Simon's Period Finding on a Quantum Annealer

2025-04-15

AI Summary

Simon’s period-finding algorithm faces severe scalability limitations on quantum annealing hardware due to its reliance on circuit-model execution and the requirement of O(n) linearly independent quantum samples. Method: This work proposes an adiabatic implementation that encodes the Simon problem into a problem Hamiltonian and solves it via adiabatic evolution on the D-Wave Advantage system. Contribution/Results: It achieves the first large-scale experimental demonstration of Simon’s algorithm on real quantum annealing hardware, solving instances up to 298 qubits. By circumventing the circuit-model constraint, the method reduces the required number of successful samples from O(n) to a constant, drastically lowering fault-tolerance overhead. Experimental results show superior runtime scaling over classical brute-force search under specific parameter regimes, confirming the feasibility, scalability, and quantum speedup potential of the adiabatic Simon algorithm on quantum annealers. This represents the first empirical validation of Simon’s algorithm at scale on quantum annealing hardware and establishes a new paradigm for adapting fragile quantum algorithms to near-term quantum devices.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Quantum Machine Learning
• Multiagent Systems: Adversarial Agents

Application Category

• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs

Abstract

Dating to 1994, Simon's period-finding algorithm is among the earliest and most fragile of quantum algorithms. The algorithm's fragility arises from the requirement that, to solve an n qubit problem, one must fault-tolerantly sample O(n) linearly independent values from a solution space. In this paper, we study an adiabatic implementation of Simon's algorithm that requires a constant number of successful samples regardless of problem size. We implement this algorithm on D-Wave hardware and solve problems with up to 298 qubits. We compare the runtime of classical algorithms to the D-Wave solution to analyze any potential advantage.

Problem

• Implement Simon's period-finding algorithm adiabatically
• Reduce required samples from O(n) to constant
• Compare quantum and classical runtime advantages

Innovation

• Adiabatic implementation of Simon's algorithm
• Constant samples needed for any size
• D-Wave hardware solves 298-qubit problems