Related papers: Quantum algorithms for computing short discrete lo…
Shor's quantum algorithm for discrete logarithms applied to elliptic curve groups forms the basis of a "quantum attack" of elliptic curve cryptosystems. To implement this algorithm on a quantum computer requires the efficient implementation…
This is an expository talk written for the Bourbaki Seminar. After a brief introduction, Section 1 discusses in the categorical language the structure of the classical deterministic computations. Basic notions of complexity icluding the…
Neutral atom arrays have recently emerged as a promising platform for fault-tolerant quantum computing. Based on these advances, including dynamically-reconfigurable connectivity and fast transversal operations, we present a low-overhead…
In this paper we give a polynomial-time quantum algorithm for computing orders of solvable groups. Several other problems, such as testing membership in solvable groups, testing equality of subgroups in a given solvable group, and testing…
Shor's algorithm is well-known for its capability to address the elliptic curve discrete logarithm problem (ECDLP) in polynomial time. The enhancement of its quantum resources continues to be a crucial focus of research. Nevertheless, the…
We formulate and numerically simulate the single control qubit Shor algorithm for the case of static imperfections induced by residual couplings between qubits. This allows us to study the accuracy of Shor's algorithm with respect to these…
The semidirect discrete logarithm problem (SDLP) is the following analogue of the standard discrete logarithm problem in the semidirect product semigroup $G\rtimes \mathrm{End}(G)$ for a finite semigroup $G$. Given $g\in G, \sigma\in…
In this paper we discuss the problem of performing elementary finite field arithmetic on a quantum computer. Of particular interest, is the controlled-multiplication operation, which is the only group-specific operation in Shor's algorithms…
We describe a group theoretic analysis of Shor's algorithm and other related hidden subgroup problems in mathematics and relate these to symmetries of molecular and condensed phase assemblies. By recasting Shor's algorithm through the lens…
We present a quantum algorithm for systems of (possibly inhomogeneous) linear ordinary differential equations with constant coefficients. The algorithm produces a quantum state that is proportional to the solution at a desired final time.…
In this paper, we first define the quantum discrete logarithm problem (QDLP)which is similar to classical discrete logarithm problem. But, this problem cannot be solved by Shor's quantum algorithm. Based on quantum discrete logarithm…
The logarithm-determinant is an widely-present operation in many areas of physics and computer science. Derivatives of the logarithm-determinant compute physically relevant quantities in statistical physics models, quantum field theories,…
We report the realization of a nuclear magnetic resonance (NMR) quantum computer which combines the quantum Fourier transform (QFT) with exponentiated permutations, demonstrating a quantum algorithm for order-finding. This algorithm has the…
Considering the large-scale quantum computer, it is important to know how much quantum computational resources is necessary precisely and quickly. Unfortunately the previous methods so far cannot support a large-scale quantum computing…
Factoring integers is considered as a computationally-hard problem for classical methods, whereas there exists polynomial-time Shor's quantum algorithm for solving this task. However, requirements for running the Shor's algorithm for…
Current asymmetric cryptography is based on the principle that while classical computers can efficiently multiply large integers, the inverse operation, factorization, is significantly more complex. For sufficiently large integers, this…
A scheme to encode arbitrarily long integer pairs on degenerate optical parametric oscillations multiplexed in time is proposed. The classical entanglement between the polarization directions and the phases of the oscillating pulses,…
Quantum-Kit is a graphical desktop application for quantum circuit simulations. Its powerful, memory-efficient computational engine enables large-scale simulations on a desktop. The ability to design hybrid circuits, with both quantum and…
We introduce hybrid classical-quantum algorithms for problems involving a large classical data set X and a space of models Y such that a quantum computer has superposition access to Y but not X. These algorithms use data reduction…
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_…