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Quantum Speed Limits for Implementation of Unitary Operators in Quantum Systems

Farmanian, Abolfazl | 2025

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 57829 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Karimipour, Vahid
  7. Abstract:
  8. Quantum speed limits are bounds that determine the maximum rate at which one quantum state can be transformed into another. In this research, instead of focusing on the speed limits for converting specific states into each other, we provide speed limits for unitary operators in arbitrary dimensions. The primary reason these limits for unitary operators are important is that they offer lower bounds on the time required to implement quantum algorithms. The bounds obtained in this study do not depend on the initial and final quantum states; rather, they depend solely on the trace of the unitary operator describing the evolution and on the general features (mean and variance) of the energy spectrum of the Hamiltonian that generates this unitary evolution. The speed limits we derive can be viewed as generalizations of the Mandestam–Tamm (MT) and Margolus–Levitin (ML) bounds for unitary operators. After obtaining these speed limits, we compare them with the findings of previ- ous research and highlight their advantages. We also examine the implications of these time bounds for quantum operators in low-dimensional cases. Finally, by using these limits, we provide temporal bounds for several well-known unitary operators used in quantum information processing and quantum algorithms, such as Shor’s and Grover’s algorithms
  9. Keywords:
  10. Quantum Speed Limits ; Quantum Speed Limits for Change of Basis ; Quantum Speed Limits for Quantum Algorithms ; Quantum Speed Limits for Unitary

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