Abstract
Due to the significant progress made in the implementation of quantum hardware, efficient methods and tools to design corresponding algorithms become increasingly important. Many of these tools rely on functional representations of certain building blocks or even entire quantum algorithms which, however, inherently exhibit an exponential complexity. Although several alternative representations have been proposed to cope with this complexity, the construction of those representations remains a bottleneck. In this work, we propose solutions for efficiently constructing representations of quantum functionality based on the idea of conducting as many operations as possible on as small as possible intermediate representations—using Decision Diagrams as a representative functional description. Experimental evaluations show that applying these solutions allows to construct the desired representations several factors faster than with state-of-the-art methods. Moreover, if repeating structures (which frequently occur in quantum algorithms) are explicitly exploited, exponential improvements are possible—allowing to construct the functionality of certain algorithms within seconds, whereas the state of the art fails to construct it in an entire day.
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Notes
- 1.
A complex-valued matrix U is unitary if \(U^\dag U = UU^\dag = \mathbb {I}\), where \(U^\dag \) denotes the conjugate transpose of U and \(\mathbb {I}\) the identity matrix.
- 2.
The authors want to point out that this construction task is conceptionally different from and should not be confused with the classical simulation of quantum circuits which aims to calculate the resulting state vector for one particular input and not the complete functionality.
- 3.
Different edge weights are indicated by dotted (\(\equiv \) negative) and/or colored (\(\equiv \) 1,
,
andÂ
) lines. This suffices to illustrate the evolution of the Decision Diagrams’ size, i.e., their node count.
- 4.
Decision Diagram packages, e.g., typically employ a unique table where all nodes are stored [26]. Thus, even when multiple different Decision Diagrams are stored concurrently, sharing reduces the memory footprint considerably.
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Acknowledgments
This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 101001318). It has partially been supported by the LIT Secure and Correct Systems Lab funded by the State of Upper Austria as well as by the BMK, BMDW, and the State of Upper Austria in the frame of the COMET program (managed by the FFG).
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Burgholzer, L., Raymond, R., Sengupta, I., Wille, R. (2021). Efficient Construction of Functional Representations for Quantum Algorithms. In: Yamashita, S., Yokoyama, T. (eds) Reversible Computation. RC 2021. Lecture Notes in Computer Science(), vol 12805. Springer, Cham. https://doi.org/10.1007/978-3-030-79837-6_14
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