The California Rules of Court were recently updated to allow for electronic service of briefs in PDF format in lieu of mailing four hard copies to the California Supreme Court. (See Rule 8.212). Until recently, there was no way to implement this rule. However, the California Supreme Court has now set up a page for submitting PDF files in lieu of four hard copies. See the details here. The technical requirements for submitting the brief seem to be pretty basic:
Brief must be a single, text-searchable PDF file, no more than 5 MB in size, and an exact duplicate of the paper copy. Please do not submit scanned documents or any other documents associated with the case such as exhibits, applications, etc.