Who has responsibility for quality on project?

Project Manager

Project Manager has the ultimate responsiblity of Quality 

I think, the quality of project is not depends one person. It's depends entire organisation. Then only it will maintain better perfomance quality on project.

In our company there is quality management, and by a whole team of engineers and supervisors, their mission control on all the details of the terms of the project and approval to be received from the consultant

Although everyone is needed to apply the quality in the project, but the ultimate responsibility for Quality in a project is the project manager's responsibility.

Everyone involved with the project has a collective responsibility for quality of the final deliverable rather then any particular indivdiual.

The Primay resposibility vests with the Implementation team, however the project plan shall mention the tools and the methods by which the quality is evaluatied at each stage. If there is a control team then they shall monitor and ensure the porject quality.

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Basically, the project manager is the project champion in making good quality of project..but generating a good quality of project framework among the teams will normally generate greater value and satisfication to the management and project team...

Every member of the team is responsible for his part of quality. As saying goes "You are as strong as your weakes link in the chain", same applies to Quality f entire project. Accountability lies with Project manager but responsibility is with individuals involved. 

In my experience I have seen immature management criticizing Quality department for failure of project/ product quality. And my take on it is that if it is responsibility of Quality department then why hafty pay to project managers?

So in nutshell PM owns quality of project but executed by all team members.