Pegasus V: Dwarf Galaxy & Quantum Hardware

• Pegasus V is an ultra-faint dwarf galaxy near M31, defined by a sparse red giant branch and a pronounced blue horizontal branch that indicate an ancient, metal-poor system.
• In quantum annealing, Pegasus V refers to a D-Wave chip architecture with enhanced connectivity that enables efficient embedding of higher-order optimization gadgets.
• The designation also appears in VLBI astrometry and other fields, reflecting its multifaceted role across astrophysics, quantum computation, and bibliographic studies.

Pegasus V is a designation used in multiple, unrelated research contexts. In extragalactic astronomy, Peg V is an ultra-faint dwarf galaxy in the constellation Pegasus and a distant satellite of Andromeda (Collins et al., 2022). In quantum annealing, “Pegasus V” is used informally for Pegasus-based D-Wave hardware, including Pegasus P16 or “Pegasus V” type chips, whose connectivity graph is central to work on quadratization gadgets and minor embedding (Dattani et al., 2019). In the Gravity Probe B astrometric series, “Pegasus V” denotes the fifth VLBI paper on the guide star IM Pegasi rather than a separate physical object (Ratner et al., 2012). Other PEGASUS literatures explicitly do not define an official model literally called “Pegasus V” (Rafi et al., 24 Jun 2026).

1. Pegasus V as an ultra-faint dwarf galaxy

Pegasus V, usually abbreviated Peg V, is a newly discovered ultra-faint dwarf galaxy in the Local Group. It was initially identified in the public imaging data release of the DESI Legacy Imaging Surveys and confirmed with deep imaging from Gemini/GMOS-N (Collins et al., 2022). The DESI image showed a very low surface-brightness patch with hints of resolved stars, and the GMOS-N follow-up established that the overdensity is stellar rather than a background galaxy concentration.

The confirmation data were obtained with Gemini North using GMOS-N in the $g$ and $r$ bands, with exposure times of $2250$ s in $g$ and $1500$ s in $r$. Data reduction used the DRAGONS pipeline, and PSF photometry was carried out with DAOPHOT/ALLFRAME. Calibration was tied to the Pan-STARRS1 $3\pi$ photometric system, with extinction corrections from Schlegel et al. dust maps as recalibrated by Schlafly and Finkbeiner. Star–galaxy separation based on DAOPHOT sharpness showed a clear, compact overdensity in the stellar map and no corresponding overdensity in the galaxy map.

The object is located in the outskirts of M31’s halo. Its projected position made it a plausible faint satellite of either M31 or M33 at the discovery stage, but the adopted distance places it as a remote satellite of Andromeda rather than a foreground Milky Way system.

2. Distance, structure, and stellar population

The adopted distance to Peg V is $D = 692^{+33}_{-31}\,\mathrm{kpc}$, derived from the horizontal branch, with a 3D distance from M31 of $D_{\rm M31} = 242^{+12}_{-11}\,\mathrm{kpc}$ (Collins et al., 2022). The horizontal-branch estimate is preferred because the red giant branch is sparsely populated and therefore yields a weakly constrained TRGB measurement.

Parameter	Value
Right Ascension (J2000)	$$23^{\rm h}\,18^{\rm m}\,27.8^{\rm s} \pm 0.1^{\rm s}$$
Declination (J2000)	$r$0
Distance from the Milky Way	$r$1
3D distance from M31	$r$2
Absolute magnitude	$r$3
Half-light radius	$r$4
Ellipticity	$r$5
Central surface brightness	$r$6

The horizontal-branch method uses a clear bump at $r$7 and adopts $r$8 mag, giving a distance modulus of $r$9 mag. The corresponding relation is

$2250$0

A Bayesian TRGB fit with a broken power-law luminosity function yielded $2250$1 and $2250$2, consistent with the horizontal-branch result but much less precise.

The color–magnitude diagram shows a sparse red giant branch and a pronounced blue horizontal branch. A BaSTI isochrone with age $2250$3 Gyr and $2250$4 provides a good fit, indicating an old and extremely metal-poor stellar population. The horizontal-branch morphology was quantified through

$2250$5

with $2250$6, placing Peg V among the bluer horizontal-branch systems in the M31 satellite population.

Structurally, Peg V is consistent with being nearly round. The fitted ellipticity is $2250$7, and the position angle is poorly constrained, as expected for a system with very low ellipticity and small-number statistics. The inferred number of member stars in the CMD selection box is $2250$8.

3. Astrophysical interpretation and Local Group significance

Peg V lies firmly in the ultra-faint dwarf regime. Its luminosity, $2250$9, absolute magnitude $g$0, and half-light radius of order $g$1 pc place it among canonical ultra-faint dwarfs rather than compact star clusters (Collins et al., 2022). Its very low metallicity and blue horizontal branch strengthen that interpretation.

The combination of $g$2, a prominent blue horizontal branch, and ultra-faint luminosity led the discovery paper to identify Peg V as a plausible reionization fossil. This suggests a system that formed most of its stars early and experienced little subsequent chemical enrichment. A plausible implication is that Peg V belongs to the same broad class of ancient, quenched, metal-poor systems that dominate the Milky Way ultra-faint dwarf population, but in the M31 environment.

Its location is also important observationally. Peg V is the first detection of an ultra-faint dwarf outside the deep Pan-Andromeda Archaeological Survey area, and the discovery was taken to point to a rich, faint satellite population in the outskirts of Andromeda. Because Peg V lies near the virial radius of M31, it is relevant to the faint end of the M31 satellite luminosity function and to the broader “missing satellites” problem.

The current characterization remains photometric. No spectroscopic radial velocities, velocity dispersion, or dynamical mass estimates are reported. The dark-matter-dominated interpretation therefore follows by analogy with other ultra-faint dwarfs of similar luminosity and size rather than from a direct kinematic measurement. The paper explicitly identifies spectroscopy of bright RGB stars as the route to systemic velocity, velocity dispersion, dynamical mass, and detailed abundances.

4. Pegasus V in quantum-annealing hardware

In quantum annealing research, “Pegasus V” is an informal hardware designation rather than the name of a galaxy. The relevant literature uses it for Pegasus-based D-Wave architectures, in practice corresponding to Pegasus P16 or “Pegasus V” type chips (Dattani et al., 2019). In this setting, Pegasus is a hardware connectivity graph whose vertices are physical qubits and whose edges are programmable couplers.

The context is higher-order binary optimization. D-Wave hardware natively implements quadratic Ising models of the form

$g$3

so cubic and quartic terms must be reduced to quadratic form by quadratization gadgets that introduce auxiliary variables. The cost of using a gadget is therefore not only the number of auxiliary variables required by the algebraic reduction, but also the additional physical qubits needed for minor embedding into the hardware graph.

Pegasus differs from Chimera by having significantly higher local degree and richer intra-cell connectivity. Two properties are central in the quadratization study. First, Pegasus contains $g$4 as a subgraph. Second, all studied gadget graphs for single cubic and quartic terms can be embedded inside a single Pegasus cell with maximum chain length $g$5. By contrast, some quartic gadgets on Chimera require multiple cells and chains of length $g$6.

These properties materially reduce qubit overhead. For cubic gadgets, all single-auxiliary constructions can be embedded on Pegasus with no additional embedding qubits. For quartic gadgets, Pegasus still requires overhead for denser graphs, but much less than Chimera. The practical recommendations can be summarized succinctly as follows.

Higher-order term	Best total auxiliary qubits on Pegasus	Embedding remark
Negative cubic	1	no extra embedding qubits
Positive cubic	1	$g$7-type gadgets embed directly
Negative quartic	1	no extra embedding qubits
Positive quartic	2	using $g$8 or $g$9 gadgets

The detailed tables in the quadratization paper show that Pegasus consistently lowers embedding overhead relative to Chimera. For positive quartic terms, for example, $1500$0 and $1500$1 gadgets both require $1500$2 total auxiliary qubits on Pegasus, whereas the corresponding totals on Chimera differ and are larger. This makes Pegasus V hardware especially effective for compact embeddings of dense small gadget graphs.

5. Minor embedding complexity on broken Pegasus graphs

A separate line of work studies Pegasus graphs not as improved hardware for gadget placement, but as the substrate of a decision problem: whether an arbitrary logical graph can be minor-embedded into a broken Pegasus hardware graph. A broken Pegasus graph is defined as a vertex-induced subgraph of a Pegasus graph, modeling unavailable qubits (Lobe et al., 2021).

The key result is formal complexity-theoretic: the BROKEN PEGASUS MINOR EMBEDDING PROBLEM is NP-complete. The decision problem is: given an arbitrary graph $1500$3 and some $1500$4, is $1500$5 a minor of $1500$6, equivalently, is $1500$7 embeddable in $1500$8? The proof proceeds by first establishing NP-completeness of Hamiltonian cycle on broken Chimera graphs and then lifting the result to Pegasus by exploiting the fact that a Chimera-like graph occurs as a vertex-induced subgraph of Pegasus.

The reduction relies on the equivalence between graph minors and minor embeddings, expressed in the paper as: given two arbitrary graphs $1500$9 and $r$0, $r$1 is a minor of $r$2 if and only if $r$3 is embeddable in $r$4. For Pegasus, the decisive structural observation is that Pegasus contains a vertex-induced subgraph built from unit cells with a $r$5-subgraph arranged and connected in a grid pattern, sufficient for the hardness construction.

This result places a limit on what the superior connectivity of Pegasus V hardware can guarantee. Richer connectivity reduces chain lengths and improves many practical embeddings, but it does not remove worst-case hardness. The implication drawn in the paper is that heuristic or template-based embedding methods remain necessary on Pegasus systems, especially when broken qubits invalidate regular constructions. The result is explicitly about worst-case complexity, not about typical performance on structured application graphs.

6. Other uses and explicit non-uses of the designation

In the Gravity Probe B astrometric literature, “Pegasus V” refers to the fifth paper in the VLBI series on IM Pegasi. That paper derived the guide star’s astrometric solution from $r$6 epochs between $r$7 and $r$8, obtaining proper motions of $r$9 mas yr$3\pi$0 in right ascension and $3\pi$1 mas yr$3\pi$2 in declination, together with a parallax of $3\pi$3 mas, corresponding to $3\pi$4 pc (Ratner et al., 2012). Here, the “V” is bibliographic rather than taxonomic.

In abstractive summarization, the terminology is more explicit about non-usage. The paper “Optimizing Abstractive Summarization With Fine-Tuned PEGASUS” states that it does not define a model literally called “Pegasus V”; instead it introduces a specialized version or configuration of PEGASUS, named pegasus_xlsum, fine-tuned on XL-Sum English (Rafi et al., 24 Jun 2026). On that benchmark, the fine-tuned model achieved ROUGE-1 $3\pi$5, ROUGE-2 $3\pi$6, and ROUGE-L $3\pi$7, outperforming the baseline mT5 scores of $3\pi$8, $3\pi$9, and $D = 692^{+33}_{-31}\,\mathrm{kpc}$0. A later medical summarization study likewise analyzes PEGASUS and PEGASUS-X checkpoints, but not a model officially named Pegasus V; in that setting, pegasus-x-base reached a best ROUGE-1 of $D = 692^{+33}_{-31}\,\mathrm{kpc}$1, while pegasus-x-large reached $D = 692^{+33}_{-31}\,\mathrm{kpc}$2, illustrating that a larger checkpoint could underperform on scarce radiology data (Benzoni et al., 18 Sep 2025).

In spyware research, Pegasus is treated as a continuously evolving product line rather than a numbered family with a version called Pegasus V. The relevant survey explicitly states that it does not use labels like “Pegasus V,” although it does describe a progression from spear-phishing and one-click attacks to zero-click exploit chains such as FORCEDENTRY (Kareem, 2024). A similar pattern holds for other PEGASUS acronyms: “PEGASUS: Physically Enhanced Gaussian Splatting Simulation System for 6DoF Object Pose Dataset Generation” names a Gaussian-splatting-based simulation system, and “Particle Event Generator: A Simple-in-Use System PEGASUS version 1.0” names a parton-level Monte Carlo event generator, but neither introduces a research object called Pegasus V (Meyer et al., 2024, Lipatov et al., 2019).

Taken together, these usages show that “Pegasus V” is not a single cross-disciplinary referent. It is, depending on context, an ultra-faint Andromeda satellite, an informal designation for Pegasus-based quantum-annealing hardware, or a fifth paper in a VLBI series; in several PEGASUS-named literatures, it is explicitly not an official model name.