⚛️ quantum physics

Dissipative ground-state preparation of a quantum spin chain on a trapped-ion quantum computer

This paper demonstrates a robust, dissipative protocol for preparing the ground state of a transverse-field Ising spin chain with up to 19 spins on a trapped-ion quantum computer, showing monotonic fidelity improvement and convergence to low-energy states despite hardware noise, with results matching noiseless simulations after zero-noise extrapolation.

Original authors: Kazuhiro Seki, Yuta Kikuchi, Tomoya Hayata, Seiji Yunoki

Published 2026-06-24

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CC BY 4.0

Original authors: Kazuhiro Seki, Yuta Kikuchi, Tomoya Hayata, Seiji Yunoki

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 are trying to find the lowest point in a vast, foggy mountain range. In the world of quantum physics, this "lowest point" is called the ground state, and it holds the secret to how a system of atoms or particles behaves when it is at its most stable and energetic. Finding this spot is incredibly hard for traditional computers, especially when the mountain range gets huge and complex.

This paper describes a clever new way to find that lowest point using a special kind of computer made of trapped ions (charged atoms held in place by magnetic fields). Instead of trying to calculate the path mathematically, the researchers use a process called dissipative ground-state preparation.

Here is how it works, using some everyday analogies:

1. The "Gravity" of the Quantum World

Usually, if you want to cool something down to its most stable state, you just let it sit there and lose energy to the environment (like a hot cup of coffee cooling down). In quantum mechanics, this is tricky because measuring or touching the system often messes it up.

The researchers used a method that acts like a one-way slide. They designed a specific set of rules (a "dissipation channel") that acts like gravity. If the system is in a high-energy state (high up on the mountain), the rules push it down. If it's already at the bottom, the rules let it stay there. Crucially, the rules are designed so the system cannot accidentally slide back up.

2. The "Filter" and the "Jump"

To make this slide work, they used a special tool called a jump operator. Think of this as a bouncer at a club.

The Goal: The bouncer's job is to let the "ground state" (the VIP) stay in the club but kick out anyone with higher energy.
The Filter: To make the bouncer effective, they used a "filter function." Imagine a sieve that only lets water flow through if it's moving in a specific direction (downhill). If the water tries to flow uphill (gain energy), the sieve blocks it. The researchers tuned this sieve perfectly so it only allows the system to lose energy, never gain it.

3. The "Reset Button" Trick

The experiment was run on a real quantum computer (Quantinuum's "Reimei"). To make the "slide" work, they used an extra helper qubit (an ancilla), which acts like a reset button.

They let the system interact with this helper.
Then, they measure the helper and "reset" it to zero, effectively throwing away the information about what happened.
This act of throwing away information is the magic trick: it forces the main system to lose energy and settle into the lowest state, just like shaking a box of marbles until they all settle at the bottom.

4. The Challenge: Noise and "Static"

Real quantum computers are noisy. They are like a radio with static; the signal gets distorted by the environment. The researchers were worried that this "static" (hardware noise) would push the system off the slide or keep it from reaching the bottom.

They tested this with systems of up to 19 spins (particles). Even though the computer circuits were massive (containing over 4,000 entangling gates, which is a lot for today's technology), the system consistently found a low-energy state. It didn't get lost in the "static" and turn into random noise. This shows the method is intrinsically robust—it's like a sturdy boat that stays upright even in choppy water.

5. Cleaning Up the Signal (Zero-Noise Extrapolation)

Even with a robust method, the "static" still made the final result slightly off. To fix this, the researchers used a technique called Zero-Noise Extrapolation (ZNE).

The Analogy: Imagine you are trying to guess the true temperature of a room, but your thermometer is slightly broken and reads a bit high. You take the reading, then you deliberately make the thermometer worse (by adding more "noise") and take another reading. Then you make it even worse and take a third.
By looking at how the readings change as you make the noise worse, you can mathematically draw a line back to what the reading would have been if the thermometer were perfect (zero noise).
Using this trick, they were able to correct their results so they matched perfectly with what a perfect, noiseless computer would have calculated.

The Bottom Line

The paper demonstrates that you can prepare a quantum system in its most stable, lowest-energy state by using a "one-way slide" that pushes it down and a "reset button" to throw away energy. Even on a noisy, imperfect quantum computer with thousands of complex steps, this method works reliably. By mathematically cleaning up the noise afterward, they got highly accurate results for systems up to 19 particles, proving that this "dissipative" approach is a powerful tool for the future of quantum computing.

Technical Summary: Dissipative Ground-State Preparation of a Quantum Spin Chain on a Trapped-Ion Quantum Computer

Problem Statement
Estimating ground-state properties of quantum many-body systems remains a significant challenge, particularly for large system sizes and dimensions greater than one, where classical methods like exact diagonalization or density-matrix renormalization group (DMRG) become intractable. While fault-tolerant quantum phase estimation offers a path to quantum advantage, current Noisy Intermediate-Scale Quantum (NISQ) devices lack the error correction required for such algorithms. Variational Quantum Eigensolvers (VQE) are widely used but suffer from issues like barren plateaus and high measurement overhead. Recently, dissipative protocols have emerged as an alternative, utilizing mid-circuit measurement and reset (MCMR) to simulate open quantum system dynamics. However, the performance and robustness of these protocols on current noisy hardware, particularly regarding their convergence guarantees under arbitrary temporal discretization, require further investigation.

Methodology
The authors propose and implement a dissipative ground-state preparation protocol for a 1D transverse-field Ising model on the Quantinuum trapped-ion quantum computer, Reimei. The methodology involves three primary components:

Theoretical Framework and Kraus Representation:
The authors reformulate a protocol previously proposed by Ding et al. [41] by deriving a Kraus representation for the dissipation channel $\Gamma_K$ . Unlike previous analyses restricted to the Lindblad dynamics regime (small time steps), this derivation holds for arbitrary temporal discretization steps $\tau$ . The channel is constructed using an ancilla qubit and a dilated unitary operator $\hat{W}(\sqrt{\tau}) = \exp(-i\hat{K}\sqrt{\tau})$ , where $\hat{K}$ is a jump operator designed to annihilate the ground state ( $\hat{K}|E_0\rangle = 0$ ). The authors prove that the fidelity between the system state and the unique ground state is monotonically non-decreasing under repeated applications of $\Gamma_K$ , regardless of the step size $\tau$ , provided the ground state is the unique steady state.
Implementation Details:
- Jump Operator: The jump operator is constructed via an Operator Fourier Transform (OFT) of a filter function $\tilde{f}(\omega)$ that suppresses energy-increasing transitions (support only on $\omega \leq 0$ ). The authors employ a filter based on the difference of Fermi-Dirac distributions.
- Discretization: The continuous time integral of the OFT is truncated to a finite interval $[-S_s, S_s]$ and discretized. The resulting unitary is implemented using a second-order Trotter formula, alternating between system Hamiltonian evolution and system-ancilla interactions (Pauli gadgets).
- Hardware Execution: Experiments were conducted on the Reimei system (20 qubits) for system sizes $N=4, 6,$ and $19$. The protocol interleaves dissipative steps with coherent unitary evolution to accelerate convergence.
Error Mitigation:
To address hardware noise, the authors applied Zero-Noise Extrapolation (ZNE) using the gate-folding method on native two-qubit $R_{ZZ}$ gates. They compared linear and exponential extrapolation schemes to estimate noise-free energy expectation values.

Key Contributions

Generalized Theoretical Proof: The paper extends the theoretical analysis of dissipative ground-state preparation beyond the small-step Lindblad limit, proving monotonic fidelity increase for arbitrary discretization steps $\tau$ .
Experimental Demonstration: The authors successfully implemented the protocol on a trapped-ion quantum computer for up to 19 spins, utilizing a single ancilla qubit.
Robustness Analysis: The study demonstrates that the protocol exhibits intrinsic robustness against hardware noise. Even with circuits containing up to 4110 entangling gates (for $N=19$ ), the dynamics consistently converged to low-energy states far from the maximally mixed state, rather than failing completely.
ZNE Validation: The application of ZNE systematically improved the energy expectation values, bringing them into agreement with noiseless simulations within statistical uncertainties.

Results

Convergence: For $N=4$ and $N=6$ , the experimental energy expectation values converged to steady states that were significantly lower in energy than the maximally mixed state, despite the presence of noise.
Scalability: For the $N=19$ system, the protocol successfully prepared low-energy states even at time steps corresponding to 4110 $R_{ZZ}$ gates.
ZNE Performance:
- For $N=6$ , ZNE with exponential extrapolation almost completely eliminated the relative error (approx. 30%) present in the raw noisy data ( $G=1$ ).
- For $N=19$ , ZNE reduced the relative error at the largest time step ( $m=30$ ) by a factor of approximately three (from $\sim0.5$ to $\sim0.15$ ).
- Exponential extrapolation consistently outperformed linear extrapolation, particularly for larger system sizes and deeper circuits.
Noise Resilience: Even in simulations where the circuit depth was pushed to 13,700 gates ( $m=100$ for $N=19$ ), the system maintained a non-zero energy expectation value, indicating the protocol does not simply degrade to a random mixed state under noise.

Significance and Claims
The paper claims to demonstrate the intrinsic robustness of dissipative ground-state preparation protocols on current noisy quantum hardware. By deriving a Kraus representation valid for arbitrary time steps, the authors provide a rigorous foundation for implementing these protocols without the strict requirement of infinitesimal time steps, which is crucial for NISQ devices with limited coherence times. The successful preparation of ground states for up to 19 spins, combined with the effectiveness of ZNE in recovering noiseless results, suggests that dissipative protocols are a viable and robust approach for ground-state preparation in the NISQ era. The authors note that while precise estimation of spectral parameters (gap and radius) is beneficial, the protocol remains effective even with approximate values, provided the filter function conditions are approximately met. They conclude that this approach offers a promising alternative to variational methods for preparing ground states of quantum many-body Hamiltonians.