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Related Concept Videos

Phase Transitions02:31

Phase Transitions

19.2K
Whether solid, liquid, or gas, a substance's state depends on the order and arrangement of its particles (atoms, molecules, or ions). Particles in the solid pack closely together, generally in a pattern. The particles vibrate about their fixed positions but do not move or squeeze past their neighbors. In liquids, although the particles are closely spaced, they are randomly arranged. The position of the particles are not fixed—that is, they are free to move past their neighbors to...
19.2K
Phase Diagram01:19

Phase Diagram

5.9K
The phase of a given substance depends on the pressure and temperature. Thus, plots of pressure versus temperature showing the phase in each region provide considerable insights into the thermal properties of substances. Such plots are known as phase diagrams. For instance, in the phase diagram for water (Figure 1), the solid curve boundaries between the phases indicate phase transitions (i.e., temperatures and pressures at which the phases coexist).
5.9K
Entropy Change in Reversible Processes01:10

Entropy Change in Reversible Processes

2.6K
In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
2.6K
Phase Transitions: Melting and Freezing02:39

Phase Transitions: Melting and Freezing

12.5K
Heating a crystalline solid increases the average energy of its atoms, molecules, or ions, and the solid gets hotter. At some point, the added energy becomes large enough to partially overcome the forces holding the molecules or ions of the solid in their fixed positions, and the solid begins the process of transitioning to the liquid state or melting. At this point, the temperature of the solid stops rising, despite the continual input of heat, and it remains constant until all of the solid is...
12.5K
Phase Changes01:19

Phase Changes

4.4K
Phase transitions play an important theoretical and practical role in the study of heat flow. In melting or fusion, a solid turns into a liquid; the opposite process is freezing. In evaporation, a liquid turns into a gas; the opposite process is condensation.
A substance melts or freezes at a temperature called its melting point and boils or condenses at its boiling point. These temperatures depend on pressure. High pressure favors the denser form of the substance, so typically, high pressure...
4.4K
Phase Diagrams02:39

Phase Diagrams

41.9K
A phase diagram combines plots of pressure versus temperature for the liquid-gas, solid-liquid, and solid-gas phase-transition equilibria of a substance. These diagrams indicate the physical states that exist under specific conditions of pressure and temperature and also provide the pressure dependence of the phase-transition temperatures (melting points, sublimation points, boiling points). Regions or areas labeled solid, liquid, and gas represent single phases, while lines or curves represent...
41.9K

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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.

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|June 16, 2023
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Summary
This summary is machine-generated.

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.

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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.