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

Roshankumar chandaliya

Published Oct 6, 2026• 0 citations
Publisher

Abstract

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.23181558

DOI
10.5281/zenodo.23183457

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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 βββ 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 βββ is a better representative of a Gibbs state prepared for a lower\textit{lower}lower βββ; 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 ??? 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 lower\textit{lower}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.
Abstract To progress in the characterization of noise for quantum computers, gate set tomography (GST) has emerged as a self-consistent protocol that accurately estimates noisy gates, state preparations, and measurements. In its original incarnation, GST improves estimation precision by applying gates sequentially, assuming the noise yields fixed completely-positive and trace-preserving (CPTP) maps independent of prior gate history. This ‘Markovian’ assumption can conflict with experiments, where time-correlated noise may induce non-Markovian dynamics, or slow drifts and cumulative calibration errors introduce context dependence, causing CP-divisible maps to vary with circuit depth. In this work, we address this issue for trapped-ion devices with phonon-mediated two-qubit gates. Using detailed microscopic modeling of high-fidelity light-shift gates, we tailor GST to capture the main source of context dependence: motional degrees of freedom. Rather than invalidating GST, context dependence can be incorporated into the gate-set parametrization, reducing sampling cost. Our results identify a promising research avenue that might be applicable to other platforms where microscopic modeling can be incorporated: the development of a context-aware GST.
We consider the problem of preparing thermal equilibrium states at finite temperature on quantum computers. Assuming thermalization, we show that states that are locally at thermal equilibrium can be prepared by evolving adiabatically an initial thermal Gibbs state of a simple Hamiltonian with an interpolating time-dependent Hamiltonian, identically to adiabatic ground state preparation. We argue that the entropy density of local density matrices is conserved during the adiabatic evolution in the thermodynamic limit, so that both the entropy and energy of the final state can be computed, and thus the final temperature too. We show that in the presence of hardware noise, the entropy created by the noisy evolution can be precisely benchmarked with mirror circuits. We give numerical evidence that the resulting thermal state preparation protocol is noise-resilient for depolarizing noise, in the sense that the energy-temperature curve measured on a noisy quantum computer is remarkably insensitive to the amplitude of depolarizing noise in the state preparation. We finally propose a protocol to estimate the lack of adiabaticity in a given actual Trotter implementation of the dynamics. We test our protocol on Quantinuum’s H1-1 ion-trap device. We measure that a circuit with 640 two-qubit gates implemented on hardware generates an entropy per site of 0.166 ± 0.0045, giving a benchmark metric for this state preparation. We report the preparation of a thermal state with temperature 2.56 ± 0.26 of the Ising model in size 5 × 4.
Fault-tolerant quantum error correction provides a strategy to protect information processed by a quantum computer against noise which would otherwise corrupt the data. A fault-tolerant universal quantum computer must implement a universal gate set on the logical level in order to perform arbitrary calculations to in principle unlimited precision. In this paper we characterize the recent demonstration of a fault-tolerant universal gate set in a trapped-ion quantum computer [Postler et al., Nature (London) 605, 7911 (2022)] and identify aspects to improve the design of experimental setups to reach an advantage of logical over physical qubit operation. We show that various criteria to assess the break-even point for fault-tolerant quantum operations are within reach for the ion trap quantum computing architecture under consideration. Furthermore, we analyze the influence of crosstalk in entangling gates for logical state preparation circuits. These circuits can be designed to respect fault tolerance for specific microscopic noise models. We find that an experimentally informed depolarizing noise model captures the essential noise dynamics of the fault-tolerant experiment that we consider, and crosstalk is negligible in the currently accessible regime of physical error rates. For deterministic Pauli state preparation, we provide a fault-tolerant unitary logical qubit initialization circuit, which can be realized without in-sequence measurement and feed-forward of classical information. Additionally, we show that nondeterministic state preparation schemes, i.e., repeat until success, for logical Pauli and magic states perform with higher logical fidelity over their deterministic counterparts for the current and anticipated future regime of physical error rates. Our results offer guidance on improvements of physical qubit operations and validate the experimentally informed noise model as a tool to predict logical failure rates in quantum computing architectures based on trapped ions.