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Quantum computers have evolved from the theoretical realm into a race to large-scale implementations. This is due to the promise of revolutionary speedups, where achieving such speedup requires designing an algorithm that harnesses the structure of a problem using quantum mechanics. Yet many quantum programming languages today require programmers to reason at a low level of quantum gate circuitry. This presents a significant barrier to entry for programmers who have not yet built up an intuition about quantum gate semantics, and it can prove to be tedious even for those who have. In this paper, we present Qwerty, a new quantum programming language that allows programmers to manipulate qubits more expressively than gates, relegating the tedious task of gate selection to the compiler. Due to its novel basis type and easy interoperability with Python, Qwerty is a powerful framework for high-level quantum-classical computation.