Reducing circuit depth with qubitwise diagonalization (2306.00170v3)
Abstract: A variety of quantum algorithms employ Pauli operators as a convenient basis for studying the spectrum or evolution of Hamiltonians or measuring multi-body observables. One strategy to reduce circuit depth in such algorithms involves simultaneous diagonalization of Pauli operators generating unitary evolution operators or observables of interest. We propose an algorithm yielding quantum circuits with depths $O(n \log r)$ diagonalizing $n$-qubit operators generated by $r$ Pauli operators. Moreover, as our algorithm iteratively diagonalizes all operators on at least one qubit per step, it is well suited to maintain low circuit depth even on hardware with limited qubit connectivity. We observe that our algorithm performs favorably in producing quantum circuits diagonalizing randomly generated Hamiltonians as well as molecular Hamiltonians with short depths and low two-qubit gate counts.
- Y. Manin, Computable and Uncomputable (in Russian) (Sovetskoye Radio, Moscow, 1980).
- P. Benioff, Journal of Statistical Physics 22, 563 (1980).
- R. P. Feynman, International Journal of Theoretical Physics 21, 467 (1982).
- R. P. Feynman, Foundations of Physics 16, 507 (1986).
- S. Lloyd, Science 273, 1073 (1996).
- M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information: 10th Anniversary Edition (Cambridge University Press, 2010).
- U. Fano, Rev. Mod. Phys. 29, 74 (1957).
- E. van den Berg and K. Temme, Quantum 4, 322 (2020).
- S. Aaronson and D. Gottesman, Phys. Rev. A 70, 052328 (2004).
- E. M. Rains, (1997), arXiv:quant-ph/9703048 .
- A. Klappenecker and P. K. Sarvepalli, Proceedings of the Royal Society of London Series A 463, 2887 (2007).
- R. Koenig and J. A. Smolin, J. Math. Phys. 55, 122202 (2014).
- R. M. Karp, “Reducibility among combinatorial problems,” in Complexity of Computer Computations: Proceedings of a symposium on the Complexity of Computer Computations, held March 20–22, 1972, at the IBM Thomas J. Watson Research Center, Yorktown Heights, New York, and sponsored by the Office of Naval Research, Mathematics Program, IBM World Trade Corporation, and the IBM Research Mathematical Sciences Department, edited by R. E. Miller, J. W. Thatcher, and J. D. Bohlinger (Springer US, Boston, MA, 1972) pp. 85–103.
- T. Volgenant and R. Jonker, The Journal of the Operational Research Society 38, 1073 (1987).
- S. E. Dreyfus, Operations Research 17, 395 (1969).
- T. Ibaraki, SIAM Review 15, 309 (1973).
- Çetin K. Koç and S. N. Arachchige, Journal of Parallel and Distributed Computing 13, 118 (1991).
- P. Høyer and R. Špalek, Theory of Computing 1, 81 (2005).
- D. Gottesman, Stabilizer codes and quantum error correction, Ph.D. thesis, California Institute of Technology (1997).
- E. Knill and R. Laflamme, Phys. Rev. A 55, 900 (1997).
- N. J. Cerf and R. Cleve, Phys. Rev. A 56, 1721 (1997).
- A. Vardy, IEEE Transactions on Information Theory 43, 1757 (1997).
- V. Bergholm et al., (2018), arXiv:1811.04968 [quant-ph] .
- S. B. Bravyi and A. Y. Kitaev, Annals of Physics 298, 210 (2002).
- Qiskit contributors, “Qiskit: An open-source framework for quantum computing,” (2023).
- M. Hostetter, “Galois: A performant NumPy extension for Galois fields,” (2020).
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