Bibhas Adhikari, from the Fujitsu Research of America, and colleagues have created a unified quantum framework that encodes graphs onto a quantum state using $2\lceil \log_2 N \rceil$ working qubits and two ancilla qubits, achieving a gate complexity of O(N²). The approach designs quantum measurement operators to identify target subgraph edge structures, enabling count estimation through measurements of the adjacency state, and demonstrates application to triangles, cycles and cliques. The framework yields quantum logspace algorithms for motif counting, representing a key advance as no classical equivalent currently exists. Logarithmic qubit scaling enables efficient quantum motif discovery A breakthrough in quantum motif counting has reduced the qubit requirement for graph encoding to $2\lceil \log_2 N \rceil$, a significant improvement over prior methods. This logarithmic scaling, where qubit numbers increase slowly with network size, surpasses a key threshold previously impossible for classical algorithms, which demand space proportional to the network’s size. Classical algorithms for subgraph counting typically require memory scaling linearly with the number of nodes, N, in the graph, making them intractable for large networks. The new framework encodes graphs as a “graph adjacency state”, representing connections rather than individual points, and utilises quantum measurement operators to identify patterns within those networks. The adjacency list representation, used to construct the quantum state, details each node’s immediate neighbours, providing a concise description of the graph’s topology. This contrasts with the adjacency matrix, which requires N² space, even for sparse graphs. The logarithmic scaling achieved here is particularly significant because it suggests the potential to analyse networks far exceeding the capabilities of classical computers. Estimation of subgraph counts, such as triangles and cycles, is now possible using a technique called tensor products, effectively combining quantum states to represent complex systems. The tensor product allows for the creation of a composite quantum state that