On Structured Design Space Exploration for Mapping of Quantum Algorithms

Abstract

Quantum algorithms can be expressed as quantum circuits when the circuit model of computation is adopted. Such a circuit description is usually hardware-agnostic, that is, it does not consider the limitations that the quantum hardware might have. In order to make quantum algorithms executable on quantum devices they need to comply to their constraints, which mainly affect the parallelism of quantum operations and the possible interactions between the qubits. The process of adapting a quantum circuit to meet the quantum chip restrictions is known as mapping. The resulting circuit usually has a higher number of gates and depth, decreasing the algorithm's reliability. Different mapping solutions have been already proposed. Most of them are meant for a specific quantum processor and differ in methodology, approach and features. In addition, they are usually only compared in terms of added gates, circuit depth and compilation time. No thorough comparative analysis of the different mapping solutions performance and features has been performed so far.In this paper, we propose to apply structured design space exploration (DSE) methodologies to the mapping procedures. This will allow not only to have a more in depth and structured analysis of their performance but also to identify what features are key and worth to implement. By using DSE we will be able to: i) determine in what regimes some mapping solutions outperform others; ii) derive optimal mapping strategies for specific quantum algorithms and quantum processors; and iii) perform an scalability analysis. In addition, DSE techniques cannot only be applied to the mapping layer that is key for bridging quantum applications to quantum devices, but also to the full-stack quantum computing system allowing for its crosslayer co-design.

Topological-Graph Dependencies and Scaling Properties of a Heuristic Qubit-Assignment Algorithm

“…As the assignment of qubits is a fundamental part of the qubitmapping process [50], [53], this work will focus on this first step using a heuristic qubit-assignment algorithm (HQAA). For a thorough review of the qubit-mapping problem, we refer the reader to [54], [55].…”

“…The SWAP gate itself degrades the final-state fidelity of the algorithm, in accordance with the commensurate two-qubit gate error rates. Due to the disadvantages of utilizing SWAP gates, many qubit-mapping algorithms explicitly attempt to minimize the amount of SWAP gates employed [54], [49]. However, we did not explicitly design our algorithm with such a notion in mind, even though necessary SWAP gates are considered.…”

“…Solutions to both the qubit-assignment and qubit-mapping problems can be separated into two broad categories: 1) optimal (or brute-force) optimization and 2) heuristic optimization algorithms [54]. As described before, current studies of qubit-mapping and assignment focus on minimizing the number of SWAP gates [49], [54], [61], [62], [55].…”

“…Solutions to both the qubit-assignment and qubit-mapping problems can be separated into two broad categories: 1) optimal (or brute-force) optimization and 2) heuristic optimization algorithms [54]. As described before, current studies of qubit-mapping and assignment focus on minimizing the number of SWAP gates [49], [54], [61], [62], [55]. However, our particular solution to the qubit-assignment problem is not the main focus of the present manuscript; rather we concentrate on the evaluation of topologically-inequivalent IGs for an HQAA, building and expanding on the work pioneered by [50], with an aim towards understanding the topological-graph properties of IGs and how they influence the performance of an HQAA, while keeping the QPU CG effectively constant.…”

“…Various other qubit-mapping algorithm proposals exist as well [49], [79], [51], [48], [52], [47], [41], [42], [54]; many of these could be analyzed and classified, as it is imperative to better understand which types of qubit-assignment algorithms may be most amenable for certain structural classes of quantum algorithms. In the interim, we expect that most (if not all) HQAAs will exhibit a topological-graph dependence via the IGs utilized, although this must be explored and verified in future work.…”