Ipad reboots continuously. Reboots after apple logo appears. Tried to restore using iTunes. Unable to restore. Error code is 4013.

Start here:

If you see error 9, 4005, 4013, or 4014 when you restore your iPhone, iPad, or iPod touch - Apple Support

While your iPad is continuously restarting, attempts to connect with your PC/Mac computer will likely fail. This issue must be resolved first.

Start by connecting your iPad to its Power Adapter and allow the iPad to charge for at least an hour - or preferably overnight. This step is advised as a battery with very low charge, or is failing, may produce symptoms that emulate a boot loop.

If the problem fails to stabilise, whilst still connected to the Power Adapter, attempt a forced restart of the iPad:

• On an iPad with a Home button: Press and hold the top button and the Home button at the same time. When the Apple logo appears, release both buttons.
• On other iPad models: Press and quickly release the volume up button, press and quickly release the volume down button, then press and hold the top button. When the Apple logo appears, release the button.

If iPad doesn’t turn on, or if it gets stuck during start up, see the Apple Support article If your iPhone, iPad, or iPod touch won't turn on or is frozen. Or if your iPad isn’t working correctly after you restart it, see the iPad Support website.

If your iPad is stuck is actually stuck in a boot-loop, you’ll need to resolve this specific issue - which may entail “restoring” the most recent version of iPadOS to the iPad. This support page outlines restoration of an iPad to Factory Settings:

Restore your iPhone, iPad or iPod to factory settings – Apple Support

You’ll need access to either a PC (with iTunes installed) or a Mac (with iTunes or Finder - as appropriate for the installed version of MacOS).

Download and use iTunes for Windows – Apple Support

Update to the latest version of iTunes – Apple Support

Use of a PC or Mac computer is unavoidable. If you don’t have access to a suitable computer of your own, that of a helpful friend or family member will suffice. Alternatively, the technicians at the Genius Bar of your local Apple Store or Apple Authorised Service Provider (AASP) will be delighted to assist.