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We wrote our O'Reilly book, "Programming Quantum Computers", precisely to fit your use case. It assumes no advanced mathematics, doesn't shy away from really delving into how algorithms work, and also has an online simulator to let you experiment with actual code. I am of course biased, but I would say that it's the resource out there requiring the least mathematics needed to get some practical knowledge and a chance to experiment in code:


Shameless plug dealt with, the text I'd next point you to for being grounded more in the Real world rather than Hilbert space is Mermin's. Modulo his insistence on using the term QBit rather than qubit, it's a great pedagogical work by someone with a very deep understanding of quantum mechanics. It's also in hardcover, which also helps lend it more weight:


As others have recommended, anything by Scott Aaronson is gold. Computational complexity is his passion, and although I think his work is very thorough and accessible, I would suggest it's a little less hands-on. However for very, very deep insights there's nowhere better to go. Alongside his book, Aaronson's blog at https://www.scottaaronson.com/blog/ is also revered by both QC enthusiasts and professionals alike and a great place to follow debate on the latest developments in the field.

The most mathematically demanding text (or most thorough, depending on how you look at it) I'd consider is Nielsen and Chuang (a.k.a "Mike 'n' Ike", a.k.a "The bible"). It's slightly out of date in some more recent concepts regarding the implementation of quantum computing (not wrong, just a tad incomplete), but is still solid and indispensable for the core concepts and insights behind quantum computing.

If you're interested in the physical implementation of a quantum computer (i.e. what does it _look_ like inside), then Mike 'n' Ike is the only one that will come close to satisfying you. The real world is so damn messy, and quantum hardware is no exception. QC tech moves fast and the money is still on the table as to just what that tech might look like inside the million qubit quantum computer of the future. Mike 'n' Ike does discuss some specific types of qubits, but I'm not aware of a book providing a truly comprehensive and up to date description of today's most promising approaches.

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