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Researchers have established a new growth rate for qubit basis equivalence classes, demonstrating that the number of possible groupings scales doubly exponentially with added qubits. By mapping these quantum states to graph isomorphism problems, the team provides an efficient classification method for complete orthogonal product bases using edge-coloured multigraphs. This breakthrough resolves previous computational bottlenecks in analyzing multiqubit systems and clarifies the structural limits of quantum information encoding.

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Researchers Establish Growth Rate for Qubit Basis Equivalence Classes Exceeds 2 Raised to the Power of N

Quantum ZeitgeistSeptember 15, 20264 min read

Multiqubit systems previously lacked efficient classification methods beyond approximately $2^n -1$ variables. Now, equivalence between these bases can be determined by solving graph isomorphism problems, revealing their structure through established combinatorial techniques. This approach demonstrates asymptotic behaviour of equivalence classes given by $a_n = 2^{2^{n+o(n)}}$, offering tighter boundaries on multiqubit system behaviours.

Classifying complete orthogonal product bases now reduces to solving graph isomorphism problems, previously achieved using more complex methods. Yvkai Zhao and Lin Chen from Beihang University accomplished this by associating each basis with a specific type of coloured network termed an edge-coloured complete multigraph. This approach enables structural analysis and provides an upper bound of 2n-1 variables, while showing that the number of possible groupings grows as 2^2n+o(n). The classification…

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