Variational Gibbs State Preparation on Trapped-Ion Devices

; or in other words, thermal fluctuations in the quantum hardware lead to digital heating, that is, an increase in the temperature of the prepared Gibbs state above what was intended.

DOI: 10.13016/m2gxel-jqf0

Related papers

Reece Robertson, Mirko Consiglio, Josey Stevens +3 more

We implement a variational quantum algorithm for Gibbs state preparation of a transverse-field Ising model on IonQ's quantum computers. To this end, we train the variational parameters via classical simulation and perform state tomography on the quantum devices to evaluate the fidelity of the prepared Gibbs state. As a main result, we find that fidelity decreases (non-monotonically) as a function of the inverse temperature $β$ of the system. Fidelity also decreases as a function of the size of the system. Interestingly, we find that a Gibbs state prepared for a specified $β$ is a better representative of a Gibbs state prepared for a $\textit{lower}$ $β$ ; or in other words, thermal fluctuations in the quantum hardware lead to digital heating, that is, an increase in the temperature of the prepared Gibbs state above what was intended.We implement a variational quantum algorithm for Gibbs state preparation of a transverse-field Ising model on IonQ's quantum computers. To this end, we train the variational parameters via classical simulation and perform state tomography on the quantum devices to evaluate the fidelity of the prepared Gibbs state. As a main result, we find that fidelity decreases (non-monotonically) as a function of the inverse temperature $β$ of the system. Fidelity also decreases as a function of the size of the system. Interestingly, we find that a Gibbs state prepared for a specified $β$ is a better representative of a Gibbs state prepared for a $\textit{lower}$ $β$; or in other words, thermal fluctuations in the quantum hardware lead to digital heating, that is, an increase in the temperature of the prepared Gibbs state above what was intended.

quant-pharXiv:2603.03801Mar 5, 20260 citations

Variational Gibbs state preparation on trapped-ion devices

Reece Robertson, Mirko Consiglio, Josey Stevens +3 more

We implement a variational quantum algorithm for Gibbs state preparation of a transverse-field Ising model on IonQ’s quantum computers. To this end, we train the variational parameters via classical simulation and perform state tomography on the quantum devices to evaluate the fidelity of the prepared Gibbs state. As a main result, we find that fidelity decreases (non-monotonically) as a function of the inverse temperature β of the system. Fidelity also decreases as a function of the size of the system. Interestingly, we find that a Gibbs state prepared for a specified β is a better representative of a Gibbs state prepared for a lower β ; or in other words, thermal fluctuations in the quantum hardware lead to digital heating, that is, an increase in the temperature of the prepared Gibbs state above what was intended.We implement a variational quantum algorithm for Gibbs state preparation of a transverse-field Ising model on IonQ’s quantum computers. To this end, we train the variational parameters via classical simulation and perform state tomography on the quantum devices to evaluate the fidelity of the prepared Gibbs state. As a main result, we find that fidelity decreases (non-monotonically) as a function of the inverse temperature β of the system. Fidelity also decreases as a function of the size of the system. Interestingly, we find that a Gibbs state prepared for a specified β is a better representative of a Gibbs state prepared for a lower β ; or in other words, thermal fluctuations in the quantum hardware lead to digital heating, that is, an increase in the temperature of the prepared Gibbs state above what was intended.

npj Quantum InformationJul 11, 20260 citations

Variational Gibbs state preparation on noisy intermediate-scale quantum devices

Mirko Consiglio, Jacopo Settino, Andrea Giordano +6 more

The preparation of an equilibrium thermal state of a quantum many-body system on noisy intermediate-scale quantum (NISQ) devices is an important task in order to extend the range of applications of quantum computation. Faithful Gibbs state preparation would pave the way to investigate protocols such as thermalization and out-of-equilibrium thermodynamics and provide useful resources for quantum algorithms, where sampling from Gibbs states constitutes a key subroutine. We propose a variational quantum algorithm (VQA) to prepare Gibbs states of a quantum many-body system. The novelty of our VQA consists of implementing a parameterized quantum circuit acting on two distinct, yet connected (via cnot gates), quantum registers. The VQA evaluates the Helmholtz free energy, where the von Neumann entropy is obtained via postprocessing of computational-basis measurements on one register, while the Gibbs state is prepared on the other register via a unitary rotation in the energy basis. Finally, we benchmark our VQA by preparing Gibbs states of the transverse-field Ising and Heisenberg XXZ models and achieve remarkably high fidelities across a broad range of temperatures in state-vector simulations. We also assess the performance of the VQA on IBM quantum computers, showcasing its feasibility on current NISQ devices.The preparation of an equilibrium thermal state of a quantum many-body system on noisy intermediate-scale quantum (NISQ) devices is an important task in order to extend the range of applications of quantum computation. Faithful Gibbs state preparation would pave the way to investigate protocols such as thermalization and out-of-equilibrium thermodynamics and provide useful resources for quantum algorithms, where sampling from Gibbs states constitutes a key subroutine. We propose a variational quantum algorithm (VQA) to prepare Gibbs states of a quantum many-body system. The novelty of our VQA consists of implementing a parameterized quantum circuit acting on two distinct, yet connected (via cnot gates), quantum registers. The VQA evaluates the Helmholtz free energy, where the von Neumann entropy is obtained via postprocessing of computational-basis measurements on one register, while the Gibbs state is prepared on the other register via a unitary rotation in the energy basis. Finally, we benchmark our VQA by preparing Gibbs states of the transverse-field Ising and Heisenberg XXZ models and achieve remarkably high fidelities across a broad range of temperatures in state-vector simulations. We also assess the performance of the VQA on IBM quantum computers, showcasing its feasibility on current NISQ devices.

arXiv:2303.11276Physical Review AJul 18, 202431 citations

Paper 13 - Cross-Device and Cross-Temperature Noise Structure in Variational Gibbs-State Preparation: A Full-Tomography Held-Out Reanalysis

Roshankumar chandaliya

Overview This study investigates how quantum noise affects variational Gibbs-state preparation on trapped-ion quantum computers. What Was Analyzed The analysis uses full two-qubit tomography instead of relying only on a single quantity such as fidelity or effective temperature. It compares complete quantum states across different field settings, three trapped-ion devices, and two temperature regimes. Noise Models Compared Several noise descriptions are tested, including scalar depolarization, Pauli-channel models, coherent-error corrections, and generalized amplitude damping (GAD). Predictive Testing The models are trained on selected conditions and then tested on unseen conditions without refitting. This allows the analysis to measure whether a noise model remains useful outside the data used to fit it. Main Result A shared GAD-based model shows the most stable predictive behaviour across the tested devices and temperatures. In the strongest frozen cross-temperature test, parameters fitted at beta = 5 are applied directly at beta = 1 without refitting. The model: improves all 9 of 9 QPU cases reduces mean Hilbert-Schmidt distance from 0.08644669 to 0.07277861 gives a 15.81% reduction in mean error Interpretation The results support a shared damping-like noise-model family within the tested system. However, the fitted parameters are not universal, and the study does not claim a unique microscopic noise mechanism, universal hardware-noise parameters, retrocausality, or a universal physical law. Reproducibility The calculations are also implemented in QDL Research Suite v1.9.0, allowing the main numerical results to be reproduced and independently checked. Software DOI: 10.5281/zenodo.23181558Overview This study investigates how quantum noise affects variational Gibbs-state preparation on trapped-ion quantum computers. What Was Analyzed The analysis uses full two-qubit tomography instead of relying only on a single quantity such as fidelity or effective temperature. It compares complete quantum states across different field settings, three trapped-ion devices, and two temperature regimes. Noise Models Compared Several noise descriptions are tested, including scalar depolarization, Pauli-channel models, coherent-error corrections, and generalized amplitude damping (GAD). Predictive Testing The models are trained on selected conditions and then tested on unseen conditions without refitting. This allows the analysis to measure whether a noise model remains useful outside the data used to fit it. Main Result A shared GAD-based model shows the most stable predictive behaviour across the tested devices and temperatures. In the strongest frozen cross-temperature test, parameters fitted at beta = 5 are applied directly at beta = 1 without refitting. The model: improves all 9 of 9 QPU cases reduces mean Hilbert-Schmidt distance from 0.08644669 to 0.07277861 gives a 15.81% reduction in mean error Interpretation The results support a shared damping-like noise-model family within the tested system. However, the fitted parameters are not universal, and the study does not claim a unique microscopic noise mechanism, universal hardware-noise parameters, retrocausality, or a universal physical law. Reproducibility The calculations are also implemented in QDL Research Suite v1.9.0, allowing the main numerical results to be reproduced and independently checked. Software DOI: 10.5281/zenodo.23181558

Oct 6, 20260 citations

Variational Quantum Gibbs State Preparation with a Truncated Taylor Series

Youle Wang, Guangxi Li, Xin Wang

The preparation of a quantum Gibbs state is an essential part of quantum computation and has wide-ranging applications in various areas, including quantum simulation, quantum optimization, and quantum machine learning. In this paper, we propose variational hybrid quantum-classical algorithms for quantum Gibbs state preparation. We first utilize a truncated Taylor series to evaluate the free energy and choose the truncated free energy as the loss function. Our protocol then trains the parameterized quantum circuits to learn the desired quantum Gibbs state. Notably, this algorithm can be implemented on near-term quantum computers equipped with parameterized quantum circuits. By performing numerical experiments, we show that shallow parameterized circuits with only one additional qubit can be trained to prepare the Ising chain and spin chain Gibbs states with a fidelity higher than 95%. In particular, for the Ising chain model, we find that a simplified circuit ansatz with only one parameter and one additional qubit can be trained to realize a 99% fidelity in Gibbs state preparation at inverse temperatures larger than $2$ .The preparation of a quantum Gibbs state is an essential part of quantum computation and has wide-ranging applications in various areas, including quantum simulation, quantum optimization, and quantum machine learning. In this paper, we propose variational hybrid quantum-classical algorithms for quantum Gibbs state preparation. We first utilize a truncated Taylor series to evaluate the free energy and choose the truncated free energy as the loss function. Our protocol then trains the parameterized quantum circuits to learn the desired quantum Gibbs state. Notably, this algorithm can be implemented on near-term quantum computers equipped with parameterized quantum circuits. By performing numerical experiments, we show that shallow parameterized circuits with only one additional qubit can be trained to prepare the Ising chain and spin chain Gibbs states with a fidelity higher than 95%. In particular, for the Ising chain model, we find that a simplified circuit ansatz with only one parameter and one additional qubit can be trained to realize a 99% fidelity in Gibbs state preparation at inverse temperatures larger than $2$.

arXiv:2005.08797Physical Review AppliedNov 18, 202180 citations

Adaptive variational algorithms for quantum Gibbs state preparation

Ada Warren, Zhu, Linghua, Nicholas J. Mayhall +2 more

The preparation of Gibbs thermal states is an important task in quantum computation with applications in quantum simulation, quantum optimization, and quantum machine learning. However, many algorithms for preparing Gibbs states rely on quantum subroutines which are difficult to implement on near-term hardware. Here, we address this by (i) introducing an objective function that, unlike the free energy, is easily measured, and (ii) using dynamically generated, problem-tailored ansätze. This allows for arbitrarily accurate Gibbs state preparation using low-depth circuits. To verify the effectiveness of our approach, we numerically demonstrate that our algorithm can prepare high-fidelity Gibbs states across a broad range of temperatures and for a variety of Hamiltonians.The preparation of Gibbs thermal states is an important task in quantum computation with applications in quantum simulation, quantum optimization, and quantum machine learning. However, many algorithms for preparing Gibbs states rely on quantum subroutines which are difficult to implement on near-term hardware. Here, we address this by (i) introducing an objective function that, unlike the free energy, is easily measured, and (ii) using dynamically generated, problem-tailored ansätze. This allows for arbitrarily accurate Gibbs state preparation using low-depth circuits. To verify the effectiveness of our approach, we numerically demonstrate that our algorithm can prepare high-fidelity Gibbs states across a broad range of temperatures and for a variety of Hamiltonians.

arXiv:2203.12757Mar 23, 202212 citations

?

of the system. Fidelity also decreases as a function of the size of the system. Interestingly, we find that a Gibbs state prepared for a specified

?

is a better representative of a Gibbs state prepared for a

\textit{lower}

?

; or in other words, thermal fluctuations in the quantum hardware lead to digital heating, that is, an increase in the temperature of the prepared Gibbs state above what was intended.

β

of the system. Fidelity also decreases as a function of the size of the system. Interestingly, we find that a Gibbs state prepared for a specified

β

is a better representative of a Gibbs state prepared for a

\textit{lower}

β

; or in other words, thermal fluctuations in the quantum hardware lead to digital heating, that is, an increase in the temperature of the prepared Gibbs state above what was intended.

2