arXiv:1905.08488quant-ph
Approximate encoded permutations and piecewise quantum adders
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Abstract
We present a paradigm for constructing approximate quantum circuits from reversible classical circuits that operate on many possible encodings of an input and send almost all encodings of that input to an encoding of the correct output. We introduce oblivious carry runways, which use piecewise addition circuits to perform approximate encoded additions and reduce the asymptotic depth of addition to $O(\lg \lg n)$. We show that the coset representation of modular integers (Zalka 2006) is an approximate encoded modular addition, and that it can be used in combination with oblivious carry runways. We prove error bounds on these approximate representations, and use them to construct 2s-complement adders and modular adders with lower costs than in previous work at register sizes relevant in practice.
In hardware this would be called a carry save adder [1]. One interesting fact about carry save adders is that the carry part of the register can be extended in order to avoid any carrying between words for very long periods of time. Instead of using 53 bits to represent 52 bits…
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