{"id":"36fec61a-3fee-444e-80b8-c96f6eb9fdb6","arxiv_id":"2606.05366","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":7.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"Quantum one-pass streaming algorithm achieves 0.7172-approximation for Max-kSAT (and 0.7425 for Max-2OR) with polylog(n) space, exceeding classical space lower bounds.","lead":"The paper claims a one-pass quantum streaming algorithm for Max-kSAT using only polylog(n) space that achieves a 0.7172 approximation ratio. If correct, this would establish an exponential space separation from classical streaming algorithms for the same approximation task.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.3","headline":"Correctness of the claimed one-pass quantum streaming algorithm achieving 0.7172-approximation for Max-kSAT in polylog(n) space","rationale":"The reader's weakest assumption matches the load-bearing point exactly. Because the full manuscript is referenced but the abstract alone supplies no supporting construction, the central claim remains unverified at the level of the algorithm itself. No other internal inconsistency is identifiable from the given material.","tokens_in":1717,"tokens_out":304,"duration_ms":43161,"concrete_test":"Locate the section(s) presenting the Max-kSAT quantum streaming algorithm; extract the claimed space bound and approximation guarantee, then check whether the analysis (e.g., via quantum query complexity or amplitude amplification) rigorously establishes at least 0.7172 and confirms polylog(n) space independent of the instance size.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim requires the existence of a quantum streaming algorithm (one-pass, polylog(n) space, 0.7172-approx for Max-kSAT) that improves on the classical √2/2 threshold from Chou et al. (FOCS 2020). This is the novel contribution; the classical lower bound is imported from prior work. The argument holds only if the quantum construction and its approximation analysis are correct. The abstract states the result without any construction, measurement scheme, or proof sketch, so this is the least secure link.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The paper claims to give a one-pass quantum streaming algorithm for Max-kSAT using polylog(n) space that achieves a 0.7172-approximation ratio for instances with n variables. This is contrasted with the classical lower bound from Chou et al. (FOCS 2020) showing that any classical streaming algorithm requires Ω(√n) space to beat the √2/2 ≈ 0.7071 threshold. The paper also claims a one-pass quantum streaming algorithm for Max-2OR achieving 0.7425-approximation and states that this yields a complete classification of quantum space advantages for all Boolean Max-2CSPs.","tokens_in":1827,"tokens_out":350,"duration_ms":45366,"significance":"If the quantum algorithm construction and approximation analysis hold, the result would establish an exponential quantum-classical separation in the one-pass streaming model for approximating Max-kSAT (and complete the picture for Max-2CSPs). Such a separation would be notable for highlighting potential quantum advantages in space-bounded approximation algorithms.","major_comments":[{"comment":"Abstract: the central claim is the existence of a one-pass quantum streaming algorithm achieving the 0.7172 approximation ratio in polylog(n) space. No algorithm description, measurement scheme, or analysis deriving the ratio (or showing it exceeds the classical threshold without increasing space) is provided, so the soundness of the claimed exponential advantage cannot be assessed.","section":"Abstract"}],"minor_comments":[],"recommendation":"uncertain","confidential_remarks":"The provided text consists only of the abstract; without access to the algorithm construction and proof, a full technical review is not possible."},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for reviewing our manuscript. We address the major comment below.","responses":[{"response":"Abstracts are concise summaries by design. The full one-pass quantum streaming algorithm for Max-kSAT, including its construction, the measurement scheme, and the analysis deriving the 0.7172 approximation ratio (exceeding the classical √2/2 threshold at polylog(n) space), appears in the body of the manuscript. The same holds for the Max-2OR result. These sections establish the claimed exponential quantum space advantage.","revision_made":"no","referee_comment":"[Abstract] Abstract: the central claim is the existence of a one-pass quantum streaming algorithm achieving the 0.7172 approximation ratio in polylog(n) space. No algorithm description, measurement scheme, or analysis deriving the ratio (or showing it exceeds the classical threshold without increasing space) is provided, so the soundness of the claimed exponential advantage cannot be assessed."}],"tokens_in":1302,"tokens_out":211,"duration_ms":38832,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The main claim is a one-pass quantum streaming algorithm for Max-kSAT that uses only polylog(n) space and hits a 0.7172 approximation ratio, while classical algorithms need Omega(sqrt(n)) space to beat sqrt(2)/2. They add a similar result for Max-2OR at 0.7425 and say this finishes the picture for all Boolean Max-2CSPs.\n\nWhat stands out is the direct comparison to the Chou-Golovnev-Velusamy FOCS 2020 classical lower bound and the attempt to give a clean classification for the 2CSP case. If the quantum construction works, that would be a concrete exponential space separation in the streaming model.\n\nThe obvious soft spot is that the abstract states the algorithm and the ratio without any description of the quantum streaming procedure, the measurement scheme, or the analysis that produces 0.7172. The margin over 0.7071 is small, so any error in the approximation calculation or in how the quantum state is maintained across the stream would collapse the result. The classical lower bound is taken from prior work, which is fine, but the quantum side has to stand on its own.\n\nThis paper is aimed at people working on quantum streaming and approximation algorithms. A reader who wants to see whether the claimed separation is real will need the full construction and proof. Based on the abstract alone it is too early to judge soundness, but the question it poses is worth checking in review if the details are there.","headline":"The abstract claims a polylog-space quantum streaming algorithm for Max-kSAT at 0.7172 approximation that beats the classical sqrt(n) lower bound for anything above ~0.707, plus a full classification for Max-2CSPs, but supplies zero construction or proof.","tokens_in":2289,"tokens_out":410,"would_cite":false,"duration_ms":20629,"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":"A quantum one-pass streaming algorithm approximates Max-kSAT to 0.7172 using only polylog(n) space.","keywords":["quantum streaming algorithms","Max-kSAT approximation","space complexity","Max-2OR","Boolean Max-2CSP","streaming model","approximation ratio"],"falsifier":"Finding that no one-pass quantum streaming procedure can reach a 0.7172 approximation ratio for Max-kSAT while staying within polylog(n) space would disprove the central result.","tokens_in":2608,"feed_emoji":"⚛️","tokens_out":672,"duration_ms":48945,"temperature":0.7,"pith_summary":"This paper constructs a quantum algorithm that processes Max-kSAT instances in a single streaming pass. The algorithm maintains only polylogarithmic space and returns an assignment that satisfies at least 0.7172 of the optimum. Classical algorithms cannot match this ratio without using much more space, specifically Omega of the square root of n. The same approach yields a 0.7425-approximation for Max-2OR and finishes the picture for all Max-2CSPs. Readers interested in quantum advantages in limited-memory computation would see a concrete exponential gap here.","feed_headline":"Quantum streaming approximates Max-kSAT to 0.7172 in polylog space","feed_subtitle":"Classical methods need sqrt(n) space above 0.7071 ratio, enabling exponential quantum space savings and full Max-2CSP classification.","key_machinery":"A one-pass quantum streaming algorithm that encodes the input into a quantum state using limited space to compute the approximate solution.","core_discovery":"The central claim is that a one-pass quantum streaming algorithm exists for Max-kSAT which uses polylog(n) space and achieves a 0.7172-approximation, in contrast to the classical lower bound of Omega(sqrt(n)) space for approximations better than sqrt(2)/2 ≈ 0.7071. A similar algorithm for Max-2OR with 0.7425-approximation completes the classification of quantum space advantages for Boolean Max-2CSPs.","pith_inferences":["Similar quantum space savings might apply to other streaming approximation problems beyond CSPs.","The separation raises the question of whether quantum methods can improve ratios or handle multi-pass variants for the same problems.","Practical tests on small instances could check whether the polylog space bound holds under realistic quantum noise."],"forward_implications":["A 0.7172-approximation for Max-kSAT is possible with polylog space in the quantum streaming model.","Any classical streaming algorithm for a better ratio than 0.7071 must use Omega(sqrt(n)) space.","A 0.7425-approximation for Max-2OR is achievable with polylog space quantumly.","All Boolean Max-2CSPs now have their quantum versus classical space advantages fully classified."],"fun_headline_variants":["Quantum polylog space for 0.7172 Max-kSAT approx in streaming","Exponential quantum space advantage for streaming Max-kSAT","0.7172-approx Max-kSAT via one-pass quantum polylog streaming","Complete Max-2CSP quantum space advantage classification"],"cache_read_input_tokens":64,"weakest_assumption_plain":"The described quantum streaming algorithm for Max-kSAT actually exists and meets the stated space and approximation bounds.","fun_headline_variants_meta":{"raw":{"variants":["Quantum polylog space for 0.7172 Max-kSAT approx in streaming","Exponential quantum space advantage for streaming Max-kSAT","0.7172-approx Max-kSAT via one-pass quantum polylog streaming","Complete Max-2CSP quantum space advantage classification"]},"model":"grok-4.3","cost_usd":0.008632,"raw_usage":{"total_tokens":3893,"prompt_tokens":665,"num_sources_used":0,"completion_tokens":73,"cost_in_usd_ticks":86324500,"prompt_tokens_details":{"text_tokens":665,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":3155,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":665,"tokens_out":73,"duration_ms":36384,"temperature":1.0,"reasoning_tokens":3155,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-28T03:25:03.003858+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"Finding that no one-pass quantum streaming procedure can reach a 0.7172 approximation ratio for Max-kSAT while staying within polylog(n) space would disprove the central result.","supporting_citations":[],"review_version":1}