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States from quantum circuits with few non-Clifford gates can be disentangled. This allows efficient classical simulation of Pauli expectation values, despite high entanglement and nonstabilizerness.

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Area of Science:

  • Quantum Information Science
  • Quantum Computing Theory

Background:

  • Random Clifford circuits are a fundamental model in quantum computation.
  • Non-Clifford gates like T gates introduce computational complexity (nonstabilizerness).
  • Understanding the properties of circuits with doped non-Clifford gates is crucial for quantum advantage.

Purpose of the Study:

  • To investigate the disentanglability of states generated by random Clifford circuits doped with non-Clifford phase gates.
  • To determine the conditions under which these complex quantum states can be simplified.
  • To explore the implications for classical simulation and quantum circuit design.

Main Methods:

  • Analytical proof using a quantum error correction formulation.
  • Numerical demonstrations of the theoretical findings.
  • Analysis of consequences for Hamiltonian dynamics and state design.

Main Results:

  • States from circuits with a limited number of non-Clifford gates (≤ number of qubits) can be completely disentangled.
  • Efficient classical simulation of Pauli expectation values is possible for these states.
  • The study reveals a novel representation for approximate state designs and a circuit compression scheme.

Conclusions:

  • The presence of a small number of non-Clifford gates does not inherently prevent disentanglement or efficient classical simulation.
  • This finding has significant implications for understanding the boundary between quantum and classical computational power.
  • The proposed methods offer practical advancements in quantum circuit generation and compression.