{"id":"d074eb24-c35b-48be-b6d6-e6f0ae7b8a8f","arxiv_id":"2506.00063","paper_version":2,"verdict":"REJECT","confidence":"HIGH","novelty_score":3.0,"correctness_risk":"high","formal_verification":"none","parameter_count":2,"one_line_summary":"A benchmark of instantaneous noise-based logic claims O(1) time for operations on exponentially large sets, but the speedup depends on free input encoding and fails against the authors' own classical algorithm.","lead":"This paper claims that a classical noise-based logic scheme can solve some problems exponentially faster than ordinary computers, challenging quantum supremacy. But the paper itself shows one of its two demonstrations has a simple classical solution, and the other assumes the input is already pre-encoded.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Superposition encoding cost is hidden: Eq. (9) assumes U_S(t) is free, but for arbitrary S constructing it costs O(n); the paper's own §4.1 note concedes the point, so the exponential-speedup claim is unsupported.","rationale":"The paper is honest in its Section 4.1 Note, which is to its credit, and the first benchmark is explicitly withdrawn as a supremacy demonstration. But the second benchmark repeats the same structural mistake without the same admission: it assumes the exponential input set has already been written into the superposition. This is not a disagreement with an external consensus; it is an internal gap, because the paper's own Note establishes the principle. Once encoding cost is counted, the INBL algorithm for arbitrary hats has at least linear cost in n, so the claimed exponential separation reduces to a comparison between an algorithm that is handed its input pre-processed and one that is not. We also note the fixed-M issue is secondary but reinforces the concern. The reader's weakest assumption is the same one we identify, and the REJECT verdict stands.","tokens_in":6973,"tokens_out":8221,"duration_ms":79454,"concrete_test":"Run the Section 4.2 hat benchmark with S a random subset of size n = 2^N from {0,...,2^M-1}, and include the construction of U_S(t) in the timed region; separately time construction of U_all(t) for the full universe. If construction time grows as Theta(n) rather than staying constant, then Eq. (11)'s O(1) removal excludes input encoding and total INBL cost is Theta(n), matching classical linear search. For the structured all-odd case, benchmark the Fig. 6 shared-LSB classical algorithm; it should match the INBL time, confirming no exponential advantage.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing premise is that U_S(t) is available at zero encoding cost. Equations (5), (7), (9), and (11) all operate on an already-formed superposition, but for the Section 4.2 hat, S is a set of n arbitrary random M-bit numbers. Forming U_S(t) = sum_{k in S} prod_{i=0}^{M-1} G_i^k(t) requires summing n product strings, costing O(n M T) in the emulation and O(n) terms in analog hardware, so the O(1) removal in Eq. (11) is contingent on an exponential encoding step that is never counted. The paper's own Section 4.1 Note concedes this: for random/arbitrary odd numbers, both classical and INBL hardware complexity would be O(2^N). No equivalent concession appears in Section 4.2, but the same reasoning applies. The only sets with compact product representations are structured sets; for the all-odd benchmark the authors themselves provide an O(1) classical shared-LSB algorithm, so that benchmark also yields no supremacy. Finally, the reported constant time fixes M=32 with N<M; in a real scaling comparison M must grow with N, making even structured-set construction O(N), not O(1). The exponential-speedup claim therefore depends on a hidden free-encoding assumption that is false for the arbitrary exponentially large heaps the paper advertises.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes Instantaneous Noise-Based Logic (INBL) as a classical alternative to quantum computing, encoding logical information in superpositions of random telegraph waves. It reports two benchmark demonstrations: converting a set of odd numbers to even numbers, and finding and removing a given number from an unsorted set (a \"hat\"). The paper claims exponential speedup over classical algorithms, with classical time O(2^N) versus INBL time O(1) and hardware complexity O(M), and extends this to a general challenge to quantum supremacy. The reported evidence is CPU timing comparisons on a laptop between a classical loop and a software emulation of INBL waveform operations.","tokens_in":7234,"tokens_out":6518,"duration_ms":60602,"significance":"If the claims were sound, INBL would be a significant classical computing paradigm with potential implications for the quantum-supremacy debate. The paper is clear in defining the INBL formalism and includes an explicit Note in Section 4.1 admitting that the first benchmark has no actual supremacy issue because of a special-purpose classical algorithm. However, the central speedup claim is undermined by (a) comparing against naive classical algorithms rather than the best known ones, (b) assuming that exponentially large input superpositions are available for free, and (c) ignoring the cost of encoding an arbitrary set into superposition form. The paper even cites Tang's work on state-preparation assumptions [4] but fails to apply that same lesson to its own analysis. These issues are load-bearing and invalidate the exponential-speedup claim as stated.","major_comments":[{"comment":"The paper's own Note in Section 4.1 states that \"there is no actual supremacy issue here\" and describes an O(1) classical solution (Figure 6) for the odd-to-even benchmark, yet Section 5 concludes that the \"observed exponential speed increase is in line with the theoretical advantages of INBL as a potential alternative to quantum computing.\" This internal contradiction is load-bearing: the first benchmark cannot support the central claim of exponential speedup when a classical O(1) algorithm exists for the same problem.","section":"Section 5 and Section 4.1 Note"},{"comment":"The claimed O(1) removal operation in Eq. (11) assumes that U_S(t) in Eq. (9) is already available as a superposition. For the problem as stated, S is a set of n arbitrary random M-bit numbers, and constructing U_S(t) = sum_{k in S} S_k(t) requires summing n product strings, i.e., O(n) time and O(n) hardware resources. The paper never counts this encoding cost, so the constant-time removal is an artifact of a free-encoding assumption. The problem as stated is not solved in O(1) time; at best, a pre-encoded superposition can be manipulated in O(1), which is a different computational problem.","section":"Section 4.2, Eqs. (9)-(11)"},{"comment":"The INBL superposition of all odd numbers has a compact closed-form expression, namely H_0 times the product over i=1..M-1 of (H_i + L_i), while the benchmarked \"Classical algorithm\" loops over each of the 2^N numbers individually. This is not a like-for-like comparison: the INBL input exploits the structure of the full set of odd numbers, whereas the classical algorithm is given an explicit list of elements. The paper's own Note concedes that for random/arbitrary sets the INBL hardware complexity would also be O(2^N), undermining the generality of the benchmark.","section":"Section 4.1 and Figure 5"},{"comment":"The complexity claims fix M=32 and T=100 and report O(1) time, but in a meaningful scaling comparison M must grow with the range of numbers represented, and the RTW duration T must grow with M to maintain the error bound (Section 3 requires T >= 83 for M=32; for fixed error probability T grows with M). Thus the actual time complexity is at least O(M) or O(M T), and the hardware complexity includes 2M noise sources and product-tree depth O(M). The stated O(1) time and O(M) hardware are therefore not robust scaling statements.","section":"Section 5 and Section 3"}],"minor_comments":[{"comment":"The notation \"O(2N)\" appears in several places where the context and the word \"exponentially\" clearly indicate O(2^N). This should be corrected throughout, as it currently reads as linear complexity.","section":"Throughout, e.g., Section 5 and Figure 5 caption"},{"comment":"The title \"Quantum supremacy challenged\" is not supported by the paper's own admissions in Section 4.1; a more modest title reflecting the limitations would be more accurate.","section":"Title"},{"comment":"The sentence \"removing a specific number does not require any search algorithm\" is only true if U_S(t) is provided; the input representation should be explicitly stated at the start of the problem so that the hidden encoding cost is visible.","section":"Section 4.2"},{"comment":"The paper cites Tang's result [4] on state-preparation assumptions but does not connect it to its own free-encoding assumption; adding such a discussion would clarify the central limitation.","section":"Section 1 and Section 4.2"},{"comment":"Figure 8 is referenced in the text but the experimental setup, parameters, and results shown in it are not described; please add a description or remove the figure.","section":"Section 4.2, Figure 8"}],"recommendation":"reject","confidential_remarks":"The paper is an invited-talk article in physics.gen-ph with a provocative title, but the technical flaws are severe. The authors' own Note in Section 4.1 already concedes that the first benchmark does not demonstrate supremacy, yet the conclusion ignores this. The second benchmark's O(1) claim depends on a free-encoding assumption that the paper itself does not justify, and the problem statement explicitly defines the input as a set of n arbitrary numbers, making the omitted encoding cost load-bearing. The comparison in the first benchmark is also unfair because it compares a compact structural representation against a naive element-wise loop. These issues cannot be fixed by local revisions; they require reframing the central claim, which would change the paper's scope and conclusion. I recommend rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: the paper contains real timings and an honest admission that its first benchmark fails, but the central claim of exponential speedup rests on a free-encoding assumption that the authors themselves concede is false for arbitrary sets. I wouldn't take the supremacy challenge seriously, but the paper is a decent illustration of how operation-counting can mislead.\n\nThe genuinely new part is the benchmark: the authors built an INBL engine, emulated the noise-bit operations, and measured CPU time against a straightforward classical loop. That is concrete and useful. They also deserve credit for including the note in §4.1 that a classical shared-LSB trick solves the odd-to-even problem in O(1), which undercuts their own first demonstration. Not every author leaves that in.\n\nThe soft spots are load-bearing. The hat-removal 'O(1)' in Eq. (11) assumes U_S(t) is already available. For a set S of n arbitrary random M-bit numbers, forming U_S(t) requires summing n product waveforms—O(n) operations in any physical implementation. The paper's own §4.1 note concedes that for random/arbitrary sets both classical and INBL hardware complexity would be O(2^N); the same reasoning applies to §4.2 but is not stated there. So the exponential speedup is purchased by not counting the encoding step. The first benchmark is already conceded to have no supremacy. What remains is a demonstration that operations on pre-encoded superpositions are fast—a property of the representation, not a computational advantage over Turing machines. The comparison against a naive linear-search baseline is also not the strongest classical algorithm, though for an unindexed heap that is at least defensible.\n\nOn the citation pattern: the core ideas (Achilles operation, NOT operator, hat removal) are from the group's earlier papers, and the paper says so. That is fine, but it means the novelty is in the timings, not the mechanism. The missing code and data is a minor issue for a physics letter, but it does make the timing results hard to check.\n\nBottom line: this paper is for someone working in noise-based logic or teaching pitfalls in 'speedup' claims. As a refutation of quantum supremacy, it fails; as an illustration of INBL operations on ready-made superpositions, it is fine but not novel. I would not send it to peer review in its current form—the conclusions overstate what the evidence supports, and the fix would require reframing the entire claim rather than a small revision.","headline":"A concrete INBL demonstration whose exponential-speedup claim collapses once you count the cost of building the superposition; the paper even admits as much in a note.","tokens_in":7810,"tokens_out":2989,"would_cite":false,"duration_ms":29376,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Classical noise-based circuits can act on all numbers in an exponential set at once, reducing tasks from O(2^N) steps to O(1) on the two benchmark problems the paper tests.","keywords":["instantaneous noise-based logic","random telegraph waves","superposition","exponential Hilbert space","special-purpose computing","quantum supremacy","unindexed set search","Deutsch-Jozsa algorithm"],"falsifier":"A decisive experiment is to benchmark the full hat-removal task on an arbitrary set of size 2^N while including the time to build the superposition U_S(t) from the n individual numbers; if that construction time grows with set size, the measured O(1) removal does not amount to an end-to-end exponential speedup.","tokens_in":6760,"feed_emoji":"⚡","tokens_out":7750,"duration_ms":84043,"temperature":0.7,"pith_summary":"The paper claims that Instantaneous Noise-Based Logic (INBL)—a classical scheme in which logical bits are independent random telegraph waves—can process an exponentially large set of numbers as a single superposition, so operations that a Turing machine would do one element at a time instead happen on all elements at once. It reports two benchmark experiments on a laptop: converting all odd numbers in a set of size 2^N to even numbers, and finding and removing one specified number from an unsorted set. In both, the classical algorithm's time and memory grow as O(2^N), while the INBL implementation is measured at constant time and O(M) memory. The paper presents this as evidence that INBL can achieve quantum-like exponential speedup without quantum hardware, decoherence, or error correction. It also flags, in the odd-to-even example, that a special-purpose classical algorithm exists with O(1) time, so the first demonstration is illustrative rather than a supremacy claim; the hat-removal result carries the stronger claim.","feed_headline":"Classical noise circuits process exponential sets in constant time","feed_subtitle":"Two benchmark experiments show O(1) INBL operations where a classical loop needs O(2^N) steps.","key_machinery":"The load-bearing object is the INBL superposition. For M noise-bits, each bit i has two independent dichotomous reference waveforms, low L_i and high H_i; the product over bits of the chosen value defines a hyperspace vector S_k(t) representing number k. Adding the S_k(t) for all elements of a set—the Achilles operation implemented by the Hilbert-space synthesizer—creates a 2^M-dimensional superposition carried on one wire. Bit manipulation is done by multiplying the superposition by an operator such as NOT_i = H_i L_i, which flips bit i in every constituent vector at once; removal of one element is done by subtracting its hyperspace vector. The fixed number of clock cycles T in the random telegraph waves sets the operation time, which is why the measured time complexity is O(1) instead of depending on set size.","core_discovery":"The central claim is that the exponential state space of an INBL superposition is the computational resource that buys the speedup. Each M-bit number k is mapped to a hyperspace vector S_k(t), the product of one reference random telegraph wave per bit; summing these product strings yields a superposition U(t) whose dimension is 2^M. The paper's two demonstrations show that a single algebraic operation on U(t)—multiplication by NOT_i = H_i L_i for the least significant bit, or subtraction of one hyperspace vector S_a(t)—changes or removes the corresponding element for every number in the set simultaneously. Because the operation count is set by the fixed clock length T of the telegraph waves, measured as O(1), not by the number of elements, the paper concludes that INBL runs these tasks with O(1) time and O(M) hardware where the classical loop needs O(2^N), and interprets this as an instance of the exponential speedup INBL's theory predicts.","pith_inferences":["The paper leaves open whether the speedup survives when the input set is arbitrary: its own note says that building the superposition of an arbitrary set would cost O(2^N) hardware for both classical and INBL systems, so the measured O(1) is the cost of the operation, not of full end-to-end computation on arbitrary inputs.","If one counted the encoding step, hat-removal would reduce to the same state-preparation caveat that limits several quantum-inspired speedups: the hard part is getting the data into superposed form, not the parallel operation itself.","A physical INBL processor would need a reference-noise system generating 2M synchronized random telegraph waves; the paper benchmarks a software emulation on an ordinary laptop, so actual hardware speedup would additionally depend on the speed and jitter of those reference generators.","The same simultaneous bit-flip and subtraction mechanisms could be assembled into a family of special-purpose parallel operations—composite gates, verification, and searches—rather than a general-purpose alternative to quantum computing."],"forward_implications":["For the two benchmark tasks, replacing element-by-element classical loops with operations on an INBL superposition changes time from O(2^N) to O(1) and memory from O(2^N) to O(M).","If the same mechanism scales, INBL phonebook search and Deutsch-Jozsa-style decision problems inherit the speedup, giving deterministic classical hardware a quantum-competitive niche for special-purpose computation.","Because INBL outputs are deterministic and involve no probabilistic measurement, the error budget is set only by the probability that two random telegraph waveforms are identical, which the paper bounds by choosing the waveform length (83 cycles for a 10^-25 error target).","The odd-to-even example, as the paper itself notes, admits a special-purpose O(1) classical solution, so that particular demonstration is not a supremacy claim; the hat-removal benchmark is the one intended to carry the exponential-gap argument."],"supporting_citations":[{"why":"Supplies the INBL architecture, the Achilles superposition operation, and the theoretical Deutsch-Jozsa speedup the engine builds on.","marker":"[1]"},{"why":"Introduces orthogonal noise reference signals and the set/algebraic logic operations that INBL inherits.","marker":"[7]"},{"why":"Shows how 2^N states are superposed in a single wire, the exponential hyperspace the benchmarks exploit.","marker":"[8]"},{"why":"Provides the reference-system method for NOT operations by swapping high and low wires, the bit-flip mechanism used in the odd-to-even benchmark.","marker":"[10]"},{"why":"Defines the hat-removal problem and the noise-based subtraction solution whose constant-time claim is benchmarked.","marker":"[12]"},{"why":"Fixes the random-telegraph clock length that makes operation time a constant with bounded error probability.","marker":"[20]"}],"fun_headline_variants":["Noise-based logic challenges quantum supremacy without qubits","Classical noise circuits run exponential tasks in constant time","Exponential speedup from classical noise, no quantum needed","Noise-bits deliver quantum-like speedup on classical hardware","INBL: deterministic exponential speedup from stochastic noise"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The exponential speedup depends on the input set already being encoded as a superposition at no extra cost; the paper itself notes that constructing that superposition for an arbitrary set would take O(2^N) hardware for both classical and INBL systems.","fun_headline_variants_meta":{"raw":{"variants":["Noise-based logic challenges quantum supremacy without qubits","Classical noise circuits run exponential tasks in constant time","Exponential speedup from classical noise, no quantum needed","Noise-bits deliver quantum-like speedup on classical hardware","INBL: deterministic exponential speedup from stochastic noise"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000243,"raw_usage":{"total_tokens":1555,"prompt_tokens":996,"completion_tokens":559,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":612,"completion_tokens_details":{"reasoning_tokens":480}},"tokens_in":612,"tokens_out":559,"duration_ms":6814,"temperature":1.0,"reasoning_tokens":480,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T12:45:12.213027+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A decisive experiment is to benchmark the full hat-removal task on an arbitrary set of size 2^N while including the time to build the superposition U_S(t) from the n individual numbers; if that construction time grows with set size, the measured O(1) removal does not amount to an end-to-end exponential speedup.","supporting_citations":[{"cited_title":"\"Quantum supremacy\" challenged. Instantaneous noise-based logic with benchmark demonstrations","cited_arxiv_id":"2506.00063","evidence_quote":"Supplies the INBL architecture, the Achilles superposition operation, and the theoretical Deutsch-Jozsa speedup the engine builds on."},{"cited_title":"Google's claim of quantum supremacy has been completely smashed","cited_arxiv_id":null,"evidence_quote":"Introduces orthogonal noise reference signals and the set/algebraic logic operations that INBL inherits."},{"cited_title":"Noise-based logic: Binary, multi-valued, or fuzzy, with optional superposition of logic states","cited_arxiv_id":null,"evidence_quote":"Shows how 2^N states are superposed in a single wire, the exponential hyperspace the benchmarks exploit."},{"cited_title":"Noise-based deterministic logic and computing: a brief survey","cited_arxiv_id":"1007.5282","evidence_quote":"Provides the reference-system method for NOT operations by swapping high and low wires, the bit-flip mechanism used in the odd-to-even benchmark."},{"cited_title":"XOR and XNOR Gates in Instantaneous Noise-Based Logic","cited_arxiv_id":null,"evidence_quote":"Defines the hat-removal problem and the noise-based subtraction solution whose constant-time claim is benchmarked."},{"cited_title":"Entanglement, and Unsorted Database Search in Noise-Based Logic","cited_arxiv_id":null,"evidence_quote":"Fixes the random-telegraph clock length that makes operation time a constant with bounded error probability."}],"review_version":1}