The challenge of creating realistic, complex states on quantum computers has driven recent research into methods beyond simply preparing ground states, and a team led by Etienne Granet and Henrik Dreyer from Quantinuum now demonstrates a robust technique for preparing thermal states, states representing systems in equilibrium with a heat bath. This work addresses a key limitation of current quantum devices, which struggle to accurately represent the mixed states common in many physical systems, and offers a pathway towards simulating more complex phenomena. The researchers show that these thermal states can be created by slowly evolving a simple initial state, much like finding a ground state, and importantly, that this process is surprisingly resilient to the noise inherent in today’s quantum hardware. By developing a method to quantify the impact of noise, and testing it on Quantinuum’s ion-trap device, they establish a benchmark for state preparation and pave the way for more accurate simulations of thermal systems, successfully preparing a thermal state representing the Ising model with a significant number of interacting quantum bits.
The team achieved this by evolving an initial thermal state adiabatically, mirroring techniques used for preparing ground states, and showed that the entropy and energy of the final state can be controlled. Importantly, the method proves robust to hardware noise, as the energy-temperature relationship remains largely unaffected despite imperfections in the quantum device.
The researchers successfully implemented this protocol on Quantinuum’s H1-1 ion-trap device, preparing a thermal state representing the two-dimensional Ising model and establishing a benchmark for hardware performance. They also developed a method for assessing the adiabaticity of the evolution, providing a means to evaluate the accuracy of the process. Future work will focus on identifying Hamiltonian properties that might slow down the thermal state preparation process and on comparing the efficiency of this method with alternative approaches. The impact of leakage errors, stemming from hardware limitations, requires further investigation with larger quantum computers.
Second Order Entropy Corrections Calculated Rigorously
The research rigorously calculates corrections to the entropy calculation, improving the accuracy of predicting system behaviour. This detailed work refines the initial first-order approximation by including higher-order terms, ensuring the validity of the conclusions. This involves employing perturbation theory, a standard technique for approximating solutions to complex problems.
The calculations centre on expanding the entropy as a series, considering small changes in the system’s Hamiltonian. This requires careful consideration of the time evolution of the system and its density matrix, a mathematical description of the probabilities of different states. The research utilizes the trace operation to extract scalar values from operators and often simplifies calculations by working in the eigenbasis of the unperturbed Hamiltonian.
The sinc function, frequently appearing in the calculations, represents the frequency response of the system and arises from the time integration of exponential terms. The partition function, used to normalize probabilities and calculate thermal averages, plays a crucial role in the analysis. The calculations involve expanding the time evolution operator to second order, utilizing techniques like the Baker-Campbell-Hausdorff formula. The entropy is then expanded, focusing on calculating the second-order correction.
This involves expressing the perturbed density matrix in terms of the unperturbed matrix and the perturbation, then calculating the trace of the logarithm of the perturbed density matrix multiplied by the first-order perturbation. Further calculation determines the trace of the product of the first-order perturbation, the inverse of the unperturbed density matrix, and the first-order perturbation again. The analysis reveals that the second-order correction scales linearly with time, rather than quadratically as might be expected.
This improved accuracy is particularly important for larger perturbations or longer timescales. The results help determine the limits of validity of the initial approximation and provide a deeper understanding of the system’s dynamics. The research rigorously justifies the assumptions made in the main analysis, solidifying the reliability of the conclusions. In summary, this detailed work provides a more accurate estimate of entropy change and enhances the understanding of system behaviour under perturbation.
👉 More information
🗞 Adiabatic preparation of thermal states and entropy-noise relation on noisy quantum computers
🧠ArXiv: https://arxiv.org/abs/2509.05206