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On one cross-platform benchmark, Google's Willow ran about 66,000 times as many operations per second as Quantinuum's Helios-1, and Helios-1 ran circuits about seven times as large. Each vendor headlines the axis it leads on.
Ranked by logical qubits, fault-tolerant applications look like a staircase. Ranked by the gates each one needs, the list within reach of announced machines is shorter. Elliptic-curve attacks come before every molecular ground-state estimate in Google's 2025 tables.
Certificate authorities, the DNS root's operator, and firmware signers generate keys under quorum, script, and witness. ML-DSA keys fit that pattern. LMS and XMSS keys cannot be backed up the classical way, since reusing a one-time key allows forgery.
Quantinuum has reported logical-qubit counts of 94, 50, 48, and one on the same machine with 98 physical qubits, from four different experiments. With five questions, a reader can tell what most such announcements demonstrated.
Chrome blocked the six compromised TLS intermediates within two hours of the researcher's report. Linux distributions, language runtimes, and devices that ship their own root lists were still being patched four days later.
Quantinuum's team cut logical errors about 12-fold with each step up in code distance on the 98-qubit trapped-ion machine, for one stored logical qubit. The preprint has not been peer reviewed.
Google's team measured the error of an encoded T state at 1 to 2 in 10,000 or less. Gidney's 2025 RSA-2048 estimate assumes cultivated states about 1,000 times cleaner, followed by a further distillation step.
The circuit uses 24% fewer logical qubits and 18% fewer Toffoli gates than Google's low-qubit design. It covers a step that Shor's algorithm repeats. In a wider test, it failed 111 times in 360,960 additions.
Google and MIT researchers spread error-correcting codes across small chip modules, with 42 to 116 physical qubits in their main examples. They have not tested the design on hardware or estimated what a complete algorithm would cost on it.
Polynomial-time quantum algorithms for factoring and quantum simulation are backed by complexity theory. Grover search gains are at most quadratic. Optimization and machine learning on ordinary data rely mostly on heuristics, and researchers have matched several claimed speedups classically.
