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Lecture notes in computer science

Reordering Decision Diagrams for Quantum Computing Is Harder Than You Might Think

Stefan Hillmich, Lukas Burgholzer, Florian Stögmüller, Robert Wille

Published Jan 1, 2022• 4 citations
Publisher
DOI
10.1007/978-3-031-09005-9_7

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With the continuous shrinkage of transistor sizes in very large scale integrated circuits, power consumption forms a serious concern to be tackled. With their ability to allow for zero energy dissipation, reversible circuits have been considered as promising solution to meetup with low power design requirements. Moreover, advances in their synthesis methodologies can be easily applied to quantum circuits due to the inherited reversibility of the latter. Although numerous algorithms have been proposed in the literature to synthesize reversible circuits and map them into their corresponding quantum circuits, the scalability and computational effort of such algorithms form a serious concern when synthesizing large size input functions. Binary Decision Diagram-based synthesis for reversible circuits has shown great evidence in realizing reversible circuits with low quantum cost through exploiting proper reduction rules for smaller graph size. However, the order of the variables in the decision diagram impacts its overall size, and thus, the cost of its corresponding reversible circuit. While several reordering algorithms have been proposed in this manner, their direct impact on the quantum cost has not been considered. In this article, a Binary Decision Diagram-based algorithm for reversible circuit synthesis is proposed to synthesize reversible circuits for a given Boolean function with low quantum cost through exploiting a linearized relationship between the decision diagram size and the corresponding quantum cost. Thereafter, different decision diagram reordering algorithms have been integrated with the proposed algorithm and compared in terms of their impact on the quantum cost. Experimental results show that Genetic Algorithm-based reordering for decision diagram, supported with, cycle crossover, inverse mutation, and tournament selection, results in the least quantum cost of the output circuit if compared with other algorithms due to its property in preserving the nodes of the decision diagram in their near-optimal locations during the optimiation recipe.

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Quantum computing is a hotspot technology for its potential to accelerate specific applications by exploiting quantum parallelism. However, current physical quantum computers are limited to a relatively small scale, simulators based on conventional machines are significantly relied on to perform quantum computing research. The straightforward array-based simulators require a tremendous amount of memory that increases exponentially with respect to the number of qubits. To mitigate such computing resource concerns, decision diagram based simulators were proposed that can efficiently exploit data redundancies in quantum states and operations. In this paper, we study two classes of quantum circuits on which the state-of-the-art decision diagram based simulators failed to perform well in terms of simulation time. We also propose a simple and powerful reorder trick to boost the simulation of such quantum circuits. Preliminary evaluation results demonstrate the usefulness of the proposed trick. Especially, for the Quantum Phase Estimation circuits, the proposed trick achieved speedups up to 313.6x compared to a state-of-the-art approach that relies on an auxiliary tool to optimize simulation order.

arXiv:2211.07110•Nov 14, 2022•1 citation
With the continuous shrinkage of transistor sizes in very large scale integrated circuits, power consumption forms a serious concern to be tackled. With their ability to allow for zero energy dissipation, reversible circuits have been considered as promising solution to meetup with low power design requirements. Moreover, advances in their synthesis methodologies can be easily applied to quantum circuits due to the inherited reversibility of the latter. Although numerous algorithms have been proposed in the literature to synthesize reversible circuits and map them into their corresponding quantum circuits, the scalability and computational effort of such algorithms form a serious concern when synthesizing large size input functions. Binary Decision Diagram-based synthesis for reversible circuits has shown great evidence in realizing reversible circuits with low quantum cost through exploiting proper reduction rules for smaller graph size. However, the order of the variables in the decision diagram impacts its overall size, and thus, the cost of its corresponding reversible circuit. While several reordering algorithms have been proposed in this manner, their direct impact on the quantum cost has not been considered. In this article, a Binary Decision Diagram-based algorithm for reversible circuit synthesis is proposed to synthesize reversible circuits for a given Boolean function with low quantum cost through exploiting a linearized relationship between the decision diagram size and the corresponding quantum cost. Thereafter, different decision diagram reordering algorithms have been integrated with the proposed algorithm and compared in terms of their impact on the quantum cost. Experimental results show that Genetic Algorithm-based reordering for decision diagram, supported with, cycle crossover, inverse mutation, and tournament selection, results in the least quantum cost of the output circuit if compared with other algorithms due to its property in preserving the nodes of the decision diagram in their near-optimal locations during the optimiation recipe.
Quantum computing is a hotspot technology for its potential to accelerate specific applications by exploiting quantum parallelism. However, current physical quantum computers are limited to a relatively small scale, simulators based on conventional machines are significantly relied on to perform quantum computing research. The straightforward array-based simulators require a tremendous amount of memory that increases exponentially with respect to the number of qubits. To mitigate such computing resource concerns, decision diagram based simulators were proposed that can efficiently exploit data redundancies in quantum states and operations. In this paper, we study two classes of quantum circuits on which the state-of-the-art decision diagram based simulators failed to perform well in terms of simulation time. We also propose a simple and powerful reorder trick to boost the simulation of such quantum circuits. Preliminary evaluation results demonstrate the usefulness of the proposed trick. Especially, for the Quantum Phase Estimation circuits, the proposed trick achieved speedups up to 313.6x compared to a state-of-the-art approach that relies on an auxiliary tool to optimize simulation order.