We give precise quantum resource estimates for Shor's algorithm to compute discrete
logarithms on elliptic curves over prime fields. The estimates are derived from a simulation of …

Most work in quantum circuit optimization has been performed in isolation from the results of
quantum fault-tolerance. Here we present a polynomial-time algorithm for optimizing …

In typical well-known cryptosystem, the hardness of classical problems plays a fundamental
role in ensuring its security. While, with the booming of quantum computation, some …

Performance of cryptanalytic quantum search algorithms is mainly inferred from query
complexity which hides overhead induced by an implementation. To shed light on …

This paper examines the asymptotic performance of multiplication and the cost of quantum
implementation for the Naive schoolbook, Karatsuba, and Toom-Cook methods in the …

In this paper, we study the close relationship between Reed-Muller codes and single-qubit
phase gates from the perspective of T-count optimization. We prove that minimizing the …

This paper presents quantum cryptanalysis for binary elliptic curves from a time-efficient
implementation perspective (ie, reducing the circuit depth), complementing the previous …

We describe in detail how to perform universal fault-tolerant quantum computation on a two-
dimensional color code, making use of only nearest neighbor interactions. Three defects …

In this work, we introduce a new circuit optimization technique to reduce the number of T
gates in Clifford+ T circuits by treating T gates conjugated by Clifford gates as $\frac {\pi}{4} …

This paper presents concrete quantum cryptanalysis for binary elliptic curves for a time-
efficient implementation perspective (ie, reducing the circuit depth), complementing the …