⚛️ quantum physics

Measurement-and Feedback-Driven Non-Equilibrium Phase Transitions on a Quantum Processor

Using a superconducting quantum processor with high-fidelity mid-circuit measurements and low-latency feedback, researchers experimentally demonstrated the coexistence of two distinct non-equilibrium phase transitions: a measurement-induced entanglement transition in individual quantum trajectories and an absorbing-state transition in the averaged quantum channel that belongs to the directed percolation universality class.

Original authors: Zhiyi Wu, Xuandong Sun, Songlei Wang, Jiawei Zhang, Xiaohan Yang, Ji Chu, Jingjing Niu, Youpeng Zhong, Xiao Chen, Zhi-Cheng Yang, Dapeng Yu

Published 2026-07-02

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CC BY 4.0

Original authors: Zhiyi Wu, Xuandong Sun, Songlei Wang, Jiawei Zhang, Xiaohan Yang, Ji Chu, Jingjing Niu, Youpeng Zhong, Xiao Chen, Zhi-Cheng Yang, Dapeng Yu

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you have a giant, complex dance floor filled with 30 dancers (the qubits). In the world of quantum physics, these dancers are in a superposition of states—they are essentially "everywhere" at once, holding hands in a massive, invisible web of connection called entanglement.

This paper describes an experiment where the researchers built a special quantum computer to watch how this dance floor behaves when you start interrupting the dance with two specific actions: checking the dancers (measurement) and telling them what to do next based on what you saw (feedback).

Here is the breakdown of what they found, using simple analogies:

The Setup: A Dance Floor with Rules

The researchers created a circuit where the dancers move in patterns (unitary gates) and then, at random intervals, a "referee" checks a specific dancer.

The Check (Measurement): The referee looks to see if a dancer is standing up (state |1⟩) or sitting down (state |0⟩).
The Feedback: If the referee sees a dancer standing, they immediately tell that dancer to sit down (apply a correction). If the dancer is already sitting, nothing happens.

The goal of this "sit down" rule is to eventually get everyone to sit down. The researchers wanted to see what happens when they change how often the referee checks the dancers.

The Two Different "Phases" of the Dance

The paper reveals that depending on how often the referee checks, the dance floor enters one of two very different states.

1. The "Active" Phase (Low Check Rate)

If the referee checks very rarely (say, once every 10 steps), the dancers keep moving around freely. Even if the referee tells a few to sit, the group dynamics (the entanglement) keep the energy high. The "standing" dancers spread out across the floor like a wave. The system stays active and chaotic.

2. The "Absorbing" Phase (High Check Rate)

If the referee checks very often (say, every step), the feedback loop is too strong. Every time a dancer stands up, they are immediately forced to sit. The "standing" energy gets crushed. Eventually, the entire floor goes silent, and everyone sits down. This is called an absorbing state because once everyone is sitting, the system gets "stuck" there and can't get up again.

The Big Discovery: Two Different Tipping Points

The most exciting part of the paper is that the researchers found two different tipping points where the behavior changes. It's not just one switch; it's two switches that happen at different times.

Switch A: The Entanglement Switch (The "Silent" Transition)
- What happens: At a lower check rate (around 20%), the dancers stop holding hands. The massive web of quantum connection (entanglement) breaks apart. The dancers become isolated individuals.
- Analogy: Imagine the dancers are still moving, but they've stopped holding hands. They are still dancing, but they are no longer a single, connected unit.
- Result: The system loses its "quantumness" (entanglement) first.
Switch B: The Absorbing Switch (The "Sit Down" Transition)
- What happens: At a higher check rate (around 35%), the system finally forces everyone to sit down completely.
- Analogy: This is when the referee is so strict that the dance floor goes completely still.
- Result: The system enters the "absorbing" state where no one is standing.

Why this matters: Before this experiment, scientists thought these two things might happen at the same time. This paper proves they are distinct. The dancers lose their connection (entanglement) before they are forced to stop moving entirely (absorbing state).

The "Directed Percolation" Connection

When the researchers looked closely at the moment right between the "Active" and "Absorbing" phases (the critical point), they found the dancers spread out in a very specific, predictable pattern.

The Analogy: Imagine a fire spreading through a forest. If the trees are spaced just right, the fire spreads in a specific, mathematical way.
The Finding: The way the "standing" dancers spread out matched a famous mathematical model called Directed Percolation (DP). This is a universal rule that describes how things spread in many different systems, from epidemics to liquid crystals. The researchers measured the "speed" of this spread and found it matched the DP prediction perfectly.

The Hardware: A Super-Fast Referee

To pull this off, the researchers had to build a quantum processor that is incredibly fast and accurate.

The Problem: Usually, checking a quantum state and telling it what to do takes too long, and the delicate quantum state collapses or gets messed up by errors before the feedback arrives.
The Solution: They built a processor that can check a dancer and give a command in just 200 nanoseconds (that's faster than a blink of an eye). They also achieved a 98.7% accuracy rate in reading the state. This speed and accuracy allowed them to keep the "dance" going long enough to see these transitions clearly.

Summary

In short, the researchers used a fast, high-quality quantum computer to simulate a dance floor where dancers are constantly being watched and corrected. They discovered that:

The dancers lose their quantum connection (entanglement) at a lower frequency of checks.
The dancers stop moving entirely (absorbing state) at a higher frequency of checks.
The transition to the "stop moving" state follows a universal mathematical rule (Directed Percolation) that describes how things spread in nature.

This proves that adaptive quantum circuits (circuits that change based on measurements) are powerful tools for exploring how complex systems behave when they are out of balance.

Technical Summary: Measurement-and Feedback-Driven Non-Equilibrium Phase Transitions on a Quantum Processor

Problem Statement
Quantum circuit models serve as a framework for exploring non-equilibrium many-body dynamics, including entanglement growth and hydrodynamics. While unitary evolution has been extensively studied, the integration of mid-circuit measurements and real-time feedback—essential for quantum error correction—introduces novel dynamic phenomena. Theoretically, adaptive circuits can exhibit two distinct non-equilibrium phase transitions:

Measurement-Induced Entanglement Transitions (MIPT): A transition in the entanglement structure of individual quantum trajectories from volume-law to area-law scaling as the measurement rate $p$ increases.
Absorbing-State Transitions: A transition in the averaged quantum channel where the system is driven into a target "absorbing" state (e.g., all qubits in $|0\rangle$ ) above a critical measurement rate, described by the directed percolation (DP) universality class.

Experimentally resolving both transitions on a single realistic device has been challenging. This is due to the need for a large number of qubits to suppress finite-size effects, high-fidelity gates, and, crucially, low-latency real-time measurement and feedback operations to preserve coherent dynamics. Previous observations of dissipation-driven transitions lacked active classical feedback.

Methodology
The authors developed a superconducting quantum processor and an adaptive circuit architecture to address these challenges:

Hardware Platform: A 66-qubit superconducting processor was used, with 30 frequency-tunable transmon qubits selected for the absorbing-state experiment and 8 qubits for the entanglement transition. The device features global mid-circuit measurement with an average quantum non-demolition (QND) fidelity of 98.7% and a real-time decision latency of 200 ns.
Circuit Architecture: The experiment utilizes a hybrid circuit with alternating layers of nearest-neighbor two-qubit unitaries (implemented via iSWAP-like entanglers with random phase rotations) and mid-circuit measurements.
Adaptive Feedback Protocol:
- Absorbing-State Experiment: A classical flag variable $f_i$ tracks the status of each qubit (active/inactive). If a measurement yields $|1\rangle$ , a corrective Pauli-X gate is applied to reset the qubit to $|0\rangle$ . Unitary gates are only applied if at least one qubit in the bond is active. This creates a competition between unitary spreading and measurement-driven resetting.
- Entanglement Experiment: An 8-qubit reduced implementation allows for full trajectory post-selection. Reduced density matrices are reconstructed via quantum-state tomography (QST) to calculate the second Rényi entropy.
Error Mitigation: For the entanglement study, a two-step procedure corrects for readout errors (using calibration matrices) and residual baseline entropy (estimated at $p=1$ ).

Key Contributions and Results
The study successfully demonstrates the coexistence of both phase transitions on the same hardware platform, with distinct critical points:

Absorbing-State Transition (30-qubit system):
- Starting from a single seed state $|0\dots010\dots0\rangle$ , the system exhibits an active phase at low measurement rates ( $p < p_{c}^{abs}$ ) where particles spread ballistically, and an absorbing phase at high rates ( $p > p_{c}^{abs}$ ) where the particle density rapidly vanishes.
- The critical point was identified at $p_{c}^{abs} \approx 0.35$ .
- Critical Exponents: At the critical point, the particle density decay/growth followed algebraic scaling consistent with the directed percolation (DP) universality class.
  - For the single-seed initial state, the dynamical exponent was found to be $z = 1.58$ (scaling $|r| \sim t^{1/z}$ ).
  - The growth exponent was $\Theta = 0.31$ ( $N(t) \sim t^\Theta$ ).
  - For a fully occupied initial state $|11\dots1\rangle$ , the decay exponent was $\alpha = -0.16$ ( $N(t) \sim t^\alpha$ ).
- These experimental exponents showed excellent agreement with theoretical predictions for 1D DP.
Measurement-Induced Entanglement Transition (8-qubit system):
- By analyzing the variance of the second Rényi entropy $\text{Var}(S_A^{(2)})$ across random circuit instances and trajectories, the authors located the entanglement transition.
- The transition occurs at a critical measurement rate of $p_{c}^{MIPT} \approx 0.20$ , where the variance peaks.
- Below this rate, the system maintains volume-law entanglement; above it, the system transitions to area-law entanglement.
Separation of Transitions:
- A crucial finding is the clear separation of the two critical points: $p_{c}^{MIPT} \approx 0.20 < p_{c}^{abs} \approx 0.35$ .
- This indicates that the loss of quantum correlations (entanglement suppression) occurs at a lower measurement rate than the macroscopic transition to the absorbing state. This confirms theoretical suggestions that these are distinct physical phenomena.

Significance and Claims
The paper claims that adaptive quantum circuits provide a powerful platform for exploring non-equilibrium quantum many-body dynamics. Specifically:

It demonstrates the first direct experimental observation of the separation between the entanglement transition and the absorbing-state transition on a quantum device.
It validates the directed percolation universality class for measurement-and feedback-driven transitions in a superconducting processor.
The work establishes measurement-feedback dynamics as a resource for controlling quantum information flow, which is central to active quantum error correction and adaptive quantum algorithms.
The authors note that while the precise values of the critical points depend on the specific gate set and finite-size effects, the qualitative separation of the transitions is robust. Future extensions to larger systems and higher dimensions may reveal new universality classes at the interface of quantum information and statistical mechanics.