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Dissipative quantum Church-Turing theorem.

M Kliesch1, T Barthel, C Gogolin

  • 1Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany.

Physical Review Letters
|October 27, 2011
PubMed
Summary
This summary is machine-generated.

Simulating open quantum systems with unitary quantum circuits is now possible, with efficiency scaling polynomially. This finding implies dissipative quantum computing offers no advantage over standard unitary circuits for simulating quantum dynamics.

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Area of Science:

  • Quantum Information Science
  • Computational Physics
  • Quantum Computing Theory

Background:

  • Open quantum systems interact with their environment, leading to complex dynamics.
  • Simulating these systems is crucial for understanding quantum phenomena and developing quantum technologies.
  • Current methods face challenges in efficiently capturing the time evolution of open quantum systems.

Purpose of the Study:

  • To demonstrate that the time evolution of open quantum systems can be efficiently simulated using unitary quantum circuits.
  • To establish a theoretical framework for simulating dissipative quantum dynamics.
  • To explore the computational power of dissipative quantum computing relative to unitary models.

Main Methods:

  • Development of a novel Trotter decomposition tailored for Liouvillian dynamics.
  • Analysis of error bounds associated with the Trotter decomposition.
  • Polynomial scaling analysis of quantum circuit size with simulation time and system size.

Main Results:

  • The time evolution of open quantum systems is efficiently simulable by unitary quantum circuits.
  • Dissipative quantum computing is shown to be no more powerful than the standard unitary circuit model.
  • Explicit error bounds for the Trotter decomposition provide a practical tool for numerical simulations.

Conclusions:

  • The study establishes a 'dissipative Church-Turing theorem,' implying efficient quantum computation for open systems under natural assumptions.
  • The findings have significant implications for the field of quantum simulation and the capabilities of quantum computers.
  • The research provides a practical framework for numerical simulations, such as those using matrix-product operators.