Full Characterization of the Depth Overhead for Quantum Circuit Compilation with Arbitrary Qubit Connectivity Constraint (2402.02403v2)
Abstract: In some physical implementations of quantum computers, 2-qubit operations can be applied only on certain pairs of qubits. Compilation of a quantum circuit into one compliant to such qubit connectivity constraint results in an increase of circuit depth. Various compilation algorithms were studied, yet what this depth overhead is remains elusive. In this paper, we fully characterize the depth overhead by the routing number of the underlying constraint graph, a graph-theoretic measure which has been studied for 3 decades. We also give reduction algorithms between different graphs, which allow compilation for one graph to be transferred to one for another. These results, when combined with existing routing algorithms, give asymptotically optimal compilation for all commonly seen connectivity graphs in quantum computing.
- P. W. Shor, Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer, SIAM Rev. 41, 303 (1999).
- L. K. Grover, A fast quantum mechanical algorithm for database search, in Proceedings of the twenty-eighth annual ACM symposium on Theory of computing (1996) pp. 212–219.
- Quantum algorithm zoo, https://quantumalgorithmzoo. org/ (2021).
- IBM Quantum, https://quantumexperience.ng.bluemix.net /qx/devices (2021).
- I. Bloch, Quantum coherence and entanglement with ultracold atoms in optical lattices, Nature 453, 1016 (2008).
- I. Buluta, S. Ashhab, and F. Nori, Natural and artificial atoms for quantum computation, Rep. Prog. Phys. 74, 104401 (2011).
- D. Maslov, S. M. Falconer, and M. Mosca, Quantum circuit placement, IEEE T. Comput. Aid. D. 27, 752 (2008).
- A. Shafaei, M. Saeedi, and M. Pedram, Optimization of quantum circuits for interaction distance in linear nearest neighbor architectures, in Proceedings of the 50th annual design automation conference (2013) pp. 1–6.
- A. Shafaei, M. Saeedi, and M. Pedram, Qubit placement to minimize communication overhead in 2d quantum architectures, in 2014 19th Asia and South Pacific Design Automation Conference (2014) pp. 495–500.
- A. Kole, K. Datta, and I. Sengupta, A heuristic for linear nearest neighbor realization of quantum circuits by swap gate insertion using n𝑛nitalic_n-gate lookahead, IEEE J. Em. Sel. Top. C. 6, 62 (2016).
- C.-C. Lin, S. Sur-Kolay, and N. K. Jha, Paqcs: Physical design-aware fault-tolerant quantum circuit synthesis, IEEE. T. Vlsi. Syst. 23, 1221 (2015).
- R. R. Shrivastwa, K. Datta, and I. Sengupta, Fast qubit placement in 2d architecture using nearest neighbor realization, in 2015 IEEE International Symposium on Nanoelectronic and Information Systems (2015) pp. 95–100.
- G. Li, Y. Ding, and Y. Xie, Tackling the qubit mapping problem for nisq-era quantum devices, in Proceedings of the Twenty-Fourth International Conference on Architectural Support for Programming Languages and Operating Systems (2019) pp. 1001–1014.
- Rigetti, http://docs.rigetti.com/en/latest/qpu.html (2021).
- J. Preskill, Quantum computing in the NISQ era and beyond, Quantum 2, 79 (2018).
- N. Alon, F. R. K. Chung, and R. L. Graham, Routing permutations on graphs via matchings, SIAM J. Discrete Math. 7, 513 (1994).
- L. Zhang, Optimal bounds for matching routing on trees, SIAM J. Discrete Math. 12, 64 (1999).
- I. Banerjee and D. Richards, New results on routing via matchings on graphs, in Fundamentals of Computation Theory (2017) pp. 69–81.
- R. Nenadov, Routing permutations on spectral expanders via matchings, Combinatorica , 1 (2023).
- I. Banerjee, D. Richards, and I. Shinkar, Sorting networks on restricted topologies, in SOFSEM 2019: Theory and Practice of Computer Science (2019) pp. 54–66.
- M. Nielsen, A geometric approach to quantum circuit lower bounds, Quantum Inf. Comput. 6, 213 (2006).
- P. Yuan, J. Allcock, and S. Zhang, Does qubit connectivity impact quantum circuit complexity?, IEEE T. Comput. Aid. D. 43, 520 (2024).
- M. Plesch and C. Brukner, Quantum-state preparation with universal gate decompositions, Phys. Rev. A 83, 032302 (2011).
- See Supplemental Material .
- A matching in a graph is a set of edges with no overlap on vertices.
- A. Roberts, A. Symvonis, and L. Zhang, Routing on trees via matchings, in Algorithms and Data Structures (1995) pp. 251–262.
- C. C. Pinter, A book of abstract algebra: second edition (Courier Corporation, 2019).
- S. Arora and B. Barak, Computational complexity: a modern approach (Cambridge University Press, 2009).
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.