REVIEW 3 major objections 5 minor 27 references
A Short History of Rocks: or, How to Invent Quantum Computing
T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash
Pith's one-line read The paper argues that quantum computing could have been invented in 1946 by quantizing Boolean operators instead of states.
desk verdict A genuinely witty counterfactual essay whose central scientific claim is explicitly deferred, so the math never actually appears; judge it as history, not as a research paper. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The central object is the 'noncommutative circuit': a circuit whose wires and switches obey the noncommutative laws of operator algebras rather than the commutative laws of Boolean algebra. The mechanism is the replacement of Boolean variables $x$ with projection operators $\Pi$ satisfying $\Pi^2 = \Pi$, and the use of the Gelfand-Naimark-Segal construction to represent abstract operator algebras as operators on a Hilbert space. This lets an algebra of 'yes/no' measurements play the role of bits while preserving classical logical structure inside a quantum setting.
What would settle it
The claim would be falsified if the promised noncommutative calculus cannot express a universal gate set, for example if it cannot reproduce controlled-NOT and arbitrary single-qubit rotations, or if it turns out to be equivalent to a classically simulable subtheory like stabilizer circuits.
Extended reading notes
Core claim
The central claim is that quantum computing is not uniquely tied to the state-based picture of qubits and reversible, unitary gates. Just as Shannon realized Boolean algebra could describe switching circuits, a von Neumann armed with functional analysis and quantum logic could realize that the operators of Boolean algebra, projections satisfying $\Pi^2 = \Pi$, can be embedded into Hilbert space via the Gelfand-Naimark construction and used as a circuit calculus. In this alternate timeline, states become derived objects, assignments or 'lines in the truth table,' while the primitive objects are noncommuting operators. The paper contends this route yields a simpler, more flexible calculus and close parallels to classical logic, though it leaves the complete derivation to a later paper.
Load-bearing premise
The load-bearing premise is that the 'noncommutative circuits' formalism actually exists as a useful quantum computing model; the paper defers the full derivation to a companion paper, so if that calculus cannot be constructed, the central claim lacks its foundation.
Editorial extensions
If this is right
- Quantum computing can be founded on operator-algebraic primitives rather than reversible circuits, making the standard qubit picture one option among several.
- A noncommutative circuit calculus would let classical Boolean reasoning carry over to the quantum setting with minimal changes, because Boolean laws reappear as operator laws.
- The counterfactual shows the first quantum computing proposal could plausibly have come decades earlier if the right mathematical tools had been aimed at circuit design.
- If the promised formalism works, it should yield a universal gate set and coherent error properties comparable to the usual circuit model, making the alternative computationally serious.
Reading between the lines
- My inference: if the companion paper delivers the calculus, quantum algorithm design would likely shift from building states to algebraic manipulation of observables, changing how textbooks introduce the subject.
- My inference: the same 'quantize the operators' move could be applied to other classical algebraic structures, such as monoids or semirings, yielding a family of operator-algebraic computational models beyond Boolean circuits.
- My inference: the historical counterfactual is partially testable by asking whether the 1946 toolkit, C*-algebras and the GNS construction, was mature enough to support a circuit model; Segal's contemporaneous work suggests it was close.
- My inference: the strongest test will be the promised companion paper's derivation of a universal gate set; until it appears, the essay is best read as a research proposal.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. This essay offers a narrative history of computation from tally marks to Boolean algebra, Shannon's digital circuits, and Feynman's state-based quantum computing proposal. In the second half, it presents a counterfactual timeline in which a cosmic ray damages ENIAC in 1946, leading von Neumann to explore quantum computing by 'quantizing' the operators of Boolean algebra rather than the states. The central claim is that replacing Boolean variables with projection operators yields a simpler and more flexible circuit calculus, with beautiful parallels to classical logic. However, the formalism is not developed in this paper; the abstract and Section 0 explicitly defer all technical details to a forthcoming companion paper.
Significance. If the central claim were substantiated, the paper would offer a genuinely novel conceptual origin for quantum computing and a potentially interesting alternative circuit model, one rooted in operator algebras rather than reversible state transformations. The historical narrative is engaging, well-written, and the counterfactual is creatively constructed; the paper is honest about the deferral of technical content, which is a commendable feature. That said, the paper contains no derivations, no explicit gate set, no composition rules, and the only concrete hint about projections is mathematically problematic for noncommuting projections. The central claim is therefore unsupported within this manuscript, and its significance remains entirely contingent on the promised companion paper.
major comments (3)
- [Abstract and Section 0] The abstract states that quantizing Boolean operators 'leads to a simpler, more flexible circuit calculus,' and Section 0 says the formalism is developed elsewhere. Because this is the paper's central claim, the essay should either include a self-contained account of the circuit calculus or explicitly label the claim as a conjecture that will be addressed in a companion paper. As written, the claim is an unsupported assertion, and the reader has no way to evaluate it.
- [Section 4] The proposal to 'replace Boolean variables by operators, and in particular ... build our theory around projectors obeying Π²=Π' does not preserve the Boolean operations for noncommuting projections. For two noncommuting projections p and q, pq is not self-adjoint and not idempotent, and p+q−pq is not a projection; hence the ordinary AND and OR operations do not map pairs of noncommuting projections to projections. The paper gives no alternative definition of AND/OR for noncommuting projections, no composition law for its 'noncommutative circuits,' and no universal gate set. The claimed 'parallels to classical logic' therefore do not follow from the idempotence of projections, and the central conceptual link is unsupported.
- [Section 4] The dialogue and surrounding text invoke C*-algebras and the GNS construction, but the connection between these algebraic tools and a working circuit model is never made precise. The essay says von Neumann and Shannon discuss 'noncommutative circuits' and 'states as programs,' but no definition, example, or complexity-theoretic intuition is provided. If the companion paper is intended to carry this burden, the essay should at least state a precise version of the main theorem or construction, or clearly mark the entire technical program as speculative.
minor comments (5)
- [Throughout] There are several typographical errors, including 'Feynmann' (Section 0), 'danceing' (Section 3), 'tranformed' (Section 2), 'Eckhert' (Section 4), and 'miniscule' (Section 3). These should be corrected in revision.
- [Section 2] The claim that von Neumann 'was one of these physicists' at Operation Crossroads in July 1946 should be checked against the historical record; if this is a counterfactual deviation it should be clearly noted as such, since the surrounding text generally distinguishes real events from the fictional fork.
- [References] The forthcoming companion paper that is supposed to contain the technical formalism is never cited or given a reference. A citation or working title would help the reader locate the promised work and assess whether the deferral is reasonable.
- [Figures] The figures are described in the text but many are not explicitly referenced in the body; consider numbering them and referring to them where relevant, particularly the 'noncommutative circuit' illustration in Section 4, which is the most technically significant figure.
- [Section 3] The aside that projective quantum logic 'can be efficiently simulated on a classical computer' is supported by a citation to Leifer (2005), but the claim is stated without context or definition; adding a brief explanation of what 'efficiently simulated' means would improve precision.
Circularity Check
No circularity: the essay makes no technical derivation; its central 'noncommutative circuits' formalism is explicitly deferred to a companion paper, which is a self-referential evidentiary gap but not a circular reduction.
full rationale
The paper contains no derivation chain that could reduce to its inputs. Its central speculative claim is that an operator-based ('noncommutative') picture of quantum computing would be 'a simpler, more flexible circuit calculus and beautiful parallels to classical logic,' with the technical support explicitly deferred: 'as we detail in a forthcoming companion paper' (Abstract) and 'We give a fuller development of this formalism elsewhere' (Section 0). This is a self-referential limitation—the load-bearing formalism is absent from the present text—but it is not circularity, because the paper does not define the claimed result in terms of an input, fit a parameter and call it a prediction, or invoke its own prior theorem as a forced choice. The historical claims about Boole, Shannon, Feynman, Fredkin, and von Neumann are supported by external references and are not used to justify the counterfactual conclusion. The only mathematical hint, replacing Boolean variables by projections obeying Π²=Π, is presented as a fictional dialogue about what von Neumann might have explored ('There's a noncommutative version of this'), not as a proof; whether noncommuting projections can support Boolean composition is a correctness concern, not a circular one. Accordingly, no circular step can be quoted and exhibited, and the paper receives a score of 0 on the circularity scale.
Assumptions & free parameters
assumptions (4)
- domain assumption Hilbert space formalism and C*-algebra theory (including the GNS construction) are valid descriptions of quantum mechanics.
- standard math Boolean algebra can be represented by projection operators (idempotent self-adjoint operators).
- ad hoc to paper The counterfactual scenario: a cosmic ray from T CrB knocked out ENIAC in February 1946, causing von Neumann to miss Operation Crossroads and instead develop quantum computing.
- ad hoc to paper A 'noncommutative circuit calculus' exists, is implementable, and is simpler than the standard state-based quantum circuit model.
invented entities (2)
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Noncommutative circuit calculus
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Alternate timeline (branch T CrB)
Cite this review
Pith. "Pith review of A Short History of Rocks: or, How to Invent Quantum Computing." pith.science (2026). https://pith.science/paper/M3HR4WTN
@misc{pith2026250300005,
author = {Pith},
title = {Pith review of: A Short History of Rocks: or, How to Invent Quantum Computing},
year = {2026},
howpublished = {\url{https://pith.science/paper/M3HR4WTN}},
note = {Machine review of arXiv:2503.00005}
}
read the original abstract
This essay gives a short, informal account of the development of digital logic from the Pleistocene to the Manhattan Project, the introduction of reversible circuits, and Richard Feynman's allied proposal for quantum computing. We argue that Feynman's state-based analogy is not the only way to arrive at quantum computing, nor indeed the simplest. To illustrate, we imagine an alternate timeline in which John von Neumann skipped Operation Crossroads to debug a military computer, got tickled by the problem, and discovered a completely different picture of quantum computing -- in 1946. Feynman suggested we "quantize" state, and turn classically reversible circuits into quantum reversible, unitary ones. In contrast, we speculate that von Neumann, with his background in functional analysis and quantum logic, would seek to "quantize" the operators of Boolean algebra, and with tools made available in 1946 could successfully do so. This leads to a simpler, more flexible circuit calculus and beautiful parallels to classical logic, as we detail in a forthcoming companion paper.
Reference graph
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