Related papers: Shor's quantum algorithm using electrons in semico…
The quantum Fourier transform (QFT) has been implemented on a three bit nuclear magnetic resonance (NMR) quantum computer, providing a first step towards the realization of Shor's factoring and other quantum algorithms. Implementation of…
High-performance techniques to simulate quantum programs on classical hardware rely on exponentially large vectors to represent quantum states. When simulating quantum algorithms, the quantum states that occur are often sparse due to…
Since Shor's discovery of an algorithm to factor numbers on a quantum computer in polynomial time, quantum computation has become a subject of immense interest. Unfortunately, one of the key features of quantum computers - the difficulty of…
It is well-known that Shor's factorization algorithm, Simon's period-finding algorithm, and Deutsch's original XOR algorithm can all be formulated as solutions to a hidden subgroup problem. Here the salient features of the…
We describe in detail a set of ideas for implementing qubits, quantum gates and quantum gate networks in a semiconductor heterostructure device. Our proposal is based on an extension of the technology used for surface acoustic wave (SAW)…
Richard Feynman's observation that quantum mechanical effects could not be simulated efficiently on a computer led to speculation that computation in general could be done more efficiently if it used quantum effects. This speculation…
In the last few years, theoretical study of quantum systems serving as computational devices has achieved tremendous progress. We now have strong theoretical evidence that quantum computers, if built, might be used as a dramatically…
Efficient realization of quantum algorithms is among main challenges on the way towards practical quantum computing. Various libraries and frameworks for quantum software engineering have been developed. Here we present a software package…
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…
We provide two improvements to Regev's recent quantum factoring algorithm (Journal of the ACM 2025), addressing its space efficiency and its noise-tolerance. Our first contribution is to improve the quantum space efficiency of Regev's…
We heuristically show that Shor's algorithm for computing general discrete logarithms achieves an expected success probability of approximately 60% to 82% in a single run when modified to enable efficient implementation with the…
We combine classical heuristics with partial shadow tomography to enable efficient protocols for extracting information from correlated ab initio electronic systems encoded on quantum devices. By proposing the use of a correlation energy…
Shor's and Grover's famous quantum algorithms for factoring and searching show that quantum computers can solve certain computational problems significantly faster than any classical computer. We discuss here what quantum computers_cannot_…
We discuss the realization of a universal set of ultrafast single- and two-qubit operations with superconducting quantum circuits and investigate the most relevant physical and technical limitations that arise when pushing for faster and…
The previously proposed Heisenberg-type relation $ E_c t_c >> \hbar {\cal C}$ for the energy used by a quantum computer, the total computation time and the logical ("classical") complexity of the problem is verified for the following…
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…
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…
Continuous improvements in quantum computing hardware are exposing the need for simultaneous advances in software. Large-scale implementation of quantum algorithms requires rapid and automated compilation routines such as circuit synthesis…
We implement the first open-source quantum computing emulator that includes arithmetic operations, the quantum Fourier transform, and quantum phase estimation. The emulator provides significant savings in both temporal and spatial resources…
Quantum computers are known for their potential to achieve up-to-exponential speedup compared to classical computers for certain problems. To exploit the advantages of quantum computers, we propose quantum algorithms for linear stochastic…