Quantum iterative framework combining QPE and Grover's algorithm for the Traveling Salesman Problem
By
[Submitted on 10 Jun 2026]
A second-rack bagel that's nearly first-rack. Tasty stuff.
Summary
This paper proposes a novel quantum computing framework for solving the Traveling Salesman Problem (TSP), a classic NP-hard combinatorial optimization challenge. Unlike existing quantum approaches that rely primarily on quantum annealing, the authors introduce an iterative framework that integrates Quantum Phase Estimation (QPE) and Grover's search algorithm. Route costs are encoded as quantum phases for efficient evaluation via QPE, while Amplitude Amplification (via the Grover-Long algorithm) iteratively refines the solution space. A proof-of-concept on a small-scale TSP instance demonstrates feasibility, and an expectation-based complexity analysis shows O(m² log₂(m) log₂(1/ε)/√ε) computational complexity dependent on error tolerance ε.
Key quotes
· 5 pulledThe Traveling Salesman Problem (TSP) is a classical NP-hard problem in combinatorial optimization, where determining the shortest route among a set of cities becomes computationally prohibitive as the problem size increases.
Unlike existing methods that primarily rely on quantum annealing, we propose a quantum iterative framework integrating Quantum Phase Estimation (QPE) and Grover's search algorithm.
Route costs are encoded as quantum phases, enabling QPE to efficiently evaluate them, while Amplitude Amplification, implemented via the Grover-Long algorithm, iteratively refines the solution space toward the optimal route.
A proof-of-concept case study on a small-scale TSP instance demonstrates the feasibility of this approach and its potential for scaling to larger optimization problems.
Under an expectation-based analysis, the algorithm exhibits an expected computational complexity of O(m² log₂(m) log₂(1/ε)/√ε) which depends on the error tolerance parameter ε.
You might also wanna read
Demonstration of Algorithmic Quantum Speedup for an Abelian Hidden Subgroup Problem
journals.aps.org·11mo ago
New Algorithm Breaks Dijkstra's Time Complexity for Directed Shortest Paths
The article presents a deterministic algorithm for single-source shortest paths (SSSP) on directed graphs with real non-negative edge weight
arxiv.org·10mo ago
Quantum Echoes Algorithm Advances Real-World Applications for Quantum Computing
The article introduces Quantum Echoes, a new quantum computing algorithm that represents a significant advancement toward practical real-wor
blog.google·7mo ago
Per-Instance TSP Solver Using PPO Achieves 1.66% Gap on d1291 Without Pre-training
A developer presents a novel approach to solving the Traveling Salesman Problem (TSP) using deep learning without pre-training. Instead of r
news.ycombinator.com·5mo agoUsing Wave Function Collapse to solve puzzle map generation at scale
New Quantum Algorithm Accelerates Timeline for Breaking Current Encryption Standards
Researchers at the Advanced Quantum Technologies Institute have developed a new quantum algorithm called JVG that dramatically accelerates t
briefglance.com·3mo ago