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PauliComposer: Compute Tensor Products of Pauli Matrices Efficiently (2301.00560v2)
Published 2 Jan 2023 in quant-ph and physics.comp-ph
Abstract: We introduce a simple algorithm that efficiently computes tensor products of Pauli matrices. This is done by tailoring the calculations to this specific case, which allows to avoid unnecessary calculations. The strength of this strategy is benchmarked against state-of-the-art techniques, showing a remarkable acceleration. As a side product, we provide an optimized method for one key calculus in quantum simulations: the Pauli basis decomposition of Hamiltonians.
- W. Pauli, Zeitschrift für Physik 43, 601 (1927).
- W. Heisenberg, Zeitschrift für Physik 49, 619 (1928).
- H. Bethe, Zeitschrift für Physik 71, 205 (1931).
- D. Sherrington and S. Kirkpatrick, Phys. Rev. Lett. 35, 1792 (1975).
- D. Panchenko, Journal of Statistical Physics 149, 362 (2012).
- J. Hubbard and B. H. Flowers, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 276, 238 (1963).
- A. Altland and B. Simons, Second quantization, in Condensed Matter Field Theory (Cambridge University Press, 2006) pp. 39–93.
- P. Jordan and E. Wigner, Zeitschrift für Physik 47, 631 (1928).
- S. B. Bravyi and A. Y. Kitaev, Annals of Physics 298, 210 (2002).
- J. T. Seeley, M. J. Richard, and P. J. Love, The Journal of Chemical Physics 137, 224109 (2012).
- M. Steudtner and S. Wehner, New Journal of Physics 20, 063010 (2018).
- S. Östlund and S. Rommer, Phys. Rev. Lett. 75, 3537 (1995).
- S. R. White, Phys. Rev. Lett. 69, 2863 (1992).
- F. Verstraete and J. I. Cirac, arxiv:cond-mat/0407066 (2004).
- C. Lanczos, J. Res. Natl. Bur. Stand. B 45, 255 (1950).
- W. Kirby, M. Motta, and A. Mezzacapo, Quantum 7, 1018 (2023).
- Qiskit, Qiskit: An Open-source Framework for Quantum Computing (2021).
- PennyLane, PennyLane: Automatic Differentiation of Hybrid Quantum-Classical Computations (2018).
- OpenFermion, OpenFermion: The Electronic Structure Package for Quantum Computers (2017).
- Cirq, Cirq (2022).
- A. Lucas, Frontiers in Physics 2, 5 (2014).
- E. Osaba, E. Villar-Rodriguez, and I. Oregi, IEEE Access 10, 55805 (2022).
- P. L. Fackler, ACM Trans. Math. Softw. 45, 1 (2019).
- R. A. Horn and C. R. Johnson, Matrix equations and the kronecker product, in Topics in Matrix Analysis (Cambridge University Press, 1991) p. 239–297.
- C. S. Burrus, Implementing Kronecker Products Efficiently, in Automatic Generation of Prime Length FFT Programs (OpenStax CNX, 2009) pp. 41–49.
- Python, Python: A Dynamic, Open Source Programming Language, Python Software Foundation (2022).
- SciPy, Nature Methods 17, 261 (2020).
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