Apart from the ones James Wotton mentioned, recently IBM collaborated with a few top quantum computing software startups:
Zapata Computing – Based in Cambridge, MA, Zapata Computing is a quantum software, applications and services company developing
algorithms for chemistry, machine learning, security, and error
Strangeworks (our site's sponsor!) – Based in Austin, TX and founded by William Hurley, Strangeworks is a quantum computing
software company designing and delivering tools for software
developers and systems management for IT Administrators and CIOs.
QC Ware – Based in Palo Alto, CA, QC Ware develops hardware-agnostic enterprise software solutions running on quantum
computers. QC Ware’s investors include Airbus Ventures, DE Shaw
Ventures and Alchemist, and it has relationships with NASA and other
government agencies. QC Ware won a NSF grant, and its customers
include Fortune 500 industrial and technology companies.
1QBit – Headquartered in Vancouver, Canada, 1QBit builds quantum and quantum-inspired software designed to solve the world’s
most demanding computational challenges. The company’s
hardware-agnostic platforms and services are designed to enable the
development of applications which scale alongside the advances in both
classical and quantum computers. 1QBit is backed by Fujitsu Limited,
CME Ventures, Accenture, Allianz and The Royal Bank of Scotland.
Apart from these, the list also includes Cambridge Quantum Computing,
QxBranch and Quantum Benchmark. But James already mentioned them! :-)
As of now, it seems USA is leading in the number of quantum computing startups. I'd like to hear from others about startups in this area, in the other countries, too. And well, congratulations to Strangeworks! They have been doing great.