A Rydberg-atom approach to the integer factorization problem

Abstract

The task of factoring integers poses a significant challenge in modern cryptography, and quantum computing holds the potential to efficiently address this problem compared to classical algorithms. Thus, it is crucial to develop quantum computing algorithms to address this problem. This study introduces a quantum approach that utilizes Rydberg atoms to tackle the factorization problem. Experimental demonstrations are conducted for the factorization of small composite numbers such as $6=2\times 3$, $15=3\times 5$, and $35=5\times 7$. This approach involves employing Rydberg-atom graphs to algorithmically program binary multiplication tables, yielding many-body ground states that represent superpositions of factoring solutions. Subsequently, these states are probed using quantum adiabatic computing. Limitations of this method are discussed, specifically addressing the scalability of current Rydberg quantum computing for the intricate computational problem.

arXiv comment12 pages, 5 figures

References in corpus (31)

• Quantum information with Rydberg atoms
• Experimental realization of Shor's quantum factoring algorithm using nuclear magnetic resonance
• Adiabatic Quantum Computing
• Logical quantum processor based on reconfigurable atom arrays
• Quantum Phases of Matter on a 256-Atom Programmable Quantum Simulator
• Observation of Rydberg blockade between two atoms
• Probing Topological Spin Liquids on a Programmable Quantum Simulator
• Observation of collective excitation of two individual atoms in the Rydberg blockade regime
• Programmable quantum simulation of 2D antiferromagnets with hundreds of Rydberg atoms
• Generation and manipulation of Schrödinger cat states in Rydberg atom arrays
• Demonstration of multi-qubit entanglement and algorithms on a programmable neutral atom quantum computer
• Realization of a scalable Shor algorithm
• Quantum Optimization of Maximum Independent Set using Rydberg Atom Arrays
• Quantum simulation and computing with Rydberg-interacting qubits
• Experimental demonstration of Shor's algorithm with quantum entanglement
• Demonstration of Shor's quantum factoring algorithm using photonic qubits
• Efficient Networks for Quantum Factoring
• High-fidelity gates with mid-circuit erasure conversion in a metastable neutral atom qubit
• Continuous Symmetry Breaking in a Two-dimensional Rydberg Array
• A concise review of Rydberg atom based quantum computation and quantum simulation
• A Quantum Adiabatic Algorithm for Factorization and Its Experimental Implementation
• Erasure conversion in a high-fidelity Rydberg quantum simulator
• Quantum optimization with arbitrary connectivity using Rydberg atom arrays
• Single-Atom Addressing in Microtraps for Quantum-State Engineering using Rydberg Atoms
• Demonstration of Shor's factoring algorithm for N=21 on IBM quantum processors
• Quantum simulation of Ising spins on Platonic graphs
• Programmable Quantum Annealing Architectures with Ising Quantum Wires
• Quantum-Ising Hamiltonian programming in trio, quartet, and sextet qubit systems
• Quantum Computing Dataset of Maximum Independent Set Problem on King's Lattice of over Hundred Rydberg Atoms
• Quantum Programming of the Satisfiability Problem with Rydberg Atom Graphs
• Functional completeness of planar Rydberg blockade structures

Cited by in corpus (6)

• Demonstration of weighted graph optimization on a Rydberg atom array using local light-shifts
• Approximate combinatorial optimization with Rydberg atoms: the barrier of interpretability
• Topological order in symmetric blockade structures
• Parallel assembly of neutral atom arrays with an SLM using linear phase interpolation
• Graph Coloring via Quantum Optimization on a Rydberg-Qudit Atom Array
• A quantum wire approach to weighted combinatorial graph optimisation problems