Related papers: An exploration of the noise sensitivity of the Sho…
Quantum computers have the potential to perform computational tasks beyond the reach of classical machines. A prominent example is Shor's algorithm for integer factorization and discrete logarithms, which is of both fundamental importance…
Considering its relevance in the field of cryptography, integer factorization is a prominent application where Quantum computers are expected to have a substantial impact. Thanks to Shor's algorithm this peculiar problem can be solved in…
Shor's factoring algorithm illustrates the potential power of quantum computation. Here we present and numerically investigate a proposal for a compiled version of such an algorithm based on a quantum-wire network exploiting the…
Shor's algorithm, which given appropriate hardware can factorise an integer $N$ in a time polynomial in its binary length $L$, has arguable spurred the race to build a practical quantum computer. Several different quantum circuits…
Shor's algorithm for integer factorization offers an exponential speedup over classical methods but remains impractical on Noisy Intermediate Scale Quantum (NISQ) hardware due to the need for many coherent qubits and very deep circuits.…
In recent years, advancements in quantum chip technology, such as Willow, have contributed to reducing quantum computation error rates, potentially accelerating the practical adoption of quantum computing. As a result, the design of quantum…
Quantum computers pose a fundamental threat to widely deployed public-key cryptosystems, such as RSA and ECC, by enabling efficient integer factorization using Shor's algorithm. Theoretical resource estimates suggest that 2048-bit RSA keys…
A quantum computer -- i.e., a computer capable of manipulating data in quantum superposition -- would find applications including factoring, quantum simulation and tests of basic quantum theory. Since quantum superpositions are fragile, the…
Quantum advantage requires overcoming noise-induced degradation of quantum systems. Conventional methods for reducing noise such as error mitigation face scalability issues in deep circuits. Specifically, noise hampers the extraction of…
The objective of this paper concerns at first the motivation and the method of Shor's algorithm including an excursion into quantum mechanics and quantum computing introducing an algorithmic description of the method. The corner stone of…
The goal of this paper is to review the theoretical basis for achieving a faithful quantum information transmission and processing in the presence of noise. Initially encoding and decoding, implementing gates and quantum error correction…
Shor's factorisation algorithm is a combination of classical pre- and post-processing and a quantum period finding (QPF) subroutine which allows an exponential speed up over classical factoring algorithms. We consider the stability of this…
Recently Shor showed how to perform fault tolerant quantum computation when the error probability is logarithmically small. We improve this bound and describe fault tolerant quantum computation when the error probability is smaller than…
The theory of stabilizer quantum error correction allows us to actively stabilize quantum states and simulate ideal quantum operations in a noisy environment. It is critical is to correctly diagnose noise from its syndrome and nullify it…
Shor's factoring algorithm is one of the most anticipated applications of quantum computing. However, the limited capabilities of today's quantum computers only permit a study of Shor's algorithm for very small numbers. Here we show how…
Usual scenarios of fault-tolerant computation are concerned with the fault-tolerant realization of quantum algorithms that compute classical functions, such as Shor's algorithm for factoring. In particular, this means that input and output…
We consider an approach to fault tolerant quantum computing based on a simple error detecting code operating as the substrate for a conventional surface code. We develop a customised decoder to process the information about the likely…
Quantum advantage is the core of quantum computing. Grover's search algorithm is the only quantum algorithm with proven advantage to any possible classical search algorithm. However, realizing this quantum advantage in practice is quite…
We present improved quantum circuit for modular exponentiation of a constant, which is the most expensive operation in Shor's algorithm for integer factorization. While previous work mostly focuses on minimizing the number of qubits or the…
We optimize fault-tolerant quantum error correction to reduce the number of syndrome bit measurements. Speeding up error correction will also speed up an encoded quantum computation, and should reduce its effective error rate. We give both…