On Tuesday, Microsoft made a series of announcements related to its Azure Quantum Cloud service. Among them was a demonstration of logical operations using the largest number of error-corrected ...

And, in a few cases, individual quantum operations (termed gates) have been demonstrated using pairs of logical qubits.

In doing so, he says, life on Earth has likely performed about 10 elementary logical operations over its 4.5-billion-year history. That number is so staggering that it defies everyday intuition.

Such missing values are coded, for logical comparison purposes, in the bit pattern of very large negative numbers. A numeric matrix can have any mixture of missing and nonmissing values. A matrix with ...