Cobble: From Planet Formation to Quantum Programming

• Cobble is a term that designates a transitional regime in planet formation, where particles around 10 cm bridge the gap between pebbles and pre-planetesimals.
• In asteroid studies, cobbles are manufactured, coherent rock-like simulants whose fidelity is evaluated through metrics like bulk density (≈1.80 g/cm³) and compressive strength (≈1.7 MPa).
• In quantum computing, Cobble is a programming language that compiles block-encoded matrix expressions into optimized quantum circuits using techniques like sum and polynomial fusion.

Cobble denotes different objects across recent technical literature. In planet-formation work, it names a size regime at the upper end of “pebble” terminology, transitional toward larger pre-planetesimal bodies. In asteroid-simulant research, it denotes a coherent, bonded rock-like simulant form distinct from loose regolith. In quantum computing, “Cobble” is the proper name of a programming language and compiler for block-encoded matrix expressions in quantum computational linear algebra (Zhang et al., 2020, Metzger et al., 2023, Yuan, 3 Nov 2025).

1. Cobble as a size regime in early planet formation

In the planet-formation sequence described for the embedded disk CB26, solids begin as submicron-to-micron interstellar grains, grow to larger porous aggregates, then to millimeter “pebbles,” centimeter pebbles or small cobbles, and eventually to decimeter- to meter-scale bodies often described as cobbles, boulders, or pre-planetesimal aggregates before assembling into kilometer-scale planetesimals (Zhang et al., 2020). Within that sequence, the sizes inferred for CB26 are explicitly beyond ordinary “large grains” in the millimeter sense.

The key fitted quantity is the disk maximum grain size,

$$a_{\max}^{\rm disk}\approx 5^{+4}_{-2}\,\mathrm{cm},$$

that is, particles with diameters of the order of $10\,\mathrm{cm}$ (Zhang et al., 2020). The paper’s title uses “Pebbles,” but the detailed discussion states that this scale is at the upper end of pebble terminology and at the large-pebble/small-cobble boundary. A plausible implication is that “cobble” in this context is not a sharply fixed class boundary, but a transitional descriptor for solids that are already substantially larger than the millimeter–centimeter regime usually emphasized in disk observations.

The terminology matters because the observational claim is not merely that CB26 contains somewhat evolved dust. The claim is that the embedded Class I disk already contains solids in a size range relevant to the earliest stages of core formation. The authors therefore connect the inferred $\sim 10\,\mathrm{cm}$ scale to the possibility that Class II disks are already seeded with large particles and may even contain planetesimals, while stopping short of claiming direct planetesimal detection (Zhang et al., 2020).

2. CB26 and the observational inference of cobble-scale solids

The CB26 study combines a spectral energy distribution from $0.9\,\mu\mathrm{m}$ to $6.4\,\mathrm{cm}$ with high-angular-resolution continuum maps at $1.3$, $2.9$, and $8.1\,\mathrm{mm}$, and models the disk-plus-envelope structure with RADMC-3D (Zhang et al., 2020). The fitted disk has

$$r_{\rm in}=16.0^{+37.4}_{-8.0}\,\mathrm{au}, \qquad r_{\rm out}=172.0\pm \sim 22\,\mathrm{au},$$

inclination $\phi \approx 88^\circ$, and stellar mass fixed to

$10\,\mathrm{cm}$0

The disk dust mass is

$10\,\mathrm{cm}$1

corresponding to

$10\,\mathrm{cm}$2

for an assumed gas-to-dust ratio of $10\,\mathrm{cm}$3, about $10\,\mathrm{cm}$4 of the stellar mass (Zhang et al., 2020).

The spectral argument is formulated through the opacity law

$10\,\mathrm{cm}$5

and, for optically thin dust emission,

$10\,\mathrm{cm}$6

For disk temperatures of about $10\,\mathrm{cm}$7–$10\,\mathrm{cm}$8, the study adopts $10\,\mathrm{cm}$9, so that

$\sim 10\,\mathrm{cm}$0

Using integrated $\sim 10\,\mathrm{cm}$1 and $\sim 10\,\mathrm{cm}$2 fluxes, it derives

$\sim 10\,\mathrm{cm}$3

implying

$\sim 10\,\mathrm{cm}$4

From $\sim 10\,\mathrm{cm}$5 to $\sim 10\,\mathrm{cm}$6,

$\sim 10\,\mathrm{cm}$7

and the main summary value for the outer disk is

$\sim 10\,\mathrm{cm}$8

These values are much lower than the $\sim 10\,\mathrm{cm}$9 often associated with diffuse ISM dust, and the paper stresses that such a low $0.9\,\mu\mathrm{m}$0 is generally understood to indicate grain growth to at least millimeter sizes and often to centimeter scales when radiative-transfer modeling supports that interpretation (Zhang et al., 2020).

A major part of the argument is the optical-depth analysis. The outer disk is optically thin at the observed millimeter wavelengths, whereas only the inner midplane becomes moderately optically thick. Along the midplane, the innermost regions are moderately thick out to roughly $0.9\,\mu\mathrm{m}$1 at $0.9\,\mu\mathrm{m}$2, $0.9\,\mu\mathrm{m}$3 at $0.9\,\mu\mathrm{m}$4, and $0.9\,\mu\mathrm{m}$5 at $0.9\,\mu\mathrm{m}$6, with peak optical depths only about

$0.9\,\mu\mathrm{m}$7

Because the outer disk is thin, the shallow long-wavelength slope is interpreted as a genuinely shallow opacity law rather than optical-depth flattening (Zhang et al., 2020).

The dust model assumes homogeneous spherical grains made of $0.9\,\mu\mathrm{m}$8 astronomical silicate and $0.9\,\mu\mathrm{m}$9 graphite, with an MRN-like distribution

$6.4\,\mathrm{cm}$0

$6.4\,\mathrm{cm}$1 fixed, and $6.4\,\mathrm{cm}$2 free. The best-fit value is

$6.4\,\mathrm{cm}$3

with uncertainties of $6.4\,\mathrm{cm}$4 and $6.4\,\mathrm{cm}$5. Residual $6.4\,\mathrm{cm}$6 emission in the inner $6.4\,\mathrm{cm}$7 suggests the possible presence of even larger particles there, but the study states that those larger sizes cannot be reliably quantified. The inference is therefore indirect and model-based rather than a direct imaging detection of individual cobbles (Zhang et al., 2020).

3. Cobble as a physical form of asteroid simulant

In asteroid-simulant work, “cobble” refers to one of two basic delivery forms, the other being loose regolith. The workshop report on asteroid simulants states that powderized mineral constituents can be bonded together to form competent cobbles or even “bounders,” whereas the alternative form is loose regolith with standard, fine, and coarse particle-size variants (Metzger et al., 2023). In this usage, a cobble-form simulant is therefore a coherent lithic analog fabricated from powdered feedstocks rather than a loose granular medium.

The manufacturing description is explicit. Cobble form is produced by grinding the mineral constituents to the desired textures, mixing them, wetting, and drying; preliminary work shows that the clay component binds these powders remarkably well, and the details of wetting and drying determine the mechanical strength of the resulting cobbles (Metzger et al., 2023). The paper does not supply a numerical clast-size definition for “cobble.” The term is operational rather than granulometric: it denotes competent bonded pieces.

This distinction is central to intended use. The workshop motivates asteroid simulants for tests of technologies and mission operational concepts, for training astronauts, for medical studies, and other purposes. Cobble-form materials are especially relevant to boulder extraction, grappling devices, sampling or manipulation of coherent fragments, astronaut training with asteroid-like rocks, and testing hardware for anchoring, excavation, volatile extraction, and planetary-defense concepts (Metzger et al., 2023). Regolith-form materials are more directly associated with mobility testing, gas-driven sample acquisition, dust mitigation, granular mechanics, and respirable-particle studies.

The program architecture is explicitly family-based. It aims to deliver simulants for major asteroid classes both in cobble and regolith form, beginning with one type of carbonaceous chondrite and expanding to additional classes. Candidate root simulants listed by the workshop include CI, CM, C2, CV, L Ordinary, LL Ordinary, H Chondrite, Iron, Enstatite Chondrite, and Basaltic Chondrite types, with reference meteorites such as Orgueil for CI, Murchison for CM, Tagish Lake for C2, Allende for CV, and Gibeon for Iron (Metzger et al., 2023).

A particularly important methodological point is that the highest-fidelity regolith would ideally be produced by first making cobbles and then re-grinding them, so that regolith grains are themselves lithic fragments of multiple minerals. The workshop states that this high-fidelity path is not the default product; instead, baseline regolith will initially be supplied as mixtures of monomineralic grains, while users may procure and crush cobbles if they require higher fidelity (Metzger et al., 2023). This suggests a fidelity ladder in which cobble form is both an end product and a precursor feedstock.

4. Fidelity metrics for asteroid cobble simulants

The paper on measuring asteroid simulant fidelity extends NASA’s Figure of Merit methodology to asteroid simulants “both regolith and cobble variety,” and applies it to the CI-type simulant UCF/DSI-CI-2, using Orgueil as the principal reference for most cobble-related properties (Metzger et al., 2019). In this framework, cobbles are coherent bonded pieces whose fidelity is assessed not only through composition but also through bulk density and mechanical strength.

Several FoMs are directly cobble-specific. Bulk density is defined by

$6.4\,\mathrm{cm}$8

and the cobble bulk-density FoM is

$6.4\,\mathrm{cm}$9

with $1.3$0. Mechanical strength is treated through a Weibull scaling relation,

$1.3$1

and a logarithmic compressive-strength FoM,

$1.3$2

with $1.3$3 (Metzger et al., 2019).

For the Orgueil-based reference model, the paper gives

$1.3$4

The simulant cobbles were made in a cylindrical mold with post-drying diameter $1.3$5 and height $1.3$6, then tested by ASTM C39/C39M-17b on an MTS Criterion Model 43 using four specimens, a loading rate of $1.3$7, and a $1.3$8 load cell. The average unconfined compressive strength was

$1.3$9

while the corresponding reference strength for the same effective size was

$2.9$0

The resulting cobble-strength FoM is $2.9$1 (Metzger et al., 2019).

The measured bulk density of UCF/DSI-CI-2 cobbles is

$2.9$2

compared with Orgueil at

$2.9$3

yielding $2.9$4. The corresponding porosities are about $2.9$5 for the simulant and about $2.9$6 for Orgueil (Metzger et al., 2019).

Property	Reference	FoM
Mineralogical composition	Orgueil	0.83
Elemental composition	Orgueil stoichiometry	0.94
Grain density	Orgueil	0.75
Cobble bulk density	Orgueil	0.72
Magnetic susceptibility	Multiple Orgueil measurements	0.96
Cobble strength	Orgueil-based model	0.77
Volatile release	Orgueil	0.53

These values support the paper’s conclusion that UCF/DSI-CI-2 is a good choice for a wide range of scientific and engineering applications, while also showing that fidelity is property-specific rather than reducible to one universal score (Metzger et al., 2019). The weakest reported non-particle-size metric is volatile release, whereas magnetic susceptibility is especially close to the reference. For cobble-specific engineering uses such as anchoring, drilling, or mining, the bulk-density and strength FoMs are the most directly relevant quantities.

5. Cobble as a language for quantum computational linear algebra

In quantum computing, “Cobble” is the name of a language for programming with quantum computational linear algebra. It is defined as a quantum programming language of mathematical operators over block-encoded matrices, with a compiler from high-level matrix expressions to quantum circuits, a type system ensuring well-typed programs compile to valid circuits, a cost model estimating leading time and space factors, and optimization passes specialized to block-encoding arithmetic (Yuan, 3 Nov 2025).

The central semantic object is the block encoding. For a matrix $2.9$7, Cobble uses a unitary operator whose top-left block is $2.9$8, where $2.9$9:

$8.1\,\mathrm{mm}$0

Its operational action is written

$8.1\,\mathrm{mm}$1

Because post-selection success scales with the subnormalization $8.1\,\mathrm{mm}$2, Cobble treats subnormalization as a core cost parameter rather than a secondary detail (Yuan, 3 Nov 2025).

The core syntax includes base block encodings, adjoint, scalar-weighted sum, product, direct sum, tensor product, and a symbolic polynomial form:

$8.1\,\mathrm{mm}$3

Compilation lowers sums through LCU, products by sequential composition, and suitable Hermitian polynomial transforms through QSVT. Cobble emits OpenQASM 2.0, invokes pyQSP or optionally PennyLane for QSP phase computation, and uses Quimb for classical simulation (Yuan, 3 Nov 2025).

Its runtime proxy is

$8.1\,\mathrm{mm}$4

The optimizer is organized around the observation that classical linear-algebra rewrites do not automatically transfer to block encodings. Cobble therefore implements sum fusion and polynomial fusion. Sum fusion rewrites nested linear combinations so that coefficient cancellation can reduce both query count and subnormalization; polynomial fusion rewrites explicit sums of powers into $8.1\,\mathrm{mm}$5 expressions that can be compiled by QSVT (Yuan, 3 Nov 2025).

On benchmark kernels for simulation, regression, search, and related applications, Cobble reports $8.1\,\mathrm{mm}$6–$8.1\,\mathrm{mm}$7 speedups over its unoptimized baseline in the query-times-subnormalization metric. For example, the simulation example improves from $8.1\,\mathrm{mm}$8 to $8.1\,\mathrm{mm}$9, and the regression example improves from $$r_{\rm in}=16.0^{+37.4}_{-8.0}\,\mathrm{au}, \qquad r_{\rm out}=172.0\pm \sim 22\,\mathrm{au},$$0 to $$r_{\rm in}=16.0^{+37.4}_{-8.0}\,\mathrm{au}, \qquad r_{\rm out}=172.0\pm \sim 22\,\mathrm{au},$$1 (Yuan, 3 Nov 2025). The paper also reports that Cobble’s high-level optimizations tie or exceed evaluated circuit optimizers on the tested workloads, because the crucial algebraic structure remains visible before lowering to gates.

6. Terminological boundaries and recurrent ambiguities

The three uses of “cobble” are not interchangeable. In the CB26 disk study, the word labels a particle-size regime inferred indirectly from millimeter/centimeter spectral behavior and radiative-transfer modeling; it does not denote fabricated objects or directly imaged clasts (Zhang et al., 2020). In asteroid-simulant work, by contrast, cobbles are manufactured, competent, bonded pieces whose mechanical strength depends on the details of wetting and drying, and whose fidelity is evaluated against selected asteroid properties rather than inferred from remote emission slopes (Metzger et al., 2023, Metzger et al., 2019).

A common terminological ambiguity concerns pebble versus cobble in planet formation. The CB26 paper repeatedly states “pebbles with diameters of the order of 10 cm,” yet the detailed discussion also places that size at the upper end of pebble terminology or into cobble-like sizes (Zhang et al., 2020). This is not a contradiction; it indicates that the inferred solids sit near a boundary where different communities may use different labels.

A second ambiguity concerns cobble versus regolith in simulant programs. The workshop report and the FoM paper both treat cobble as distinct from loose particulate material. High-fidelity regolith may require making cobbles and then crushing them, but the resulting regolith remains a different product class with different fidelity criteria (Metzger et al., 2023, Metzger et al., 2019).

A third ambiguity is lexical rather than conceptual. The blockchain paper “Cob: a consensus layer enabling sustainable sharding-based consensus protocols” does not mention “Cobble”; it discusses Cob, a leaderless Byzantine Fault Tolerant consensus protocol used as a synchronization layer for sharded blockchains (Flamini et al., 2022). This suggests that superficially similar names in arXiv metadata can refer to unrelated technical objects, and that “Cobble” must be interpreted from disciplinary context rather than string similarity alone.