⚛️ quantum physics

Observation of feedback-directed quantum dynamics in large-scale quantum processors

This paper demonstrates the implementation of feedback-directed circuit architectures on large-scale IBM superconducting quantum processors, where real-time mid-circuit measurements and conditional operations are used to steer random quantum dynamics and generate robust, noise-resilient signatures of feedback-induced asymmetry distinct from the non-Hermitian skin effect.

Original authors: Ruizhe Shen, Ching Hua Lee

Published 2026-04-15

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Ruizhe Shen, Ching Hua Lee

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, chaotic dance floor filled with 100 dancers (these are the qubits on a quantum computer). Normally, if you tell them to dance randomly, they will eventually spread out evenly across the room. If you start in the middle, they will drift left and right equally, mixing up their positions until no one knows where anyone started. This is how quantum information usually behaves: it's symmetric and messy.

But in this paper, the researchers (Ruizhe Shen and Ching Hua Lee) discovered a way to make the dancers move in one specific direction only, creating a "traffic jam" of information flowing to the right, even though the dance floor itself is perfectly symmetrical.

Here is how they did it, explained through simple analogies:

1. The Problem: The "Chaotic Dance Floor"

Think of a standard quantum computer as a room where people are constantly swapping places with their neighbors in a random pattern. If you drop a ball of red paint (representing information) in the center, it will slowly spread out to the left and right, eventually coloring the whole room evenly. There is no "arrow" pointing one way.

2. The Solution: The "Smart Referee"

The researchers introduced a new rule: Mid-circuit measurements with feedback.

Imagine a referee standing on the dance floor who can peek at the dancers' positions while the music is playing (this is the measurement).

Old way: The referee just watches and writes down who is where. This doesn't change the dance.
New way (The Innovation): The referee doesn't just watch; they intervene.
- If the referee sees a dancer in a specific spot, they immediately blow a whistle and tell that dancer to "flip" or "swap places" with their neighbor.
- Crucially, the referee is programmed to be biased. They are more likely to intervene if the dancer is on the left side of the room, or they give instructions that only push people to the right.

3. The Two Tricks Used

The paper tested two different ways to make the referee bias the flow:

Trick A: The "Position-Sensitive Whistle" (Conditional X-gates)
Imagine the referee has a rule: "If I see a dancer on the left side of the room, I will force them to flip their position."
- Because the referee is more active on the left, the dancers on the left keep getting shuffled and pushed.
- Over time, this creates a "loss" on the left side and a buildup on the right. It's like a leaky bucket on the left side of a boat; the water (information) naturally flows to the dry side (the right).
Trick B: The "One-Way Swap" (Conditional SWAP gates)
Imagine the referee has a rule: "If I see a dancer in a specific state, I will force them to swap places with the person to their right, but never the person to their left."
- This is like a conveyor belt. Every time the referee checks, they physically move a person one step to the right.
- Even though the underlying dance (the random unitary gates) is still chaotic, this tiny, repeated "nudge" to the right adds up, creating a strong current flowing in one direction.

4. The Big Achievement: Doing it at Scale

Usually, when you try to do complex things on a quantum computer, the machine gets "noisy" (like a radio with static), and the signal gets lost.

The Challenge: They tried this with 100 dancers (qubits). That is a huge number for current technology.
The Result: Despite the noise and the fact that the computer isn't perfect, the "directional flow" still worked! The information still piled up on the right side.
Why it matters: They proved that you can use "measurement" not just to read the result at the end, but to steer the process in real-time. They turned the act of looking at the system into a tool for controlling it.

5. The "Non-Hermitian Skin Effect" Analogy

The paper mentions a famous physics concept called the "Non-Hermitian Skin Effect."

The Old Way: Usually, to make particles pile up on one side, you have to build the machine with "one-way doors" built into the walls (asymmetric physics).
The New Way: The researchers showed you don't need special walls. You can just have a smart referee who checks the players and nudges them. The "one-way" nature comes from the control strategy, not the hardware itself. It's like making a river flow uphill not by changing the landscape, but by having a team of people constantly pushing the water in one direction.

Summary

This paper is a breakthrough because it shows that feedback (using what you learn now to decide what to do next) is a powerful new tool.

Before: Quantum computers were like a blindfolded person throwing darts; they could do complex math, but they couldn't "steer" the chaos.
Now: They have given the computer "eyes" and "hands." They can look at the quantum state, make a decision, and immediately change the path of the information.

They successfully demonstrated this on a massive scale (100 qubits), proving that we can engineer "directional" quantum dynamics on real, noisy hardware. This opens the door to building quantum systems that can transport information like a one-way street, which is essential for future quantum networks and simulations of complex, non-equilibrium physics.

1. Problem Statement

Quantum computers are increasingly capable of simulating non-unitary physics, which is typically associated with open systems, dissipation, or decoherence. While previous research has focused on measurement-induced phase transitions and the non-Hermitian skin effect (NHSE), these phenomena often rely on intrinsic asymmetries in Hamiltonian couplings or stochastic measurement processes that lack active control.

The core challenge addressed in this work is: Can mid-circuit measurements be transformed from passive readout tools into active control signals to engineer specific, directional, non-unitary dynamics on large-scale, noisy quantum hardware? Specifically, the authors aim to demonstrate that feedback loops can break the spatial symmetry of random quantum circuits, creating a robust "arrow of time" or directional flow of information that is distinct from standard NHSE mechanisms.

2. Methodology

The authors propose and implement a feedback-directed circuit architecture on IBM superconducting quantum processors (up to 100 qubits). The methodology involves three main components:

A. Circuit Architecture

The system utilizes a "brickwork" random unitary circuit ( $U_{rand}$ ) composed of random single-qubit rotations ( $R_X$ ) and controlled-Z (CZ) gates to scramble information. To this, they add mid-circuit measurements followed by real-time conditional operations (feedforward). Two primary feedback protocols are tested:

Position-Dependent Feedback (Conditional-X):
- Qubits are measured with a spatially varying probability $f(x) = (L-x)g$ .
- If the outcome is $|0\rangle$ , a conditional Pauli-X gate is applied to flip the qubit.
- Mechanism: This creates a position-dependent loss of the $|0\rangle$ state, effectively engineering a drift.
Feedback-Conditioned Operator (Conditional-SWAP):
- Qubits are measured with a uniform probability $p_{SWAP}$ .
- If the outcome is $|0\rangle$ , a SWAP gate is applied between the measured qubit ( $x$ ) and its right neighbor ( $x+1$ ).
- Mechanism: This induces a directed transfer of population from $x \to x+1$ , creating a unidirectional current.

B. Hardware Implementation

Platform: IBM Quantum processors (specifically the "marrakesh" device).
Scale: Simulations performed on chains of 20, 50, 80, and 100 qubits.
Error Mitigation:
- Scrambling Strength: The authors optimized the randomness of the unitary gates (rotation angles) to ensure that intrinsic hardware noise is averaged out by the circuit's own chaos, preventing spurious directional signals.
- Classical Stochastic Modeling: To validate results, they developed a classical discrete-time Markov model that simulates the bit-string evolution, accounting for the probabilistic nature of measurements and feedback.

C. Observables

Center of Mass ( $N_c$ ): Tracks the average position of the excitation density.
Local Density ( $\langle n_x \rangle$ ): Visualizes the spatial distribution of excitations over time.
Effective Polarization ( $J_c$ ): A boundary-to-boundary imbalance metric defined as $\langle n_{L-1} - n_0 \rangle / \sum \langle n_x \rangle$ , designed to detect directional flow even when bulk density profiles appear symmetric.

3. Key Contributions

Active Control via Feedback: The paper demonstrates that measurement backaction can be converted into a programmable resource. By coupling the quantum state to its classical measurement record, the authors engineer directional information flow that is not present in purely unitary or purely stochastic measurement circuits.
Distinction from NHSE: The observed asymmetry is operationally generated by the feedback loop (measurement outcomes $\to$ conditional gates) rather than being encoded in the microscopic Hamiltonian (as in the non-Hermitian skin effect). This establishes a new class of non-unitary dynamics driven by quantum trajectories.
Scalability: The framework is successfully demonstrated on 100 qubits, a scale significantly larger than previous attempts at simulating measurement-induced dynamics. The results show that the feedback-induced directionality remains robust despite hardware noise.
Theoretical-Experimental Bridge: The authors provide a rigorous link between the quantum hardware data and an effective classical stochastic model (and continuum drift-diffusion equations), validating that the observed dynamics match theoretical predictions.

4. Key Results

Symmetry Breaking: Purely unitary circuits and circuits with only stochastic measurements (no feedback) exhibited symmetric spreading of information. In contrast, circuits with conditional-X and conditional-SWAP feedback showed clear asymmetric flow (drift) toward one edge of the chain.
Robustness at Scale:
- On 100-qubit chains, the feedback-induced directional flow persisted.
- The effective polarization metric ( $J_c$ ) reached values up to 0.6, providing a clear, size-independent signature of directed transport, whereas local density profiles were sometimes obscured by noise.
Tunability: The strength of the directional drift was shown to be tunable by adjusting the measurement gradient parameter $g$ . Increasing $g$ linearly increased the net center-of-mass shift.
Boundary Effects: When the initial state was placed near the boundary where the measurement rate was low, the feedback effect was suppressed, confirming that the mechanism relies on the interplay between measurement probability and conditional operations across the chain.
Noise Resilience: The intrinsic randomness of the chaotic circuit effectively averaged out systematic hardware errors, allowing the feedback signal to emerge clearly even on noisy intermediate-scale quantum (NISQ) devices.

5. Significance

New Paradigm for Non-Unitary Control: This work establishes feedback as a programmable resource for engineering non-unitary physics. It moves beyond simulating open systems via dissipation to actively steering quantum dynamics using measurement outcomes.
Scalable Platform for Non-Hermitian Physics: It provides a viable route to study non-Hermitian phenomena, measurement-induced criticality, and non-equilibrium phase transitions on digital quantum computers, which are often difficult to realize in analog platforms (like cold atoms) due to control limitations.
Hardware Validation: By successfully running these protocols on 100 qubits, the paper proves that current quantum hardware, despite latency and readout errors, is sufficient to explore complex, measurement-driven many-body dynamics.
Future Directions: The approach opens avenues for engineering tunable open-system behaviors, directional quantum transport, and potentially stabilizing specific quantum states (like topological phases) through real-time feedback, paving the way for more sophisticated quantum control protocols.

In summary, the paper successfully demonstrates that measurement-based feedback can be used to break spatial symmetry in random quantum circuits, creating robust, tunable, and directional quantum dynamics on large-scale hardware, distinct from traditional non-Hermitian mechanisms.