I think the best, and also most popular, textbook for a Quantum Mechanics 1 course is "Introduction to Quantum Mechanics" by David J. Griffiths. This is also what Claude says.
But you also need some math: Complex numbers, linear algebra, some basics of partial differential equations.
But a traditional university course in quantum mechanics aims at doing quantum mechanics in 3-dimensional space, to solve electron orbitals and energy levels of hydrogen atom. But all this 3-dimensional mathematics, you don't necessarily need if you just want to read about quantum computers. Maybe some quantum computers textbook has a presentation of the basics of quantum mechanics that leaves out the topics that traditional physics needs, because traditionally physics was interested in how atoms are build.
But you also need some math: Complex numbers, linear algebra, some basics of partial differential equations.
But a traditional university course in quantum mechanics aims at doing quantum mechanics in 3-dimensional space, to solve electron orbitals and energy levels of hydrogen atom. But all this 3-dimensional mathematics, you don't necessarily need if you just want to read about quantum computers. Maybe some quantum computers textbook has a presentation of the basics of quantum mechanics that leaves out the topics that traditional physics needs, because traditionally physics was interested in how atoms are build.