Free tools Windows power users keep installed
One-click scans. No signup required.
The closest match to this headline is a September 30, 2026 arXiv preprint by Fernando Granha Jeronimo, Xiaojuan Ma, and Nikhil Shagrithaya. Its abstract reports a framework for constructing quantum locally testable code families and explicit quantum list-decodable codes with optimal list sizes. The match is not certain: the headline itself does not appear in the available records, and a separate preprint from the same date reports a related result with different decoding claims.
What the likely paper claims
In “From Random Quantum Codes to Explicit qLDPC Codes via Local Properties,” Jeronimo, Ma, and Shagrithaya introduce a quantum local-coordinate-wise-linear framework for nested spaces used in CSS quantum codes. The abstract says the framework expresses properties including list decoding, list recovery, and subspace design, and reports explicit qLDPC constructions for these properties. It specifically claims optimal list sizes for its quantum list-decodable and list-recoverable constructions.
These are the authors’ abstract-level claims. The available record does not establish particular theorem parameters, practical hardware performance, or an implementation. “Optimal list sizes” is qualitative here: the abstract does not give a numerical list-size value, so it should not be read as a specific number.
What quantum list decoding means
In ordinary unique decoding, a decoder aims to identify one codeword consistent with the received data and the assumed error bound. List decoding addresses cases where that is not possible: a decoder may instead return a bounded list of candidates. For quantum error-correcting codes, the codewords and errors are part of a quantum coding setting, so classical list-decoding intuition is useful only as a high-level explanation, not as a complete account of the quantum guarantees.
#1 Best Overall
- Read Before You Buy — No Video Output: These adapters support charging and USB 2.0 data transfer, but cannot transmit video signals. Except for standard USB webcams (which use USB data only), they are not compatible with HDMI/DisplayPort cables, video-capable USB-C hubs, or docking stations with video output.
- Convert USB-A Ports to USB-C: Designed to connect USB-C earphones, cables, flash drives, card readers, and other USB-C accessories to standard USB-A ports. Plug-and-play with no drivers or software required.
- Aluminum Alloy Housing: Built with a sturdy aluminum alloy shell that aids in heat dissipation and protects against daily wear and scratches. Designed to maintain a stable and secure connection.
- Compact & Travel-Friendly: The ultra-compact design allows the adapter to stay plugged into your device without blocking adjacent ports or adding bulk, reducing wear and tear on your original USB ports.
- 12-Month Warranty: Backed by a 12-month manufacturer warranty for peace of mind. Designed to meet strict quality control standards for reliable everyday performance.
An explicit family is one whose members can be constructed by a specified method, rather than one known only to exist through a nonconstructive argument. The paper’s abstract attributes its constructions to the local-properties framework; it does not, in the available material, specify an algorithmic complexity or implementation procedure.
Why the local-properties framework matters
The abstract’s central distinction is between local constraints on physical representatives and independence measured in a logical quotient. In plain terms, physical representatives are the concrete descriptions subject to local checks, while the logical quotient tracks distinctions that matter at the code’s logical level. The framework is presented as a way to use local witnesses for nested spaces while keeping those two kinds of properties distinct.
Rank #2
- 5-in-1 USB-C Hub: Experience comprehensive connectivity featuring a Power Delivery input, two USB-A 2.0 ports, a USB-A 3.0 port, and an HDMI port. (Note: The USB-C power delivery input port is only for connecting an external wall charger to power your laptop and cannot power peripheral devices.)
- 90W Pass-Through Charging: Achieve optimal charging with 90W pass-through power to your laptop, supported by a total input of 100W, with the hub reserving 10W for operational efficiency. (Note: Wall charger not included.)
- Quick Data Transfers: Accelerate your productivity with rapid data transfers using a high-speed 5Gbps USB 3.0 port and two 480Mbps USB 2.0 ports.
- 4K HDMI Display: Enhance your visual experience with a hub capable of delivering 4K resolution at 30Hz in both mirror and extend modes. Please note that this hub is compatible with MacBook (macOS 12 and newer), Windows 10 and 11, ChromeOS, and laptops equipped with DP Alt Mode and Power Delivery. Note: This device is not compatible with Linux.
- What You Get: Anker USB-C Hub (5-in-1, 4K HDMI), welcome guide, 18-month warranty, and our friendly customer service.
This organization is intended to unify several code properties under one framework, rather than presenting list decoding as an isolated construction. The abstract names list decoding, list recovery, and subspace design. It does not provide enough detail to infer exact local-check sizes, decoding radii, list bounds, or other numerical performance measures.
How the nearby preprint differs
A separate paper by William Gay, Fernando Granha Jeronimo, and Abhi Shukul, “Explicit Capacity-Achieving Quantum LDPC Codes List Decodable in Near-linear Time,” also appeared on September 30, 2026. It should not be treated as the same result: its abstract emphasizes decoding performance, while the likely headline match emphasizes a general local-properties framework and optimal list sizes.
What’s actually slowing this PC down?
Pick the symptom - the matching free tool is one click away.
Rank #3
- Sleek 7-in-1 USB-C Hub: Features an HDMI port, two USB-A 3.0 ports, and a USB-C data port, each providing 5Gbps transfer speeds. It also includes a USB-C PD input port for charging up to 100W and dual SD and TF card slots, all in a compact design.
- Flawless 4K@60Hz Video with HDMI: Delivers exceptional clarity and smoothness with its 4K@60Hz HDMI port, making it ideal for high-definition presentations and entertainment. (Note: Only the HDMI port supports video projection; the USB-C port is for data transfer only.)
- Double Up on Efficiency: The two USB-A 3.0 ports and a USB-C port support a fast 5Gbps data rate, significantly boosting your transfer speeds and improving productivity.
- Fast and Reliable 85W Charging: Offers high-capacity, speedy charging for laptops up to 85W, so you spend less time tethered to an outlet and more time being productive.
- What You Get: Anker USB-C Hub (7-in-1), welcome guide, 18-month warranty, and our friendly customer service.
| Paper | Stated emphasis | Decoding claim in the available abstract |
|---|---|---|
| Jeronimo, Ma, and Shagrithaya, “From Random Quantum Codes to Explicit qLDPC Codes via Local Properties” | Local-coordinate-wise-linear framework for nested spaces; explicit qLDPC constructions for list decoding, list recovery, and subspace design. | Claims optimal list sizes; a decoding runtime is not stated in the available abstract. |
| Gay, Jeronimo, and Shukul, “Explicit Capacity-Achieving Quantum LDPC Codes List Decodable in Near-linear Time” | Capacity-approaching explicit quantum LDPC codes. | Claims constant list sizes and near-linear-time list-decoding algorithms approaching capacity; it also describes constructions approaching the quantum Singleton bound. |
The guarantees are therefore not interchangeable. The near-linear-time algorithm and capacity/Singleton-bound emphasis belong to the second paper’s stated result; they should not be attributed to the first without support from its full text.
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.What is established—and what remains unclear
Both records are arXiv preprints submitted September 30, 2026. The available information does not establish peer review or a later publication for either paper. For the first paper, the abstract supports the framework and construction claims but not detailed parameters or practical deployment conclusions. The headline’s connection to that paper remains a likely match rather than a confirmed identification.
Quick Recap
Best Value
- 5-in-1 Connectivity: Equipped with a 4K HDMI port, a 5 Gbps USB-C data port, two 5 Gbps USB-A ports, and a USB C 100W PD-IN port. Note: The USB C 100W PD-IN port supports only charging and does not support data transfer devices such as headphones or speakers.
- Powerful Pass-Through Charging: Supports up to 85W pass-through charging so you can power up your laptop while you use the hub. Note: Pass-through charging requires a charger (not included). Note: To achieve full power for iPad, we recommend using a 45W wall charger.
- Transfer Files in Seconds: Move files to and from your laptop at speeds of up to 5 Gbps via the USB-C and USB-A data ports. Note: The USB C 5Gbps Data port does not support video output.
- HD Display: Connect to the HDMI port to stream or mirror content to an external monitor in resolutions of up to 4K@30Hz. Note: The USB-C ports do not support video output.
- What You Get: Anker 332 USB-C Hub (5-in-1), welcome guide, our worry-free 18-month warranty, and friendly customer service.
Rank #4
- Dual Converters, Infinite Potential：Includes 2× USB C male to USB A female adapters and 2× USB A male to USB C female adapters. Perfect for a wide range of uses—tablets with Bluetooth keyboards, expand USB ports on macbook, and more. Two different converters for all your daily needs
- Next-Level 10Gbps & 3A Charging: No more slow 480Mbps, this usb to usb c adapter has a transfer speed of up to 10Gbps, allowing you to do more transferring in less time. This usb adapter fits both USB A and USB C charger, supporting up to 3A fast charging
- Upgraded Exquisite Craftsmanship: With an aluminum alloy housing and metal connector, the usbc to usb adapter is extremely durable and sturdy. Rigorously tested to withstand more than 10,000 times of plugging and unplugging, ensuring long-lasting performance
- Broad Compatible: The usb c to usb adapter widely supports all USB C/ USB A devices like laptops, tablets, cellphones, car chargers, and phone chargers. Such as compatible with MacBook Pro/Air 2023/2022, Thunderbolt 4/3 Devices,Apple MagSafe Watch 9/8/7/SE/Ultra, iPad Pro 2022/2021, Samsung Galaxy S23/S20/S10, and iPhone 17/16/15 Pro. Plug and play
- Please Note: To reach 10Gbps speed, keep the cable under 3.3 ft. For USB A Male to USB C adapters, try flipping the USB C connector. USB C Male to USB A adapters support bidirectional 10Gbps transfer within 3.3 ft
Product prices and availability are accurate as of the date/time indicated and are subject to change. Any price and availability information displayed on Amazon at the time of purchase will apply.
