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Cross Entropy Benchmark for Measurement-Induced Phase Transitions
Yaodong Li1,2, Yijian Zou2, Paolo Glorioso2
1Department of Physics, University of California, Santa Barbara, California 93106, USA.
Physical Review Letters
|June 16, 2023
Summary
Linear cross entropy measures entanglement in quantum systems, distinguishing between volume and area law phases. This method allows experimental access to measurement-induced phase transitions without postselection.
Area of Science:
- Quantum Information Science
- Condensed Matter Physics
Background:
- Measurement-induced phase transitions (MIPs) are a key phenomenon in quantum information.
- Characterizing these transitions often requires postselection of quantum trajectories, which is experimentally challenging.
- The linear cross entropy (Lχ) has been proposed as a potential order parameter for MIPs.
Purpose of the Study:
- To investigate the use of linear cross entropy (Lχ) as an order parameter for measurement-induced phase transitions.
- To develop a postselection-free experimental protocol for accessing MIPs.
- To explore the impact of noise on the detection of MIPs.
Main Methods:
- Utilizing two random quantum circuits with identical bulk but different initial states.
- Calculating the linear cross entropy (Lχ) between bulk measurement outcome distributions.
- Employing a hybrid quantum-classical approach for efficient sampling of Lχ.
- Numerically simulating Clifford circuits to estimate sampling complexity.
Main Results:
- Linear cross entropy (Lχ) effectively distinguishes between volume and area law phases.
- In the volume law phase, Lχ approaches 1, indicating indistinguishable states.
- In the area law phase, Lχ is less than 1.
- The Lχ can be sampled with accuracy ϵ from O(1/ϵ²) trajectories for Clifford circuits.
- MIP signatures persist under weak depolarizing noise for intermediate system sizes.
Conclusions:
- Linear cross entropy serves as a viable postselection-free order parameter for measurement-induced phase transitions.
- The proposed hybrid quantum-classical protocol offers an efficient route for experimental verification.
- The robustness of MIP signatures to noise suggests potential for experimental observation in near-term devices.
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