Alice & Bob Shor Algorithm Cat Qubits RSA-2048 Explained: 22,593 Qubits Could Break Internet Encryption in 3 Days

alice bob shor algorithm cat qubits rsa-2048 explained — quantum computer hardware

Image: A quantum computer (Wikimedia Commons, CC BY-SA 4.0) — illustrative photo of quantum hardware, not Alice & Bob's cat-qubit machine. No official product photo of the cat-qubit system appears in the announcement.

TL;DR: Alice & Bob's Shor algorithm cat qubits RSA-2048 explained in one line: its new paper says a fault-tolerant machine with 22,593 cat qubits could factor RSA-2048 in 3.14 days — 40 times fewer qubits than Google's 2025 estimate. No such machine exists yet, but the runway for switching to post-quantum encryption just got shorter.

📌 KEY HIGHLIGHTS

Alice & Bob's preprint paper, published 29 October 2026, puts Shor's algorithm on cat qubits at 22,593 physical qubits for RSA-2048 in 3.14 days — a record low for total quantum resources.
The same hardware estimate cracks the elliptic-curve key behind Bitcoin and Ethereum (ECDLP-256) with 29,588 qubits in 61.8 minutes.
Three advances drive the cut: hardware-level bit-flip suppression in cat qubits, more efficient LDPC-cat error-correction codes, and a redesigned adder.
The headline figures assume no bit-flips during the run; if bit-flips occur about once an hour, RSA-2048 would need roughly 45,000 qubits.
Nothing is broken today — no machine at this scale exists — but US and UK guidance calls for the post-quantum switch to be complete by 2035, and migration takes years.

Alice Bob Shor algorithm cat qubits RSA-2048 explained: what happened?

On 29 October 2026, Paris- and Boston-based quantum company Alice & Bob announced a new resource estimate for running Shor's algorithm — the famous 1994 quantum algorithm that can factor large numbers and solve discrete logarithms far faster than any classical computer. The paper, titled "Shor's algorithm compiled on cat qubits: 22 593 qubits for RSA-2048 in 3.14 days", is posted to the IACR ePrint archive by Pappalardo, Goudarzi and colleagues.

Why does a paper about counting qubits matter? Because RSA-2048 secures much of the internet: online banking, email, digital signatures and encrypted web connections all rely on the fact that factoring a 2,048-bit number is practically impossible for classical computers. Shor's algorithm changes that equation — if a large, reliable quantum computer ever runs it. Every time the estimated hardware requirement falls, the date when today's encryption stops being safe moves closer.

Most earlier estimates counted the logical qubits an algorithm needs and multiplied by an average number of physical qubits per logical qubit. This team went further: for the most resource-hungry parts of the algorithm, it worked out exactly what each physical qubit does and when, producing complete chip layouts and schedules. That full compilation is what makes the new numbers unusually concrete — and unusually low.

How cat qubits cut the count from 49,649 to 22,593

The result rests on three advances. First, cat qubits suppress bit-flip errors at the hardware level, so error correction only has to handle phase-flips — sharply cutting the physical qubits needed per logical qubit. Second, LDPC-cat codes (from 2024) replace the repetition code used in Alice & Bob's 2023 estimate and more than halve the RSA-2048 count, from 49,649 to 22,593. Third, a redesigned adder — addition is one of Shor's algorithm's most repeated operations — was rebuilt from the ground up for cat qubits, so it runs at a steady speed without stopping to wait for error correction. The team also drew on recent algorithm breakthroughs from Inria and Google.

alice bob shor algorithm cat qubits rsa-2048 explained — quantum circuit diagram

Image: A quantum circuit diagram (Wikimedia Commons, CC BY-SA 4.0) — illustrative. Shor's algorithm is a quantum circuit; the paper compiles it down to physical qubits and chip layouts.

Target	Physical cat qubits	Time	What it protects
RSA-2048	22,593	3.14 days	Online banking, email, digital signatures, much of web encryption
ECDLP-256 (elliptic curve)	29,588	61.8 minutes	Bitcoin and Ethereum signatures (ECDSA), ECDH web key exchange
RSA-2048 if bit-flips occur ~hourly	~45,000	Longer	Same RSA-2048 systems, under less ideal hardware assumptions
Alice & Bob's 2023 estimate (repetition code)	49,649	—	RSA-2048, before LDPC-cat codes

Why it matters for readers in India and the world

For most readers, nothing changes today. Your bank login, UPI payments and WhatsApp chats are not suddenly readable — no quantum computer anywhere near 22,593 fault-tolerant qubits exists, and the paper is a resource estimate, not a demonstration. The company itself says substantial engineering challenges remain, and expects hardware improvements and falling resource requirements to converge in the early 2030s.

The Bitcoin detail deserves a calm reading. At 61.8 minutes, deriving a Bitcoin private key would take longer than Bitcoin's 10-minute block time, so a transaction already in flight stays out of reach — but coins sitting at addresses whose public keys are already on-chain would be exposed to an "at-rest" attack. That is why cryptographers talk about a "harvest now, decrypt later" risk: encrypted data stolen today could be decrypted by a future machine.

The practical clock is the migration, not the machine. Replacing cryptographic infrastructure across banks, governments and companies takes years, which is why US and UK guidance calls for the transition to post-quantum cryptography to be complete by 2035. Alice & Bob's advice — echoed by PQShield's CEO in the announcement — is that organisations should start that transition now, beginning with their most mission-critical systems, rather than waiting for a machine to appear. For India, where digital payments and online banking run on exactly this public-key infrastructure, the same long migration applies.

Should you care? ✅ / ⏳

Verdict: ⏳ No action needed for everyday users — but a real deadline for organisations. Don't change passwords or move coins because of this paper; no encryption is broken today. But if you run systems that must stay secret for years, the falling qubit count is your signal to plan the post-quantum migration now, not in the 2030s. Treat the 22,593 figure as a planning estimate with stated assumptions, not a countdown.

FAQs

What is Shor's algorithm? Shor's algorithm, devised by Peter Shor in 1994, is a quantum algorithm that factors large integers and solves discrete logarithms exponentially faster than the best known classical methods. It is the reason a large enough quantum computer threatens RSA and elliptic-curve cryptography, which both rely on those problems being hard.

Can a quantum computer break RSA-2048 today? No. Today's quantum processors have tens to low hundreds of physical qubits with significant error rates — far from the roughly 22,593 high-quality, fault-tolerant cat qubits this estimate requires. The paper estimates future hardware needs; it does not demonstrate a break.

How long would cracking a Bitcoin key take — and are my coins at risk? Under this estimate, about 62 minutes with 29,588 cat qubits for an elliptic-curve key. Because that exceeds Bitcoin's 10-minute block time, transactions in progress remain out of reach, but coins held at addresses with exposed public keys would be vulnerable to a future machine — one more reason the ecosystem is moving toward quantum-resistant signatures.

What is post-quantum cryptography, and when must the switch happen? Post-quantum cryptography (PQC) is a new generation of encryption designed to resist both classical and quantum attacks; standards already exist. US and UK guidance calls for the transition to be complete by 2035, and because large-scale migration takes years, Alice & Bob and other experts advise starting now.

TAKEAWAY: The quantum threat to today's encryption didn't arrive overnight — but its hardware price tag just fell 40-fold against Google's 2025 estimate. The smart response is unglamorous: plan the post-quantum migration early, and don't panic.

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