Experimental protocol for observing single quantum many-body scars with transmon qubits

This paper proposes experimental protocols for observing single, isolated quantum many-body scars in superconducting transmon qubit architectures by utilizing trotterized cross-resonance interactions and investigating alternative signatures such as dynamical responses to local deformations and noise.

The Gist

The "Ghost in the Machine": Finding a Single Quantum Rebel

Imagine you are at a massive, crowded music festival. There are tens of thousands of people, all dancing, talking, and moving in a chaotic, swirling mass. If you look at the crowd as a whole, it looks like a predictable, blurry sea of movement. This is what physicists call "thermalization"—the idea that in a large enough system, individual details get lost in the collective noise, and everything settles into a predictable, "average" state of chaos.

But, imagine that amidst this massive, swirling crowd, there is one single person who is doing something completely different. While everyone else is jumping and shouting, this person is standing perfectly still, or perhaps performing a very specific, elegant ballet routine. They don't follow the rhythm of the crowd, and they don't get swept up in the chaos. They are a "Quantum Many-Body Scar."

In the world of quantum physics, these "scars" are rare, special states that refuse to "melt" into the thermal chaos of the rest of the system.

The Problem: Finding a Needle in a Haystack

Until now, scientists have mostly found "towers" of these scars—groups of rebels all dancing the same way. It’s like finding a whole troupe of ballet dancers in the middle of a mosh pit; it’s easy to spot them because they are a large, organized group.

But this paper asks a much harder question: Can we find just one single rebel?

A single scar is much harder to detect. It’s like trying to find one person standing still in a crowd of thousands. If they are just one person, they might not change the "average" look of the crowd at all. Most scientists thought a single scar might be too weak to actually see in an experiment.

The Solution: The "Deformation" Test

The researchers in this paper have come up with a clever way to spot this lone rebel using superconducting qubits (tiny, man-made quantum machines). Since they can't rely on seeing a whole group, they use a "stress test."

Here is their three-step plan:

1. The Perfect State: First, they prepare the system in what they believe is the "scar" state (the calm dancer).
2. The Nudge (The Deformation): They then create a "copy" of that state, but they give it a tiny "nudge"—they slightly mess up the pattern of just one qubit. This is like taking the calm dancer and giving them a little shove to make them stumble.
3. The Comparison: They watch both states over time.
   • If the first state is truly a Scar, it will remain calm and orderly, ignoring the chaos around it. It’s like the dancer is so focused that even the noise of the crowd doesn't move them.
   • If the second (nudged) state is just a normal part of the crowd, it will immediately get swept up in the chaos, spreading out and becoming "thermal" (messy).

By comparing the "Calm Rebel" to the "Messy Nudged State," they can prove the scar exists.

Why Does This Matter?

You might wonder, "Why do we care about one weirdly calm quantum state?"

It turns out that understanding how information stays "organized" in a sea of chaos is the holy grail of Quantum Computing. If we can learn how to protect these "scars," we might be able to create quantum computers that are much more stable and less prone to the "noise" and "heat" that currently cause them to make mistakes.

In short: This paper provides the "instruction manual" for finding the most elusive, individual rebels in the quantum world, opening a new door to controlling the chaos of the subatomic universe.

Technical Summary

Technical Summary: Experimental Protocol for Observing Single Quantum Many-Body Scars with Transmon Qubits

1. Problem Statement

Quantum many-body scars (QMBSs) are exceptional energy eigenstates in otherwise thermalizing quantum systems that violate the Eigenstate Thermalization Hypothesis (ETH). While "towers" of scar states (multiple, equally spaced states) have been experimentally observed via coherent dynamical revivals, single isolated scars remain elusive. Single scars are theoretically significant because they represent the weakest possible violation of ETH and offer a closer connection to the original concept of quantum scarring in dynamical systems theory (which does not require a tower of states). However, because they do not produce periodic revivals, they are notoriously difficult to detect amidst the "thermal crowd" of the surrounding many-body spectrum.

2. Methodology

The authors propose a comprehensive experimental blueprint to detect single scars using a 1D array of fixed-frequency, fixed-coupling superconducting transmon qubits (similar to IBM Quantum architectures).

• Model Selection: They adapt two specific models that possess single scar states:
  1. The $x$-polarized state: A simple product state.
  2. The 1D Cluster state: A highly entangled state used in measurement-based quantum computing.
• Hardware Implementation: The target Hamiltonians are realized using the cross-resonance (CR) effect. Since the CR effect naturally produces $\sigma_z^i \sigma_x^j$ interactions, it is perfectly suited for the "annihilation operators" required by these scar models. To correct for undesired terms (like $\sigma_x^j$ or $\sigma_z^i \sigma_z^j$) inherent in the CR drive, the authors propose using additional single-qubit resonant drives and $z$-rotations.
• Digital Simulation (Trotterization): Because all qubits cannot be driven simultaneously, the authors employ a Lie-Suzuki-Trotter sequence. They divide the lattice into three sub-steps, driving specific subsets of qubits to implement the effective Floquet Hamiltonian ($H_F$).
• Detection Protocols: Since coherent revivals are absent, the authors propose three dynamical signatures based on comparing the scar state to a locally deformed version of itself:
  1. Persistence of Local Observables: Monitoring the expectation value of a local operator (e.g., $\langle \sigma_x \rangle$ or a stabilizer).
  2. Entanglement Entropy Dynamics: Comparing the growth of von Neumann/Rényi entropy.
  3. Trotter Resolution Sensitivity: Testing how the state responds to changes in the Trotter step size ($T$).

3. Key Contributions

• Hardware-Efficient Mapping: They bridge the gap between abstract mathematical models (projector-embedding methods) and actual superconducting hardware by utilizing the native cross-resonance interaction.
• Novel Detection Framework: They move beyond the "revival" paradigm, providing a robust method to identify scars by their stability (resistance to thermalization) compared to nearby states.
• Robustness Analysis: The paper provides a theoretical guarantee that the scar state is uniquely stable against both stochastic noise (randomized Hamiltonian coefficients) and digitization errors (coarse Trotter steps).

4. Results

Numerical simulations confirm the feasibility of the proposed protocols:

• Thermalization Gap: When the system is quenched, the scar state remains nearly stationary (high fidelity, low entropy, constant local observables), whereas the locally deformed state thermalizes rapidly to the Page entropy.
• Noise Tolerance: The scar signatures remain distinguishable from thermal states even when the Hamiltonian coefficients are subject to random errors of up to $\sim 5\%$.
• Trotter Stability: The scar state is remarkably insensitive to the size of the Trotter step $T$. Even when $T$ is large enough that the high-frequency description of the Hamiltonian breaks down for generic states, the scar state's local observables remain stable. This is attributed to the fact that the higher-order commutators in the Baker-Campbell-Hausdorff expansion still annihilate the scar state.

5. Significance

This work provides a practical roadmap for experimentalists to explore the frontier of non-ergodic quantum dynamics. By enabling the observation of single scars, it allows for the study of scar-state phase transitions and provides a way to test the fundamental limits of thermalization. Furthermore, the ability to control and identify these states has potential implications for quantum information processing, where maintaining specific non-thermal states is crucial for protecting quantum information.