Related papers: Period Finding with Adiabatic Quantum Computation

Adiabatic quantum computing is a universal model for quantum computing whose implementation using a gate-based quantum computer requires depths that are unreachable in the early fault-tolerant era. To mitigate the limitations of near-term…

A major challenge in quantum computing is to solve general problems with limited physical hardware. Here, we implement digitized adiabatic quantum computing, combining the generality of the adiabatic algorithm with the universality of the…

It is believed that there is no efficient classical algorithm to determine the linear structure of Boolean function. We investigate an extension of Simon's period-finding quantum algorithm, and propose an efficient quantum algorithm to…

Quantum computation has emerged as a powerful computational medium of our time, having demonstrated the remarkable efficiency in factoring a positive integer and searching databases faster than any currently known classical computing…

We show that by a suitable choice of a time dependent Hamiltonian, Deutsch's algorithm can be implemented by an adiabatic quantum computer. We extend our analysis to the Deutsch-Jozsa problem and estimate the required running time for both…

We propose a hybrid quantum-classical approximate optimization algorithm for photonic quantum computing, specifically tailored for addressing continuous-variable optimization problems. Inspired by counterdiabatic protocols, our algorithm…

In this Letter, we construct the quantum algorithms for the Simon problem and the period-finding problem, which do not require initializing the auxiliary qubits involved in the process of functional evaluation but are as efficient as the…

We illustrate the adiabatic quantum computing solution of the knapsack problem with both integer profits and weights. For problems with $n$ objects (or items) and integer capacity $c$, we give specific examples using both an Ising class…

Dimensionality reduction is the fundamental problem for machine learning and pattern recognition. During data preprocessing, the feature selection is often demanded to reduce the computational complexity. The problem of feature selection is…

Quantum computers can execute algorithms that dramatically outperform classical computation. As the best-known example, Shor discovered an efficient quantum algorithm for factoring integers, whereas factoring appears to be difficult for…

We present an optimized adiabatic quantum schedule for unstructured search building on the original approach of Roland and Cerf [Phys. Rev. A 65, 042308 (2002)]. Our schedule adiabatically varies the Hamiltonian even more rapidly at the…

Due to Shor's algorithm, quantum computers are a severe threat for public key cryptography. This motivated the cryptographic community to search for quantum-safe solutions. On the other hand, the impact of quantum computing on secret key…

The NP-complete problem of the travelling salesman (TSP) is considered in the framework of quantum adiabatic computation (QAC). We first derive a remarkable lower bound for the computation time for adiabatic algorithms in general as a…

The goal of this paper is to outline a general-purpose scalable implementation of Shor's period finding algorithm using fundamental quantum gates, and to act as a blueprint for linear optical implementations of Shor's algorithm for both…

We report the realization of a nuclear magnetic resonance computer with three quantum bits that simulates an adiabatic quantum optimization algorithm. Adiabatic quantum algorithms offer new insight into how quantum resources can be used to…

Properties of Shor's algorithm and the related period-finding algorithm could serve as benchmarks for the operation of a quantum computer. Distinctive universal behaviour is expected for the probability for success of the period-finding…

Quantum adiabatic optimization seeks to solve combinatorial problems using quantum dynamics, requiring the Hamiltonian of the system to align with the problem of interest. However, these Hamiltonians are often incompatible with the native…

Let $f: \mathbb{F}_2^n \rightarrow \mathbb{F}_2^n$ be a Boolean function with period $\vec s$. It is well-known that Simon's algorithm finds $\vec s$ in time polynomial in $n$ on quantum devices that are capable of performing…

The study of quantum computation has been motivated by the hope of finding efficient quantum algorithms for solving classically hard problems. In this context, quantum algorithms by local adiabatic evolution have been shown to solve an…

Simon's algorithm is a polynomial period-finding algorithm that has been used to exploit the algebraic structure of specific symmetric ciphers, showing that exponential speedups in their cryptanalysis are theoretically possible. While the…