Resource Bounds for Quantum Circuit Mapping via Quantum Circuit Complexity
CoRR(2024)
摘要
Efficiently mapping quantum circuits onto hardware is an integral part of the
quantum compilation process, wherein a quantum circuit is modified in
accordance with the stringent architectural demands of a quantum processor.
Many techniques exist for solving the quantum circuit mapping problem, many of
which relate quantum circuit mapping to classical computer science. This work
considers a novel perspective on quantum circuit mapping, in which the routing
process of a simplified circuit is viewed as a composition of quantum
operations acting on density matrices representing the quantum circuit and
processor. Drawing on insight from recent advances in quantum information
theory and information geometry, we show that a minimal SWAP gate count for
executing a quantum circuit on a device emerges via the minimization of the
distance between quantum states using the quantum Jensen-Shannon divergence.
Additionally, we develop a novel initial placement algorithm based on a graph
similarity search that selects the partition nearest to a graph isomorphism
between interaction and coupling graphs. From these two ingredients, we then
construct a polynomial-time algorithm for calculating the SWAP gate lower
bound, which is directly compared alongside the IBM Qiskit compiler for over
600 realistic benchmark experiments, as well as against a brute-force method
for smaller benchmarks. In our simulations, we unambiguously find that neither
the brute-force method nor the Qiskit compiler surpass our bound, implying
utility as a precise estimation of minimal overhead when realizing quantum
algorithms on constrained quantum hardware. This work constitutes the first use
of quantum circuit uncomplexity to practically-relevant quantum computing. We
anticipate that this method may have diverse applicability outside of the scope
of quantum information science, and we discuss several of these possibilities.
更多查看译文
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要