相关论文: Robustness of Shor's algorithm

Quantum algorithms allow to outperform their classical counterparts in various tasks, most prominent example being Shor's algorithm for efficient prime factorization on a quantum computer. It is clear that one of the reasons for the speedup…

The stabiliser formalism plays a central role in quantum computing, error correction, and fault tolerance. Conversions between and verifications of different specifications of stabiliser states and Clifford gates are important components of…

We consider a probabilistic quantum implementation of a variable of the Pocklington-Lehmer $N-1$ primality test using Shor's algorithm. O($\log^3 N \log\log N \log\log\log N$) elementary q-bit operations are required to determine the…

We give the first quantum circuit for computing $f(0)$ OR $f(1)$ more reliably than is classically possible with a single evaluation of the function. OR therefore joins XOR (i.e. parity, $f(0) \oplus f(1)$) to give the full set of logical…

Quantum computing has the potential to revolutionize cryptography by breaking classical public-key cryptography schemes, such as RSA and Diffie-Hellman. However, breaking the widely used 2048-bit RSA using Shor's quantum factoring algorithm…

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…

The discrete logarithm problem (DLP) over finite fields, commonly used in classical cryptography, has no known polynomial-time algorithm on classical computers. However, Shor has provided its polynomial-time algorithm on quantum computers.…

We analyze the influence of errors on the implementation of the quantum Fourier transformation (QFT) on the Ising quantum computer (IQC). Two kinds of errors are studied: (i) due to spurious transitions caused by pulses and (ii) due to…

We give algorithms to factorize large integers in the duality computer. We provide three duality algorithms for factorization based on a naive factorization method, the Shor algorithm in quantum computing, and the Fermat's method in…

This paper proposes a new factorization algorithm for computing the phase factors of quantum signal processing. The proposed algorithm avoids root finding of high degree polynomials by using a key step of Prony's method and is numerically…

(Abridged abstract.) In this thesis we introduce new models of quantum computation to study the emergence of quantum speed-up in quantum computer algorithms. Our first contribution is a formalism of restricted quantum operations, named…

The construction of large, coherent quantum systems necessary for quantum computation remains an entreating but elusive goal, due to the ubiquitous nature of decoherence. Recent progress in quantum error correction schemes have given new…

In recent decades, the field of quantum computing has experienced remarkable progress. This progress is marked by the superior performance of many quantum algorithms compared to their classical counterparts, with Shor's algorithm serving as…

The optimal design of a fault-tolerant quantum computer involves finding an appropriate balance between the burden of large-scale integration of noisy components and the load of improving the reliability of hardware technology. This balance…

Shor's algorithm has seriously challenged information security based on public key cryptosystems. However, to break the widely used RSA-2048 scheme, one needs millions of physical qubits, which is far beyond current technical capabilities.…

The Quantum Fourier Transform (QFT) grants competitive advantages, especially in resource usage and circuit approximation, for performing arithmetic operations on quantum computers, and offers a potential route towards a numerical…

Recent research has demonstrated that quantum computers can solve certain types of problems substantially faster than the known classical algorithms. These problems include factoring integers and certain physics simulations. Practical…

Quantum computers require quantum arithmetic. We provide an explicit construction of quantum networks effecting basic arithmetic operations: from addition to modular exponentiation. Quantum modular exponentiation seems to be the most…

As quantum computing progresses steadily from theory into practice, programmers will face a common problem: How can they be sure that their code does what they intend it to do? This paper presents encouraging results in the application of…

In ensemble (or bulk) quantum computation, measurements of qubits in an individual computer cannot be performed. Instead, only expectation values can be measured. As a result of this limitation on the model of computation, various important…