This chapter covers product formulas that approximate the time evolution of a quantum system—a fundamental technique in quantum simulation. The most notable product formulas, Lie–Trotter and the family of Suzuki–Trotter formulas are presented with their approximation error bounds. The procedure for exponentiating Pauli strings is provided with the corresponding circuits. Two example codes outline the error scaling of product formulas for various parameters including the number of repetitions and order of the product formula.

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Trotterization

  • Osama M. Raisuddin,
  • Suvranu De

摘要

This chapter covers product formulas that approximate the time evolution of a quantum system—a fundamental technique in quantum simulation. The most notable product formulas, Lie–Trotter and the family of Suzuki–Trotter formulas are presented with their approximation error bounds. The procedure for exponentiating Pauli strings is provided with the corresponding circuits. Two example codes outline the error scaling of product formulas for various parameters including the number of repetitions and order of the product formula.