Abstract
Mapping quantum circuits to real quantum architectures (while keeping the respectively considered cost as small as possible) has become an important research task since it is required to execute algorithms on real devices. Since the underlying problem is NP-complete, several heuristic approaches have been proposed. Recently, approaches utilizing A\(^*\) search to map quantum circuits to, e.g., Nearest Neighbor architectures or IBM QX architectures have gained substantial interest. However, their performance usually has only been evaluated in a rather narrow context, i.e., for single architectures and objectives only. In this work, we evaluate the flexibility of A\(^*\) in the context of mapping quantum circuits to physical devices. To this end, we review the underlying concepts and show its flexibility with respect to the considered architecture. Furthermore, we demonstrate how easy such solutions can be adjusted towards optimizing different design objectives or cost metrics by providing a generalized and parameterizable cost function for the A\(^*\) search that can also be easily extended to support future cost metrics.
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Notes
- 1.
The new state of the qubit is determined by multiplying the corresponding state vector and the unitary matrix [27].
- 2.
Albert Einstein referred to this effect as spooky action at a distance.
- 3.
Note that we do not further specify the functionality of the single qubit gates since it is irrelevant for the mapping process.
- 4.
Note that this constraint is still valid for many recent architectures, e.g., Google’s Bristlecone relies on such a 2D architecture [29].
- 5.
Note that there also exist other methods to overcome the problems [25], but they tend to generate larger overhead for bigger circuits.
- 6.
Note that 1-qubit gates can be neglected when forming the sub-circuits.
- 7.
Note that a similar strategy is used in [24] (even though the permutation is not found using A\(^*\) search).
- 8.
More precisely, the distance of the physical qubits to which the logical ones are mapped is taken.
- 9.
Note that the distance might also include 4 Hadamard gates to indicate that the direction of the CNOT has to be switched.
- 10.
Note that we store the depth and the workload distribution for each physical qubit (considering the already mapped part of the circuit) to keep track of these values.
- 11.
- 12.
Note that no Hadamard operations have to be inserted since these architectures allow CNOTs in any direction between neighboring qubits.
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Acknowledgements
This work has partially been supported by the LIT Secure and Correct System Lab funded by the State of Upper Austria and the European Union through the COST Action IC1405.
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Zulehner, A., Bauer, H., Wille, R. (2019). Evaluating the Flexibility of A* for Mapping Quantum Circuits. In: Thomsen, M., Soeken, M. (eds) Reversible Computation. RC 2019. Lecture Notes in Computer Science(), vol 11497. Springer, Cham. https://doi.org/10.1007/978-3-030-21500-2_11
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