Related papers: Factoring $2048$ bit RSA integers with a half-mill…
Recently, Cai showed that Shor's quantum factoring algorithm fails to factor large integers when the algorithm's quantum Fourier transform (QFT) is corrupted by a vanishing level of random noise on the QFT's precise controlled rotation…
In 1994, Shor introduced his famous quantum algorithm to factor integers and compute discrete logarithms in polynomial time. In 2023, Regev proposed a multi-dimensional version of Shor's algorithm that requires far fewer quantum gates. His…
This paper describes several new improvements of modular arithmetic and how to exploit them in order to gain more efficient implementations of commonly used algorithms, especially in cryptographic applications. We further present a new…
We present a detailed analysis of the impact on modular exponentiation of architectural features and possible concurrent gate execution. Various arithmetic algorithms are evaluated for execution time, potential concurrency, and space…
Integer factorization is a significant problem, with implications for the security of widely-used cryptographic schemes. No efficient classical algorithm for polynomial-time integer factorization has been found despite extensive research.…
We present an approach to simulating quantum computation based on a classical model that directly imitates discrete quantum systems. Qubits are represented as harmonic functions in a 2D vector space. Multiplication of qubit representations…
Quantum computing represents a paradigm shift in computation, offering the potential to solve complex problems intractable for classical computers. Although current quantum processors already consist of a few hundred of qubits, their…
Modular quantum computing architectures offer a promising alternative to monolithic designs for overcoming the scaling limitations of current quantum computers. To achieve scalability beyond small prototypes, quantum architectures are…
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 a Toffoli gate network for controlled elliptic curve point…
Integer factorization has been one of the cornerstone applications of the field of quantum computing since the discovery of an efficient algorithm for factoring by Peter Shor. Unfortunately, factoring via Shor's algorithm is well beyond the…
Frequently, subroutines in quantum computers have the structure $\mathcal{F}\mathcal{U}\mathcal{F}^{-1}$, where $\mathcal{F}$ is some unitary transform and $\mathcal{U}$ is performing a quantum computation. In this paper we suggest that if,…
This article proposes a new method to inject backdoors in RSA and other cryptographic primitives based on the Integer Factorization problem for balanced semi-primes. The method relies on mathematical congruences among the factors of the…
An alternative quantum algorithm for the discrete logarithm problem is presented. The algorithm uses two quantum registers and two Fourier transforms whereas Shor's algorithm requires three registers and four Fourier transforms. A crucial…
Reversible circuits for modular multiplication $Cx$%$M$ with $x<M$ arise as components of modular exponentiation in Shor's quantum number-factoring algorithm. However, existing generic constructions focus on asymptotic gate count and…
String sorting is an important part of tasks such as building index data structures. Unfortunately, current string sorting algorithms do not scale to massively parallel distributed-memory machines since they either have latency (at least)…
An N-bit quantum state requires a vector of length $2^N$, leading to an exponential increase in the required memory with N in conventional statevector-based quantum simulators. A proposed solution to this issue is the decision diagram-based…
Quantum computing has transformative computational power to make classically intractable computing feasible. As the algorithms that achieve practical quantum advantage are beyond manual tuning, quantum circuit optimization has become…
Cat qubits provide appealing building blocks for quantum computing. They exhibit a tunable noise bias yielding an exponential suppression of bit flips with the average photon number and a protection against the remaining phase errors can be…
Major obstacles remain to the implementation of macroscopic quantum computing: hardware problems of noise, decoherence, and scaling; software problems of error correction; and, most important, algorithm construction. Finding truly quantum…
Modular quantum computing architectures are a promising alternative to monolithic QPU (Quantum Processing Unit) designs for scaling up quantum devices. They refer to a set of interconnected QPUs or cores consisting of tightly coupled…