Quantum Computing Breakthroughs: Shor's Algorithm Feasible with Just 10,000 Qubits
Two landmark papers published this week have dramatically reduced the resource requirements for breaking modern cryptography using quantum computers. The results, announced on March 30-31, 2026, represent a significant shift in the timeline for quantum threats to current encryption standards.
The Caltech Paper: 10,000 Qubits for Shor's Algorithm
A team from Caltech, including renowned physicist John Preskill, demonstrated that Shor's algorithm — the quantum algorithm capable of breaking RSA and elliptic curve cryptography — can be executed at cryptographically relevant scales with as few as 10,000 reconfigurable atomic qubits.
Key findings:
- With 26,000 physical qubits, discrete logarithms on the P-256 elliptic curve could be computed in just a few days
- Factoring RSA-2048 would take one to two orders of magnitude longer
- Recent neutral-atom experiments have already demonstrated arrays with more than 6,000 highly coherent qubits
The Google Paper: Zero-Knowledge Proof for Responsible Disclosure
Google's quantum computing team, including Craig Gidney and Hartmut Neven, published new resource estimates showing that breaking 256-bit elliptic curve cryptography requires:
- Fewer than 1,200 logical qubits and fewer than 90 million Toffoli gates, OR
- Fewer than 1,450 logical qubits and fewer than 70 million Toffoli gates
In an unprecedented move, Google chose to validate these results using a zero-knowledge proof — proving the circuit exists without revealing its details to potential attackers. This is the first time a mathematical result has been announced via cryptographic proof.
Implications for Bitcoin and Cryptocurrencies
The Caltech paper specifically notes that Bitcoin signatures look "vulnerable to quantum attack earlier than was previously known." Previous estimates required millions of physical qubits; the new research suggests just 25,000 physical qubits could suffice — a reduction of two orders of magnitude.
The Google paper introduces a critical distinction between fast-clock architectures (superconducting, photonic) and slow-clock architectures (neutral atom, ion trap), noting that the first fast-clock Cryptographically Relevant Quantum Computers (CRQCs) could enable on-spend attacks on public mempool transactions.
Expert Commentary
Scott Aaronson, a leading quantum computing researcher at UT Austin, commented that while these results don't change the fundamental principles of quantum computing, they "do change the numbers" significantly. He emphasized the urgency of upgrading to quantum-resistant cryptography.
What Should Organizations Do?
- Immediately assess reliance on elliptic curve and RSA cryptography
- Begin migration to post-quantum cryptographic standards (NIST PQC standards)
- Audit blockchain and cryptocurrency holdings for quantum vulnerability
- Monitor quantum hardware development timelines closely
Sources: arXiv:2603.28627, arXiv:2603.28846, Shtetl-Optimized