Arithmetic Archives - IEEE Transactions on Quantum Engineering

Exploration of Design Alternatives for Reducing Idle Time in Shor’s Algorithm: A Study on Monolithic and Distributed Quantum Systems

September 17, 2025Moritz Schmidt Abhoy Kole Leon Wichette Rolf Drechsler Frank Kirchner Elie MounzerQuantum Computing, UncategorizedArithmetic, Computer architecture, Hardware, Logic gates, Optimization, Quantum circuit, Quantum computing, Qubit, Registers, Standards

Abstract: Shor’s algorithm is one of the most prominent quantum algorithms, yet finding efficient implementations remains an active research challenge. While many approaches focus on low-level modular arithmetic optimizations, a broader perspective can provide additional opportunities for improvement. By adopting a midlevel abstraction, we analyze the algorithm as a sequence of computational tasks, enabling systematic […]

On the Realistic Worst-Case Analysis of Quantum Arithmetic Circuits

We provide evidence that commonly held intuitions when designing quantum circuits can be misleading. In particular, we show that 1) reducing the T-count can increase the total depth; 2) it may be beneficial to trade controlled NOTs for measurements in noisy intermediate-scale quantum (NISQ) circuits; 2) measurement-based uncomputation of relative phase Toffoli ancillae can make […]