Logical Qubit

A logical qubit is an error-corrected quantum bit encoded redundantly across many physical qubits so that computations can run reliably despite hardware noise. Depending on error rates and codes, estimates commonly run from hundreds to a few thousand physical qubits per logical qubit, which is why machines with a thousand physical qubits remain far from cryptographic relevance.

Why it matters

Logical qubits are the honest unit for measuring quantum progress. Headlines cite physical qubit counts, but algorithms that threaten cryptography, such as Shor's, require thousands of stable logical qubits running millions of sequential operations. Google's Willow chip demonstrated in December 2024 that error rates can fall as the correcting code grows, a milestone called operating below threshold, but sustained fault-tolerant computation at scale has not been shown publicly.

Estimates for breaking bitcoin's 256-bit elliptic curve keys generally land in the low thousands of logical qubits, implying millions of physical qubits with current techniques, a gap most researchers measure in years to decades.

In the gold vs bitcoin debate

The logical qubit count is effectively the countdown clock in the quantum argument between gold and bitcoin. Gold advocates note their asset needs no defense against any qubit count. Bitcoin advocates track the same numbers to argue there is ample time to deploy post-quantum signatures before any machine approaches relevance.