Prethermalization by Random Multipolar Driving on a 78-Qubit Superconducting Processor

Using a 78-qubit superconducting processor, researchers experimentally demonstrated long-lived prethermal phases in many-body systems driven by structured random multipolar protocols, revealing a doubly tunable heating suppression mechanism and observing non-equilibrium dynamics that exceed the capabilities of classical tensor-network simulations.

The Gist

Imagine you have a giant, chaotic dance floor with 78 dancers (the qubits) holding hands in a grid. Normally, if you start playing music that changes randomly, the dancers would eventually get so excited and confused that they'd spin out of control, forget their original formation, and end up in a hot, messy, featureless crowd. In physics, we call this "heating up" to an "infinite temperature" state. It's the ultimate party crash where order is lost forever.

Usually, scientists try to stop this chaos by playing music on a perfect, repeating loop (like a metronome). But what if the music isn't a perfect loop? What if it's random? For a long time, scientists thought random music would always lead to a quick meltdown.

The Big Discovery
This paper reports on an experiment using a super-powerful quantum computer called "Chuang-tzu 2.0" (named after the ancient Chinese philosopher) that found a way to keep the dancers organized for a surprisingly long time, even with random music. They discovered a "prethermal" phase—a long, stable plateau where the system stays cool and ordered before eventually heating up.

The Secret Sauce: "Multipolar" Driving
The researchers didn't just play random notes; they played random notes with a specific, hidden structure. They call this Random Multipolar Driving (RMD).

Think of it like this:

• Normal Random (Monopole): Imagine a DJ throwing darts at a playlist. The music is chaotic, and the dancers get confused immediately.
• Dipolar (Level 1): The DJ starts pairing up the random songs. Every time a fast song plays, it's immediately followed by a slow song that cancels out the energy. The dancers wobble but don't fall over.
• Quadrupolar (Level 2): The DJ gets even smarter. They group the songs into triplets or quadruplets, creating a complex rhythm where the chaos cancels itself out even better.

The more complex the grouping (the higher the "multipolar order"), the longer the dancers can stay organized. The paper shows that by increasing the speed of the music (frequency) and the complexity of these groupings, they can delay the "heat death" of the system for over 1,000 cycles of music.

The "Double Dial" Control
The most exciting part is that the researchers found they have two knobs to control how long the party lasts:

1. Speed: How fast the music changes.
2. Complexity: How many songs they group together to cancel out the chaos.

They found a universal rule: if you double the complexity of the grouping, the time before the system melts down increases dramatically. It's like finding a magic formula where the more complex your rhythm is, the longer your system survives.

Watching the Entanglement
In quantum physics, "entanglement" is like a secret telepathic link between dancers. As the system heats up, these links spread everywhere, connecting everyone to everyone else.

• The researchers used a special camera (Quantum State Tomography) to watch these links form.
• They saw that at first, the links only formed between neighbors (like a small circle of friends).
• As time went on, the links spread to cover the whole room (the whole grid).
• Crucially, they saw that the way these links spread wasn't uniform. Some parts of the dance floor stayed linked in a wavy, oscillating pattern, while others settled down. This "non-uniform" behavior is a new discovery that helps us understand how quantum systems behave in 2D space.

Why Classical Computers Couldn't Do This
The researchers tried to simulate this dance on a supercomputer using advanced math (tensor networks).

• The Problem: As the dancers get more entangled, the math required to describe them grows exponentially. It's like trying to write down the instructions for a dance where every dancer is connected to every other dancer; the list of instructions becomes longer than the universe.
• The Result: The supercomputer could only simulate the first few seconds of the dance before it ran out of memory and crashed.
• The Win: The quantum processor (Chuang-tzu 2.0) didn't crash. It ran the full 1,000+ cycles. This proves that for certain complex, chaotic quantum problems, a quantum computer is simply better than any classical computer we have today.

In Summary
This paper shows that by using a clever, structured form of randomness, scientists can keep a large quantum system stable for a long time, preventing it from heating up and losing its information. They proved this on a 78-qubit chip, observed how the internal connections (entanglement) grow, and demonstrated that this specific quantum task is too hard for even the world's best supercomputers to simulate. It's a major step forward in understanding how to control quantum systems that are far from equilibrium.

Technical Summary

Technical Summary: Prethermalization by Random Multipolar Driving on a 78-Qubit Superconducting Processor

Problem Statement
Time-dependent drives offer a pathway to realize non-equilibrium many-body phenomena absent in static systems, such as discrete-time crystals and Floquet topological matter. However, a fundamental challenge in generic time-dependent many-body systems is inevitable heating due to the lack of energy conservation, which drives the system toward a featureless infinite-temperature state. While periodic (Floquet) drives can suppress heating exponentially in the high-frequency regime or via many-body localization (MBL), stabilizing non-periodically driven systems remains difficult. Specifically, random drives typically open deleterious energy absorption channels that lead to swift heating, even in clean systems where MBL is absent. The extent to which highly controllable quantum simulators can suppress heating in non-periodically driven systems, and the resulting scaling laws, has remained largely unknown.

Methodology
The authors utilized the "Chuang-tzu 2.0," a 78-qubit superconducting quantum processor arranged in a $6 \times 13$ square lattice with 137 tunable couplers. The system simulates a 2D hard-core Bose-Hubbard model. The core experimental protocol involves Random Multipolar Driving (RMD), a structured random driving scheme characterized by a temporal multipolar order $n$.

• Driving Protocol: The protocol constructs evolution operators $\hat{U}_{\pm} = \exp(-i\hat{H}_{\pm}T)$, where $\hat{H}_{\pm}$ differ by a staggered potential along the y-axis.
  • 0-RMD: A random sequence of $\hat{U}_+$ and $\hat{U}_-$.
  • n-RMD: Constructed recursively by anti-aligning two $(n-1)$-th order operators. For example, 1-RMD uses random sequences of $\hat{U}_+\hat{U}_-$ and $\hat{U}_-\hat{U}_+$. In the limit $n \to \infty$, this converges to self-similar Thue-Morse driving.
• Initialization and Measurement: The system was initialized in a density wave state (even y-sites occupied). The heating process was monitored over more than 1,000 driving cycles by measuring:
  1. Particle Imbalance ($I$): A local observable tracking the decay of the initial density wave order.
  2. Subsystem Entanglement Entropy ($S$): Measured via Quantum State Tomography (QST) on various subsystems to track non-local correlations and the approach to the Page value (infinite temperature).
• Numerical Benchmarks: The authors employed Tensor Network methods, specifically Grouped Matrix Product States (GMPS) and Projected Entangled Pair States (PEPS), to simulate the dynamics. These simulations were used to benchmark the 8-qubit regime and analyze early-time dynamics in the 78-qubit system, though they became computationally intractable as entanglement grew.

Key Contributions and Results

1. Observation of Long-Lived Prethermal Plateaus:
   The experiment successfully demonstrated the existence of long-lived prethermal phases in a non-periodically driven system. By measuring both particle imbalance and entanglement entropy, the authors observed a distinct "prethermal plateau" where heating is significantly suppressed before the system eventually thermalizes.

2. Doubly Tunable Heating Suppression:
   The prethermal lifetime ($\tau$) was found to be "doubly tunable":

   • Frequency Tuning: Increasing the driving frequency (decreasing period $T$) extends the lifetime.
   • Multipolar Order Tuning: Increasing the multipolar order $n$ significantly suppresses the heating rate.
     The heating rate follows a universal power-law scaling with the driving frequency: $\tau \propto (1/T)^{\alpha}$, where the exponent $\alpha$ depends on the multipolar order.

3. Universal Scaling Exponent:
   The experimental data confirmed the theoretical prediction that the scaling exponent is $\alpha \approx 2n + 1$.

   • For $n=0$, $\alpha \approx 0.9$ (close to 1).
   • For $n=1$, $\alpha \approx 2.7\text{--}3.0$ (close to 3).
   • For $n=2$, $\alpha \approx 3.3\text{--}4.2$ (approaching 5, though convergence is challenging due to the need for extremely fast drives and long evolution times).
     This contrasts with conventional Floquet systems where the lifetime scales exponentially with frequency ($\tau \sim e^{1/T}$). The power-law behavior in RMD arises because the multipolar structure suppresses low-frequency components of the drive, constraining heating channels.

4. Spatial Entanglement Dynamics:
   Using QST on different subsystem configurations, the authors observed a non-uniform spatial distribution of entanglement.

   • Subsystems aligned with the x-axis exhibited pronounced oscillatory dynamics during the prethermal regime, attributed to coherent particle exchange stabilized by the effective Hamiltonian.
   • The system demonstrated a crossover from area-law to volume-law entanglement scaling as time evolved, marking the transition from the prethermal regime to the heating phase.

5. Quantum Advantage in Simulation:
   The rapid growth of entanglement during the heating process rendered the 78-qubit dynamics beyond the reach of classical tensor-network simulations (GMPS and PEPS) within a realistic timeframe. While numerical methods could capture early-time dynamics, they failed to track the system as it approached the infinite-temperature state, highlighting the quantum processor's capability to emulate regimes where classical simulation faces formidable challenges.

Significance and Claims
The paper claims to provide the first experimental observation of long-lived prethermal phases in many-body systems driven by structured random protocols with tunable heating rates. The work highlights the "Chuang-tzu 2.0" processor as a powerful platform for exploring universal scaling laws and non-equilibrium phases of matter in regimes inaccessible to classical simulation.

The authors emphasize that their work demonstrates a potential quantum advantage in emulating the entire heating dynamics of driven systems. By stabilizing non-equilibrium phases through temporal correlations (multipolar driving) rather than spatial disorder (MBL), the study opens new avenues for engineering non-equilibrium phases of matter beyond the conventional Floquet paradigm. The results validate theoretical predictions regarding the suppression of heating in random multipolar drives and demonstrate the feasibility of controlling thermalization in large-scale, clean quantum simulators.