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REVIEW 4 major objections 5 minor 22 references

"Quantum supremacy" challenged. Instantaneous noise-based logic with benchmark demonstrations

T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read 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.

desk verdict 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. read the letter →

arxiv 2506.00063 v2 pith:P6N6YBYU submitted 2025-05-29 physics.gen-ph

Nasir Kenarangui , Walter C. Daugherity , Arthur Powalka , Laszlo B. Kish This is my paper
classification physics.gen-ph
keywords instantaneousnoise-basedlogicrandomtelegraphwavessuperpositionexponentialHilbertspacespecial-purposecomputingquantumsupremacyunindexedsetsearchDeutsch-Jozsaalgorithm
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

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.

What carries the argument

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.

What would settle it

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.

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Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

  • 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.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • 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.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

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.

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 (4)
  1. [Section 5 and Section 4.1 Note] 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.
  2. [Section 4.2, Eqs. (9)-(11)] 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.
  3. [Section 4.1 and Figure 5] 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.
  4. [Section 5 and Section 3] 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.
minor comments (5)
  1. [Throughout, e.g., Section 5 and Figure 5 caption] 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.
  2. [Title] 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.
  3. [Section 4.2] 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.
  4. [Section 1 and Section 4.2] 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.
  5. [Section 4.2, Figure 8] 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.

Circularity Check

2 steps flagged · score 8.0 of 10

Hidden superposition-encoding cost: Eq. (9) assumes U_S(t) is available for free, so the O(1) removal and the exponential-speedup conclusion reduce to the paper's own representation rather than to a first-principles derivation.

  1. self definitional [Section 4.2, Eqs. (9)-(11); cf. Eq. (1) and Section 4.1 note]
    "U_S(t)=Σ_{k=1}^{n} S_k(t) (9) ... Removing hyperspace vector S_a from the superposition: U_S*(t)=U_S(t)-S_a(t) (11) ... removing a hyperspace vector from the superposition requires exactly 100 subtraction operations. Importantly, this number remains constant regardless of the size or arrangement of the set, ensuring that the INBL algorithm maintains constant time complexity for the removal process."

    Equation (11) is not a computation from the problem instance; it is the definition of set difference in the superposition representation. Because S_a is, by construction, one of the terms in the sum U_S(t) in Eq. (9), subtracting it must remove it. The O(1) count covers only this final subtraction, not the construction of U_S(t). For a set of n arbitrary random numbers, each S_k(t) is an M-factor product of reference noises (Eq. 1), so forming U_S(t) requires O(nM) multiplications and additions. The paper's own Section 4.1 note concedes that for random/arbitrary sets the INBL hardware complexity would be O(2^N), and Section 4.2 explicitly uses 'n unique random numbers'.

  2. other [Section 4.1 note; Section 5 conclusions]
    "Note: after carrying out this simulation, one of us (WD) found that the problem can also be solved by a special-purpose classical algorithm, thus there is no actual supremacy issue here... if the system of odd numbers would have been random/arbitrary instead of all the numbers then, paradoxically, the hardware complexity of both the Classical and INBL system would have been O(2N). ... The observed exponential speed increase is in line with the theoretical advantages of INBL as a potential alternative to quantum computing."

    The paper explicitly withdraws the Section 4.1 benchmark ('no actual supremacy issue') and concedes that its arbitrary-set version is O(2^N) for both systems. Section 5 nevertheless reuses that benchmark to conclude an 'exponential speed increase' and to position INBL as an alternative to quantum computing. The conclusion therefore relies on a premise that the paper itself has already refuted; the 'predicted' speedup is not independent evidence but a restatement of the abandoned comparison.

full rationale

The central claim reduces by construction. Section 4.2 defines the input set through its superposition U_S(t)=ΣS_k(t) (Eq. 9) and 'removes' a number by subtracting its hyperspace vector (Eq. 11). This operation is O(1) only because the paper counts the subtraction and not the encoding of the arbitrary set into U_S(t). Encoding n arbitrary random numbers requires n product strings of M reference noises (Eq. 1), i.e. O(nM) cost, which is exponential for the exponentially large heaps the paper advertises. The paper itself concedes this in Section 4.1 for random/arbitrary odd sets ('the hardware complexity of both the Classical and INBL system would have been O(2N)'), and it also concedes that the all-odd benchmark has a classical O(1) shared-LSB solution, 'thus there is no actual supremacy issue here.' Despite these concessions, Section 5 uses the same benchmark to claim exponential speedup and an alternative to quantum computing. The many self-citations (e.g., [12], [19], [20]) are secondary; even if the cited theory is granted, the load-bearing step is the free-availability of U_S(t), which is assumed rather than derived. The experimental timings therefore measure an operation on a pre-built superposition, not the full solution of the stated problems. This is a self-definitional reduction rather than a prediction from first principles, supporting a high circularity score.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central claims rest on a small number of free parameters and several domain assumptions inherited from the authors' prior INBL work. The most consequential assumption is the free encoding of input sets as superpositions, which the paper itself partially concedes in Section 4.1. No new physical entities are introduced.

free parameters (2)
  • T (RTW duration in clock cycles) = 100
    Chosen to make the probability of two random telegraph wave strings colliding negligible (target error probability around 10^-25 or 10^-30).
  • M (noise-bit resolution) = 32
    The number of noise bits used in the benchmark, fixing the size of the 'Universe' as 2^32. It is a chosen scale for the demonstration, not fitted to data, but the claimed hardware complexity O(M) is presented without any scaling measurements.
assumptions (4)
  • domain assumption The Achilles operation can build the equal superposition of all 2^M numbers with polynomial hardware complexity.
    Invoked in Section 2 as the 'Universe' generator, analogous to Hadamard gates in quantum computing. The paper does not prove or demonstrate a physical implementation with O(M) components for general M; this is a foundational assumption from the authors' prior work.
  • domain assumption Input sets are provided in superposition form at zero cost.
    Section 4.2 assumes U_S(t) exists without counting the cost of constructing it from the n elements of an arbitrary set. Section 4.1's Note admits that arbitrary sets require O(2^N) complexity for both classical and INBL systems, so this free-encoding premise is load-bearing for the O(1) claims.
  • domain assumption Random telegraph wave product strings are orthogonal with negligible error over T clock cycles.
    The paper relies on the statistical orthogonality of 2^M product waveforms (Section 2 and the missing Section 3). The error probability 0.5^T is stated, but the probability of any collision among 2M reference noises grows with M, so T must scale with M for a fixed error bound.
  • domain assumption Ideal analog hardware can add and multiply noise waveforms instantaneously without physical delay or noise.
    The complexity model counts clock cycles but ignores the analog electronics time, cross-talk, and thermal noise. Any real implementation would add physical overhead, but the paper treats the operations as ideal.

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Pith. "Pith review of "Quantum supremacy" challenged. Instantaneous noise-based logic with benchmark demonstrations." pith.science (2026). https://pith.science/paper/P6N6YBYU

@misc{pith2026250600063,
  author       = {Pith},
  title        = {Pith review of: "Quantum supremacy" challenged. Instantaneous noise-based logic with benchmark demonstrations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/P6N6YBYU}},
  note         = {Machine review of arXiv:2506.00063}
}
read the original abstract

Instantaneous Noise-Based Logic (INBL) represents a computational paradigm that offers a deterministic alternative to quantum computing, potentially challenging the notion of quantum supremacy without relying on quantum hardware. INBL encodes logical information in orthogonal stochastic processes ("noise-bits") and exploits their superpositions and nonlinear interactions to achieve an exponentially large computational space of dimension 2^M, where M corresponds to the number of noise-bits analogous to qubits in quantum computing. This approach enables an exponential increase in computational throughput, with a computational speedup scaling on the order of O(2^M), while maintaining hardware complexity comparable to quantum systems. Unlike quantum computers, INBL operates without decoherence, error correction, or probabilistic measurement, yielding deterministic outputs with low error probability. Demonstrated applications include exponential speed-gain compared to classical computers, such as INBL phonebook searches (for number or name lookup) and the implementation of the Deutsch-Jozsa algorithm, illustrating INBL's capability to perform special-purpose computations with quantum-like exponential speedup using classical-physical noise-based hardware. We present an experimental comparison between the execution speeds of a Classical Turing machine algorithm - which changes the values of odd numbers in an exponentially large set to their next lower even numbers - and its INBL counterpart. Another experimental demonstration of the exponential speedup in finding and removing a given number from an exponentially large, unsorted set of integers.

Figures

Figures reproduced from arXiv: 2506.00063 by the authors.

Figure 2
Figure 2. Generic noise-based logic hardware scheme (e.g. [1]). Logic operations can be executed by the gates or by operations on the reference signals. The Reference Noise System is based on a truly random number generator. The interesting concrete schemes and algorithms are those can be implemented by a binary classical computer (Turing machine) with a bit resolution that is polynomial in M. 1.2 Instantaneous Noise-Based Lo… view at source ↗
Figure 5
Figure 5. The time requirement of the INBL and Classical algorithms for changing 2N odd numbers to even ones. Both the hardware and time complexity of the Classical algorithm were growing exponentially with O(2N ), while the hardware complexity of INBL scaled only polynomially, O(M), where the number M of noise-bit resolution was fixed at 32. The time complexity of INBL was constant, O(1). For these simulations we emulated 2N… view at source ↗
Figure 7
Figure 7. Finding and removing a given number from a heap (unsorted set, Hat). [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗

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