Doesn't need to be a PK, just the clustering index. The Quality_ID by itself would typically be the (nonclustered) PK.
Create the _test table from scratch. Add the UNIQUE CLUSTERED index and the PK:
CREATE UNIQUE CLUSTERED INDEX Quality_Test__CL
ON dbo.Quality_Test ( Quality_Date, Quality_ID )
WITH ( DATA_COMPRESSION = ROW /*or PAGE, if you prefer*/, FILLFACTOR = 98, SORT_IN_TEMPDB = ON) ON [PRIMARY] /*or your preferred filegroup name here*/
/* yes, technically NONCLUSTERED is not needed when the clus index is built first, but I prefer to explicitly specify it */
ALTER TABLE dbo.Quality_Test ADD
CONSTRAINT Quality_Test__PK PRIMARY KEY NONCLUSTERED ( Quality_ID )
WITH ( DATA_COMPRESSION = ROW, FILLFACTOR = 99, SORT_IN_TEMPDB = ON ) ON [PRIMARY] /*or your preferred filegroup name here*/
Then load the table in batches in clus key (which is believe is Quality_ID) order from the main table. Batch size will depend on the total row width and any trans log constraints, but you'd want to do at least 100,000 rows at a time, or 1M if doable. And be sure to specify "INSERT INTO dbo.Quality_Test WITH (TABLOCK)" to help the chances of getting minimal logging, if possible (which will depend on your version of SQL and other factors).
Btw, SQL should automatically PERSIST the computed column when you use it in an index, you shouldn't have to explicitly specify it as PERSISTED yourself, although of course that wouldn't hurt.
SQL DBA,SQL Server MVP(07, 08, 09) Prosecutor James Blackburn, in closing argument in the Fatal Vision murders trial: "If in the future, you should cry a tear, cry one for them [the murder victims]. If in the future, you should say a prayer, say one for them. And if in the future, you should light a candle, light one for them."