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Many-body thermodynamics on quantum computers via partition function zeros.

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Area of Science:

  • Quantum Computing
  • Statistical Physics
  • Condensed Matter Physics

Background:

  • Partition functions are fundamental in physics for determining thermodynamic properties and phase transitions.
  • Analytically continuing partition functions to the complex plane reveals zeros that characterize the entire function.
  • The scaling and nature of these zeros provide insights into phase transitions.

Purpose of the Study:

  • To demonstrate a scalable method for finding partition function zeros on noisy intermediate-scale quantum computers.
  • To use the XXZ spin chain model as a prototype for this quantum computation.
  • To observe the transition of partition function zeros from XY-like to Ising-like behavior.

Main Methods:

  • Utilizing trapped-ion quantum computers to compute partition function zeros.
  • Employing the XXZ spin chain model to study the behavior of these zeros.
  • Varying anisotropy parameters to observe transitions in zero behavior.

Main Results:

  • Successfully located partition function zeros on a quantum computer.
  • Observed a transition in the behavior of partition function zeros as a function of anisotropy.
  • Demonstrated a shift from XY-like to Ising-like behavior in the XXZ spin chain model.

Conclusions:

  • The developed method provides a pathway to calculate critical phenomena using quantum computers as hardware improves.
  • This work paves the way for studying complex systems and phase transitions beyond the limits of classical computation.
  • Future quantum hardware advancements will enable calculations in the thermodynamic limit.