' yet supplies neither the explicit form of the bound, the derivation steps, nor quantitative comparison (with/without the bound) on the mitigated data. Without these, the theoretical support for the prime-composite distinction cannot be evaluated.","section":"Analytical bound derivation"}],"minor_comments":[{"comment":"Figure captions and table entries should include the number of shots, the precise definition of the rescaling factor, and the integers tested so that the extrapolation procedure can be reproduced.","section":null},{"comment":"The manuscript should state the initial state actually prepared on the hardware and quantify any deviation from the uniform superposition assumed in the bound.","section":null}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the detailed and constructive report. We address the two major comments below. Both points identify areas where the manuscript can be strengthened with additional material, and we will incorporate the requested clarifications and supporting data in a revised version.","responses":[{"response":"We agree that explicit validation of the extrapolation is necessary. In the revised manuscript we will add (i) the full set of raw and mitigated Fourier-mode values for all tested integers together with statistical error bars obtained from multiple circuit executions, (ii) a systematic study of the rescaling factor as a function of circuit depth, and (iii) a direct comparison of prime-composite separation before and after rescaling for several depths. These additions will substantiate that the single scalar remains effective across the reported range of integers and depths.","revision_made":"yes","referee_comment":"[Noise-mitigation technique and experimental results sections] The global rescaling factor is calibrated on a subset of circuits and extrapolated; the analytical bound (derived for the ideal uniform-superposition case) is then invoked to guarantee separation. No data, error bars, or circuit-depth dependence are supplied to show that the same scalar restores the claimed Fourier-mode distinction across different integers and depths. This assumption is load-bearing for the experimental claim."},{"response":"We will include a dedicated subsection that states the explicit analytical bound, provides the complete derivation from the ideal uniform-superposition initial state, and presents quantitative comparisons of the Fourier-mode separation on the mitigated experimental data both with and without application of the bound. These additions will make the theoretical support fully evaluable.","revision_made":"yes","referee_comment":"[Analytical bound derivation] The abstract states that the bound 'enhances separation under moderate experimental deviations,' yet supplies neither the explicit form of the bound, the derivation steps, nor quantitative comparison (with/without the bound) on the mitigated data. Without these, the theoretical support for the prime-composite distinction cannot be evaluated."}],"tokens_in":1236,"tokens_out":433,"duration_ms":13780,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The paper links primality to specific Fourier components in the time evolution of entanglement for a bipartite system, with an analytical bound derived for the uniform superposition case, and they run a version on IBM hardware using a global rescaling factor calibrated on some circuits and applied elsewhere.\n\nThe new element is the specific combination of that entanglement dynamics approach with the rescaling mitigation and the bound meant to improve prime-composite separation under noise. Running the protocol on actual processors counts as concrete work, and the bound itself looks like a useful theoretical handle if the derivation holds.\n\nThe soft spot is exactly the one flagged in the stress test. A single global rescaling assumes noise behaves similarly across different integers and circuit depths. If decoherence or gate errors vary with the number being tested, the extrapolation can erase the Fourier distinction the bound is supposed to protect. The abstract gives no error bars, circuit counts, or subset details, so it is hard to judge whether the experimental results survive that issue.\n\nThis is aimed at people working on NISQ applications to number theory or entanglement-based algorithms. A reader interested in practical quantum number tasks could get some value from the bound and the hardware attempt, but only if the full derivations and raw data check out.\n\nI would send it to peer review so the mitigation and data can be examined properly, though the rescaling step will need close attention.","headline":"The rescaling mitigation is the weak link here; the entanglement Fourier idea for primes is a modest step but needs real data to back the separation claim.","tokens_in":2194,"tokens_out":354,"would_cite":false,"duration_ms":21832,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"Primality is identified by specific Fourier components in the time evolution of entanglement within a bipartite quantum system on NISQ hardware.","keywords":["prime number identification","quantum entanglement dynamics","Fourier components","noise mitigation rescaling","NISQ devices","bipartite quantum systems","IBM quantum processors"],"falsifier":"After applying the rescaled protocol to a known composite number, if the relevant Fourier component lies inside the interval the bound reserves for primes, the claimed separation is refuted.","tokens_in":2522,"feed_emoji":"⚛️","tokens_out":632,"duration_ms":21290,"temperature":0.7,"pith_summary":"The paper establishes that an integer's primality corresponds to particular Fourier modes extracted from how entanglement changes over discrete time steps in a two-part quantum system started in uniform superposition. The protocol is executed on IBM quantum processors, where noise is addressed by calibrating a single global rescaling factor on a subset of circuits and applying it to the rest. A new analytical bound on those Fourier modes is derived to keep the prime-composite separation visible even when moderate experimental errors remain. A sympathetic reader cares because the work shows a concrete route for number-theoretic tasks on current noisy devices rather than waiting for fault-tolerant machines.","feed_headline":"Entanglement Fourier modes identify primes on quantum processors","feed_subtitle":"A rescaling correction applied to IBM hardware keeps the prime-composite separation visible via specific frequency components of entanglemen","key_machinery":"The mapping from primality to selected Fourier modes of bipartite entanglement evolution, reinforced by an analytical bound that assumes uniform superposition and separates primes from composites.","core_discovery":"The primality of an integer is linked to specific Fourier components extracted from the time evolution of entanglement in a bipartite quantum system. A new analytical bound for the Fourier modes, derived under an initial uniform superposition, enhances the separation between prime and composite numbers under moderate experimental deviations. Implementation on IBM processors uses a global rescaling noise-mitigation factor calibrated on a subset of circuits and extrapolated across configurations.","pith_inferences":["Similar dynamical signatures might be sought for other arithmetic properties such as primality of higher-order forms or factorization hints.","The rescaling calibration procedure could be generalized to adaptive or circuit-specific corrections for larger integers.","Hybrid workflows that pre-select candidate numbers classically and verify them via this quantum signature become conceivable once the bound is tightened."],"forward_implications":["The Fourier-mode distinction remains observable on NISQ hardware provided the new bound holds under the observed noise levels.","A single calibrated rescaling factor suffices to restore usable separation across multiple circuit configurations.","The protocol constitutes a step toward number-theoretic applications on current quantum processors rather than purely theoretical demonstrations."],"fun_headline_variants":["Entanglement Fourier modes detect primes on quantum processors","Rescaling improves noise mitigation for quantum prime experiments","Analytical bound separates primes in noisy entanglement evolution","Prime identification via Fourier modes on IBM quantum hardware"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The global rescaling factor calibrated on a subset of circuits can be accurately extrapolated across different configurations without introducing systematic bias that erases the prime-composite distinction.","fun_headline_variants_meta":{"raw":{"variants":["Entanglement Fourier modes detect primes on quantum processors","Rescaling improves noise mitigation for quantum prime experiments","Analytical bound separates primes in noisy entanglement evolution","Prime identification via Fourier modes on IBM quantum hardware"]},"model":"grok-4.3","cost_usd":0.004695,"raw_usage":{"total_tokens":2271,"prompt_tokens":571,"num_sources_used":0,"completion_tokens":56,"cost_in_usd_ticks":46949500,"prompt_tokens_details":{"text_tokens":571,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":1644,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":571,"tokens_out":56,"duration_ms":17970,"temperature":1.0,"reasoning_tokens":1644,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-29T11:21:08.440096+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"After applying the rescaled protocol to a known composite number, if the relevant Fourier component lies inside the interval the bound reserves for primes, the claimed separation is refuted.","supporting_citations":[],"review_version":1}