Diverse facets Of the Theory of Quantum Walks on Graph are reviewed Till now .In specific, Quantum network routing, Quantum Walk Search Algorithm, Element distinctness associated to the eigenvalues of Graphs and the use of these relation /connection in the study of Quantum walks is furthermore described. Different Researchers had contribution and put their benchmark idea Pertaining with this research concept. I furthermore try to investigate recent Application of Quantum walks, In specific the problem pertained with Graph matching i.e Matching nodes(vertices) of the Graphs. In this research paper,I consider how Continuous-time quantum walk (CTQW) can be directed to Graph-matching problems. The matching problem is abstracted using weighted(attributed) Graphs that connects vertices's of one Graph to other and Try to compute the distance b/n those Graphs Node's Beside that finding the matched nodes and the Cost related to Matching. eventually measuring the distance between two Graphs which might have different size then by using k-nearest neighbor (k-NN) method try to classifying those graph based on closest training examples in the feature space.Diverse facets Of the Theory of Quantum Walks on Graph are reviewed Till now .In specific, Quantum network routing, Quantum Walk Search Algorithm, Element distinctness associated to the eigenvalues of Graphs and the use of these relation /connection in the study of Quantum walks is furthermore described. Different Researchers had contribution and put their benchmark idea Pertaining with this research concept. I furthermore try to investigate recent Application of Quantum walks, In specific the problem pertained with Graph matching i.e Matching nodes(vertices) of the Graphs. In this research paper,I consider how Continuous-time quantum walk (CTQW) can be directed to Graph-matching problems. The matching problem is abstracted using weighted(attributed) Graphs that connects vertices's of one Graph to other and Try to compute the distance b/n those Graphs Node's Beside that finding the matched nodes and the Cost related to Matching. eventually measuring the distance between two Graphs which might have different size then by using k-nearest neighbor (k-NN) method try to classifying those graph based on closest training examples in the feature space.

arXiv:1801.10339Jan 31, 20180 citations

Graph Similarity Using Interfering Quantum Walks

David Emms, Edwin R. Hancock, Richard C. Wilson

Lecture notes in computer scienceAug 17, 20072 citations

A matching decomposition algorithm for simulating quantum walk Hamiltonians

Mostafa Atallah, Alvin Gonzales, Daniel Dilley +3 more

In this work, we present a new algorithm for generating quantum circuits that efficiently implement continuous time quantum walks on arbitrary simple sparse graphs. The algorithm, called matching decomposition, works by decomposing a continuous-time quantum walk Hamiltonian into a collection of exactly implementable Hamiltonians corresponding to matchings in the underlying graph followed by a novel graph compression algorithm that merges edges in the graph. We develop a greedy matching heuristic and a compression-aware matching heuristic, both of which can be used in the quantum circuit algorithm. Lastly, we convert the walks to a circuit and Trotterize over these components. The dynamics of the walker on each edge in the matching can be implemented in the circuit model as sequences of CX and CRx gates. We do not use Pauli decomposition when implementing walks along each matching. Furthermore, we compare greedy (compression-aware) matching decomposition to a standard Pauli-based simulation pipeline and find that greedy (compression-aware) matching decomposition consistently yields substantial resource reductions, requiring up to 43 $\%$ (70\%) fewer controlled gates and up to 54 $\%$ (75\%) shallower circuits than Pauli decomposition across multiple graph families. Finally, we also present examples and theoretical results for when matching decomposition can exactly simulate a continuous-time quantum walk on a graph.In this work, we present a new algorithm for generating quantum circuits that efficiently implement continuous time quantum walks on arbitrary simple sparse graphs. The algorithm, called matching decomposition, works by decomposing a continuous-time quantum walk Hamiltonian into a collection of exactly implementable Hamiltonians corresponding to matchings in the underlying graph followed by a novel graph compression algorithm that merges edges in the graph. We develop a greedy matching heuristic and a compression-aware matching heuristic, both of which can be used in the quantum circuit algorithm. Lastly, we convert the walks to a circuit and Trotterize over these components. The dynamics of the walker on each edge in the matching can be implemented in the circuit model as sequences of CX and CRx gates. We do not use Pauli decomposition when implementing walks along each matching. Furthermore, we compare greedy (compression-aware) matching decomposition to a standard Pauli-based simulation pipeline and find that greedy (compression-aware) matching decomposition consistently yields substantial resource reductions, requiring up to 43$\%$ (70\%) fewer controlled gates and up to 54$\%$ (75\%) shallower circuits than Pauli decomposition across multiple graph families. Finally, we also present examples and theoretical results for when matching decomposition can exactly simulate a continuous-time quantum walk on a graph.

quant-pharXiv:2601.11418Jan 19, 20260 citations

A Continuous - Time Quantum Walk for Attributed GraphsMatching

Tewabe Chekole Workneh

Oct 30, 20130 citations

Continuous Time Quantum Walk Propagation for Irregular Temporal Graph Forecasting

Jiaqi Sun, Tianhao Li, Zhihao Bian

Continuous time quantum walks built on graph Laplacians produce non monotonic graph propagation features through quantum interference during evolution, which classical diffusion cannot achieve. Such walks deliver a physically motivated propagation scheme for temporal graph signal modeling. We propose Quantum Walk Temporal Architecture (QWTA), which replaces classical graph propagation with a CTQW-type parameterized spectral propagator. QWTA embeds effective observation intervals into the spectral phase modulation of the propagation kernel. QWTA-Base preserves exact CTQW spectral evolution and serves as a physically faithful propagation reference. QWTA-GR further introduces phase soft clipping and gated residual fusion to stabilize propagation. The results show that explicit phase encoding of irregular time intervals, when combined with suitable stabilization, provides a physically motivated and competitive graph propagation design for temporal graph forecasting with missing historical observations.Continuous time quantum walks built on graph Laplacians produce non monotonic graph propagation features through quantum interference during evolution, which classical diffusion cannot achieve. Such walks deliver a physically motivated propagation scheme for temporal graph signal modeling. We propose Quantum Walk Temporal Architecture (QWTA), which replaces classical graph propagation with a CTQW-type parameterized spectral propagator. QWTA embeds effective observation intervals into the spectral phase modulation of the propagation kernel. QWTA-Base preserves exact CTQW spectral evolution and serves as a physically faithful propagation reference. QWTA-GR further introduces phase soft clipping and gated residual fusion to stabilize propagation. The results show that explicit phase encoding of irregular time intervals, when combined with suitable stabilization, provides a physically motivated and competitive graph propagation design for temporal graph forecasting with missing historical observations.

quant-pharXiv:2607.17273Jul 21, 20260 citations

\%

(70\%) fewer controlled gates and up to 54

\%

(75\%) shallower circuits than Pauli decomposition across multiple graph families. Finally, we also present examples and theoretical results for when matching decomposition can exactly simulate a continuous-time quantum walk on a graph.