Windowed quantum arithmetic

TL;DR

This paper introduces a windowing technique for quantum circuits that reduces gate counts by grouping control qubits, improving efficiency in quantum arithmetic operations like modular exponentiation.

Contribution

It presents a novel windowed quantum arithmetic method that optimizes circuit complexity, outperforming previous approaches in Toffoli gate counts for large register sizes.

Findings

Lower Toffoli counts in windowed modular exponentiation

Efficient control qubit iteration via small table lookups

Applicable to quantum registers from tens to thousands of qubits

Abstract

We demonstrate a technique for optimizing quantum circuits that is analogous to classical windowing. Specifically, we show that small table lookups can allow control qubits to be iterated in groups instead of individually. We present various windowed quantum arithmetic circuits, including a windowed modular exponentiation with nested windowed modular multiplications, which have lower Toffoli counts than previous work at register sizes ranging from tens of qubits to thousands of qubits.