Quantum Circuits That Can Be Simulated Classically in Polynomial Time
SIAM Journal on Computing
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
SIAM Journal on Computing
Basis Collapse in Holographic Algorithms
Computational Complexity
Holographic algorithms: The power of dimensionality resolved
Theoretical Computer Science
On the Theory of Matchgate Computations
Theory of Computing Systems
On Symmetric Signatures in Holographic Algorithms
Theory of Computing Systems - Special Issue: Theoretical Aspects of Computer Science; Guest Editors: Wolgang Thomas and Pascal Weil
Holographic algorithms: From art to science
Journal of Computer and System Sciences
Some observations on holographic algorithms
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
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An essential problem in the design of holographic algorithms is to decide whether the required signatures can be realized by matchgates under a suitable basis. For domain size two, [1,3] characterized all functions directly realizable as matchgate signatures without a basis transformation, and [7] gave a polynomial time algorithm for the realizability problem for symmetric signatures under basis transformations. We generalize this to arbitrary domain size k . Specifically, we give a polynomial time algorithm for the realizability problem on domain size k ≥3. Using this, one can decide whether suitable signatures for a holographic algorithms on domain size k are realizable and if so, to find a suitable linear basis to realize these signatures by an efficient algorithm.