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This summary is machine-generated.

Deterministic quantum computation with one quantum bit (DQC1) is a quantum computing model. A modified DQC1(k) model shows that measuring 3 or more qubits prevents efficient classical simulation, implying quantum advantage.

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Area of Science:

  • Quantum computing
  • Computational complexity theory
  • Theoretical computer science

Background:

  • Deterministic quantum computation with one quantum bit (DQC1) is a quantum computing model.
  • DQC1 utilizes a single pure qubit and multiple mixed qubits.
  • The computational power of DQC1 compared to classical computation remains an open question.

Purpose of the Study:

  • To introduce a modified DQC1 model, termed DQC1(k).
  • To investigate the classical simulation complexity of DQC1(k).
  • To determine the conditions under which DQC1(k) offers a quantum advantage.

Main Methods:

  • Modification of the DQC1 model to DQC1(k) by allowing measurement of k output qubits.
  • Analysis of the classical simulation efficiency for DQC1(k).
  • Relating simulation complexity to the polynomial hierarchy.

Main Results:

  • DQC1(k) cannot be efficiently classically simulated for any k >= 3.
  • This result holds unless the polynomial hierarchy collapses at the third level.
  • Demonstrates a threshold (k=3) for quantum advantage in this model.

Conclusions:

  • The modified DQC1(k) model provides a framework for studying quantum advantage.
  • Measuring three or more qubits in DQC1(k) implies a significant computational power beyond classical capabilities.
  • The findings contribute to understanding the boundaries of quantum computation and its separation from classical computation.