⚛️ quantum physics

Shift of quantum critical point of discrete time crystal on a noisy quantum simulator

This study uses a 156-qubit IBM Quantum system to demonstrate that decoherence in noisy quantum simulators shifts the quantum critical point of discrete time crystals, potentially leading to the inaccurate identification of phase boundaries.

Original authors: Yuta Hirasaki, Toshinari Itoko, Naoki Kanazawa, Eiji Saitoh

Published 2026-02-11

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CC BY 4.0

Original authors: Yuta Hirasaki, Toshinari Itoko, Naoki Kanazawa, Eiji Saitoh

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

The "Glitchy Metronome" Problem: Why Noise Changes the Rules of Physics

Imagine you are a conductor leading a massive orchestra of 70 musicians. You want them to play a very specific, rhythmic pattern: every two beats, they should strike a drum in perfect unison. This steady, repeating rhythm is what physicists call a Discrete Time Crystal (DTC). It’s a strange state of matter where things don't just sit still; they dance to a beat that is slower than the "music" you are playing for them.

In a perfect world, this orchestra would play this rhythm forever. But we don't live in a perfect world. We live in a world of noise.

The Problem: The "Distracted Musician"

In this paper, researchers used a real quantum computer (an IBM system with 156 qubits) to try and create this "rhythmic orchestra." However, quantum computers are incredibly sensitive. They are like musicians who are easily distracted by a fly buzzing in the room or a sudden cough from the audience. In physics, we call these distractions decoherence.

Every time a "distraction" (noise) happens, it’s like a musician accidentally hitting the wrong note or losing the beat. You might think, "Okay, the music sounds a bit messy now, but the rhythm is still there, right?"

The researchers discovered something much more profound: The noise doesn't just make the music messy; it actually changes the rules of the song.

The Discovery: Shifting the Goalposts

In physics, there is a "tipping point" called a Quantum Critical Point. Think of this like a tightrope walker. On one side of the rope, they are walking steadily (the Time Crystal phase); on the other side, they fall off (the disordered phase). The "Critical Point" is the exact moment they lose their balance.

The researchers found that when they added noise to the simulation, the tipping point moved.

Imagine you are playing a game of "Musical Chairs." In a perfect room, the music stops at exactly 30 seconds, and everyone knows when to sit. But if the room is noisy and chaotic, the players might think the music stops at 25 seconds. They sit down too early because the noise tricked them into thinking the "rule" had changed.

This is exactly what happened in the quantum simulator. The noise (decoherence) tricked the system, making the "phase transition" (the moment the rhythm breaks) happen at a different setting than it should in a perfect world.

Why Does This Matter?

If we are using quantum computers to discover new medicines, create super-strong materials, or solve complex math, we need to know exactly where the "tipping points" are. If the noise is lying to us about where those points exist, our scientific conclusions will be wrong. It’s like trying to follow a map where the landmarks keep shifting because of the wind.

The Silver Lining: Learning to Tune the Noise

The good news? The researchers didn't just find a problem; they found a pattern. By studying exactly how the noise shifts the tipping point, they realized they might be able to use a technique called Error Mitigation.

Think of it like this: If you know that a certain amount of wind always pushes a sailboat three inches to the left, you don't just hope for no wind—you learn to steer three inches to the right to compensate. By understanding the "shift" caused by the noise, scientists can eventually "steer" their quantum simulations back to the truth.

Summary in a Nutshell

The Goal: Create a "Time Crystal"—a quantum system that pulses with a steady rhythm.
The Obstacle: "Decoherence"—random noise that acts like a distraction to the system.
The Surprise: The noise doesn't just dampen the rhythm; it shifts the "tipping point" where the rhythm breaks.
The Lesson: To trust quantum computers, we must learn to account for how noise "tricks" the physics of the system.

Technical Summary: Shift of Quantum Critical Point of Discrete Time Crystal on a Noisy Quantum Simulator

1. Problem Statement

As quantum computing moves into the Noisy Intermediate-Scale Quantum (NISQ) era, researchers are increasingly using quantum simulators to explore complex many-body phenomena, such as quantum phase transitions. However, real quantum hardware is inherently subject to decoherence (noise). While existing research has focused on using quantum error mitigation to improve the accuracy of expectation values, the fundamental impact of decoherence on critical phenomena—specifically how noise shifts the location of phase boundaries—remains insufficiently understood. There is a risk that noisy simulations might lead to the incorrect identification of quantum phases and their critical points.

2. Methodology

The researchers investigated this problem by simulating a one-dimensional Discrete Time Crystal (DTC), a non-equilibrium phase of matter characterized by subharmonic oscillations in magnetization.

Hardware & Model: The study utilized a 156-qubit IBM Quantum system (specifically the ibm aachen Heron processor). They modeled a 1D spin chain with a Floquet Hamiltonian involving a periodic drive and random interaction strengths ( $J_q$ ) to induce many-body localization.
Simulating Decoherence: To model phase decoherence, the team used a stochastic approach by randomly inserting Pauli $Z$ gates into the quantum circuit after each Floquet unitary time evolution. The decoherence rate was controlled by a probability $p$ , where a $Z$ gate is applied with probability $p$ and an identity gate with probability $1-p$ .
Observables:
- Order Parameter ( $h$ ): Defined as the amplitude of the Fourier spectrum at the subharmonic frequency $\omega = \pi/T$ .
- Criticality Indicator: The researchers analyzed the variance of the order parameter ( $\text{Var}(h)$ ) across different realizations of disorder. A peak in this variance identifies the quantum phase transition point.
Validation: The experimental results were compared against classical numerical simulations (using density matrix tracking for $N=12$ qubits) to ensure the observed shifts were physical and not artifacts of the hardware.

3. Key Contributions

Experimental Demonstration of Critical Shift: The study provides direct experimental evidence that decoherence does not merely "blur" a phase transition but physically shifts the location of the critical point in the parameter space.
Scaling Analysis: They demonstrated that this shift is not a finite-size effect by varying the system size from 10 to 70 qubits, showing the phenomenon is expected to persist in the thermodynamic limit.
Error Mitigation Strategy: The paper proposes a connection between the observed shift and probabilistic error amplification, suggesting that understanding the shift allows for better calibration of error mitigation techniques.

4. Results

Suppression of Order: As the decoherence rate $p$ increased, the amplitude of the order parameter $h$ decreased, confirming that DTC order is fragile against noise.
Shift in Criticality:
- In the absence of decoherence ( $p=0$ ), the variance of the order parameter peaked at a perturbation parameter $\epsilon \approx 0.284$ .
- With decoherence ( $p=0.06$ ), the peak shifted significantly to $\epsilon \approx 0.231$ .
Numerical Consistency: The classical simulations (Fig. 3) mirrored the experimental findings, showing a clear heatmap where increasing $p$ leads to both a suppression of the variance peak and a shift toward smaller $\epsilon$ values.
System Size Independence: The peak position remained essentially constant regardless of whether 10 or 70 qubits were used, confirming the robustness of the observed shift.

5. Significance

This work is significant for the field of quantum simulation because it highlights a fundamental challenge: noise can lead to "false" physics by misidentifying the boundaries of quantum phases.

The findings suggest that to reliably simulate many-body systems on near-term hardware, researchers must account for the fact that noise alters the very phase diagrams they are trying to map. Furthermore, the ability to characterize the shift as a function of $p$ opens a pathway for using zero-noise extrapolation and other error mitigation protocols to "back-calculate" the true, noise-free critical points of quantum systems.