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Detecting Measurement-Induced Entanglement Transitions with Unitary Mirror Circuits.

Yariv Yanay1,2, Brian Swingle3, Charles Tahan2

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Researchers developed a hybrid quantum-classical algorithm to detect phase transitions in monitored quantum circuits. This method uses a matrix product state (MPS) to mirror the circuit, enabling experimental observation of the entanglement transition.

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Area of Science:

  • Quantum Information Science
  • Condensed Matter Physics

Background:

  • Monitored random circuits exhibit a quantum phase transition between volume-law and area-law entanglement.
  • Experimental observation of this transition is challenging due to the low probability of repeating measurement outcomes.

Purpose of the Study:

  • To develop a novel hybrid quantum-classical algorithm for experimentally detecting the entanglement phase transition in monitored random circuits.
  • To utilize matrix product states (MPS) for approximating quantum states and identifying the critical point.

Main Methods:

  • A hybrid quantum-classical algorithm employing an MPS-based unitary mirror of the projected circuit was developed.
  • The algorithm leverages the ability of polynomial-sized tensor networks (like MPS) to represent area-law entangled states.

Main Results:

  • The MPS-based unitary mirror accurately approximates states above the critical point (p > p_c) but fails for volume-law entangled states below it (p < p_c).
  • The breaking of the unitary mirror serves as a precise indicator of the critical point (p_c).
  • Bounds on entanglement entropy for MPS-representable states were derived, with implications for bounding the volume-law phase.

Conclusions:

  • The developed hybrid algorithm provides an experimentally feasible method to pinpoint the entanglement phase transition in monitored quantum circuits.
  • This approach overcomes the limitations of ensemble measurements and exponentially small repetition probabilities.
  • Numerical simulations with random Clifford gates validate the algorithm's effectiveness for small qubit systems.