Researchers at the University of Maryland, Baltimore County and the University of Malta have demonstrated a variational quantum algorithm for preparing Gibbs states, representing probabilities of different energy levels, on IonQ’s quantum computers. The team trained the algorithm using classical simulation before implementing it on the quantum hardware and evaluating the resulting state fidelity through state tomography. A theoretical proposal for this approach appeared in 2021, and an implementation on Quantinuum hardware was demonstrated in 2025. They found that fidelity decreases as a function of the inverse temperature β of the system, and also decreases as a function of the size of the system. Interestingly, a Gibbs state prepared for a specified β is a better representative of a Gibbs state prepared for a lower β, suggesting that thermal fluctuations in the quantum hardware lead to an increase in the temperature of the prepared Gibbs state above what was intended.
Variational Gibbs State Preparation with Trapped-Ion Devices
Quantum simulations are expanding beyond superconducting circuits, with trapped-ion devices now demonstrating the ability to prepare complex quantum states. This achievement broadens the toolkit for simulating complex systems, offering an alternative to superconducting qubits. The team employed a variational quantum algorithm originally developed by Consiglio et al., previously demonstrated on superconducting hardware. A key advantage of trapped-ion systems is their full connectivity, eliminating the need for complex “SWAP” operations, often a source of error in other architectures, to map the algorithm onto the hardware. This direct mapping allows for a more compact and efficient implementation. Instead, the team found that fidelity decreases as a function of the inverse temperature β of the system, revealing a relationship between thermal parameters and state preparation accuracy. Fidelity also decreases as a function of the size of the system, highlighting a current limitation in scaling up quantum state preparation.
The implications of these findings extend beyond fundamental quantum simulations. Gibbs states are essential for various applications, including quantum machine learning, quantum thermodynamics, and quantum chemistry. The researchers note that many quantum machine learning algorithms utilize Gibbs states as an initial state for Metropolis-Hastings sampling routines. This work, therefore, represents a step toward realizing these applications on increasingly powerful and versatile quantum platforms, even as challenges related to noise and scalability remain.
Recent advances in quantum computing increasingly focus on demonstrating practical applications beyond simple algorithmic proofs, and a new implementation of a variational quantum algorithm on IonQ hardware signifies progress toward that goal. The core of the experiment involved a hybrid quantum-classical approach, training variational parameters through classical simulation before implementing the resulting quantum circuit on IonQ’s devices. The team’s objective was to prepare Gibbs states, crucial for modeling complex systems in statistical physics and with applications ranging from quantum machine learning to quantum thermodynamics. This presents a significant challenge for practical quantum computation, as larger systems generally require higher fidelity to produce meaningful results. The researchers detail their method, employing a parameterized unitary UG(θ, φ) acting on two quantum registers, an ancilla and a system register, to initialize a probability distribution and transform it into the eigenbasis of the TFIM Hamiltonian. This work builds on previous theoretical proposals and an implementation on Quantinuum hardware demonstrated in 2025, demonstrating the potential of trapped-ion technology for tackling complex quantum simulations.
Consiglio et al. Algorithm for Quantum Gibbs State Preparation
Researchers are increasingly turning to real quantum hardware to test and refine algorithms previously confined to classical simulation, and a recent demonstration utilizing IonQ’s trapped-ion computers marks a step forward in Gibbs state preparation. This builds on earlier work; the team notes a theoretical proposal for trapped-ion implementation appeared in 2021, and an implementation on Quantinuum hardware was demonstrated in 2025. The researchers explain that running the algorithm on fully-connected trapped-ion machines avoids difficulties caused by topology and allows for a more compact representation of the algorithm. The algorithm itself leverages a hybrid quantum-classical approach, minimizing the Helmholtz free energy to arrive at the desired Gibbs state. The process involves preparing a probability distribution on an ancilla register and then transferring it to a system register via controlled-NOT gates, followed by a parameterized unitary transformation.
However, the experiments revealed a surprising nuance in the fidelity of the prepared states. The researchers state that a Gibbs state prepared for a specified β is a better representative of a Gibbs state prepared for a lower β, suggesting that thermal fluctuations in the quantum hardware lead to an increase in the temperature of the prepared Gibbs state above what was intended. This observation points to the need for further refinement of error mitigation techniques and a deeper understanding of how hardware imperfections impact the accuracy of quantum simulations.
Fidelity Reduction with Inverse Temperature and System Size
Successfully preparing quantum states is fundamental to realizing the potential of quantum computers, yet maintaining fidelity, a measure of how closely the created state matches the intended one, remains a significant hurdle, particularly as systems grow in complexity. Recent work utilizing IonQ’s trapped-ion technology demonstrates a nuanced relationship between fidelity, temperature, and system size during the preparation of Gibbs states, revealing challenges beyond simple expectations. Researchers at the University of Maryland, Baltimore County and the University of Malta have demonstrated that fidelity decreases as a function of the inverse temperature β of the system, and also decreases as a function of the size of the system.
Interestingly, a Gibbs state prepared for a specified β is a better representative of a Gibbs state prepared for a lower β, suggesting that thermal fluctuations in the quantum hardware lead to an increase in the temperature of the prepared Gibbs state above what was intended. This scaling issue is a persistent problem in quantum computation; larger systems are inherently more susceptible to errors, and this work quantifies that effect during state preparation. The researchers trained the variational parameters via classical simulation and performed state tomography on the quantum devices to evaluate the fidelity, allowing for a direct comparison between the intended and realized states. While the algorithm benefits from the full connectivity of IonQ’s trapped-ion architecture, avoiding the need for error-prone SWAP operations common in other platforms, it doesn’t fully overcome these fidelity limitations. The team notes that the work provides a foundation for future research into more robust and accurate quantum state preparation methods, essential for unlocking the full potential of quantum simulation and computation.
While quantum computers are often touted for their potential to revolutionize fields like cryptography and materials science, a more subtle but equally compelling application is emerging: accurately simulating the thermodynamics of complex systems. This isn’t simply about achieving a result; it’s about how that result changes with increasing system complexity. Researchers at the University of Maryland, Baltimore County and the University of Malta have demonstrated a variational quantum algorithm for Gibbs state preparation of a transverse-field Ising model on IonQ’s quantum computers. The choice of IonQ’s hardware was deliberate; trapped-ion systems offer full connectivity, eliminating the need for error-inducing SWAP operations required by other architectures like those from IBM. The ability to accurately prepare Gibbs states, even with current hardware limitations, represents a step towards harnessing the power of quantum computers to solve problems previously intractable for classical computers, and opens new avenues for exploring the fundamental laws governing complex systems.
Impact of Hardware Noise and Digital Heating on State Fidelity
Quantum state preparation, even with advanced trapped-ion technology, is demonstrably susceptible to subtle but significant distortions introduced by the hardware itself. The team implemented a variational quantum algorithm, training the parameters using classical simulation before assessing the resulting state fidelity on IonQ’s devices. This alteration manifests as an effective increase in temperature, a process the team aptly describes as digital heating. Researchers at the University of Maryland, Baltimore County and the University of Malta, including Reece Robertson, Mirko Consiglio, Josey Stevens, Emery Doucet, Tony J. G. Apollaro, and Sebastian Deffner, conducted this work. They found that fidelity decreases as a function of the inverse temperature β of the system, and also decreases as a function of the size of the system.
Interestingly, they find that a Gibbs state prepared for a specified β is a better representative of a Gibbs state prepared for a lower β, suggesting that thermal fluctuations in the quantum hardware lead to an increase in the temperature of the prepared Gibbs state above what was intended. This scaling limitation is critical; while quantum computers promise to model increasingly complex systems, the accuracy of those models is demonstrably reduced with each added qubit. The team’s work provides a crucial benchmark for evaluating the performance of near-term quantum devices and guiding the development of more accurate and reliable quantum algorithms.
