Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2505.12013

Variational quantum simulation of a nonadditive relaxation dynamics in a qubit coupled to a finite-temperature bath

Lucas Queiroz Galvão, Clebson Cruz, Antonio Cesar do Prado Rosa Junior, Marcelo Albano Moret

Published May 17, 2025• 0 citations
arXivHTMLPDF

Abstract

In this paper, we present an application of the variational quantum simulation (VQS) framework to capture finite-temperature open-system dynamics on near-term quantum hardware. By embedding the generalized amplitude-damping channel into the VQS algorithm, we modeled the energy exchange with a thermal bath through its Lindblad representation and thereby simulated realistic dissipative effects. To explore a wide range of activation behaviors, we introduce a nonadditive relaxation-time model using a generalized form of the Arrhenius law, based on the phenomenological parameter q. We compare our method on a driven qubit subject to both static and composite time-dependent fields, comparing population evolution and trace distance errors against exact solutions. Our results demonstrate that (i) VQS accurately maps the effective nonunitary generator under generalized amplitude damping, (ii) smoother drive envelopes induced by nonaddtive parameters suppress high frequency components and yield lower simulation errors, and (iii) the variational manifold exhibits dynamical selectivity, maintaining mapping fidelity even as the exact solution's sensitivity to q increases. Our results demonstrate that (i) VQS accurately maps the effective nonunitary generator under generalized amplitude damping, (ii) smoother drive envelopes induced by nonaddtive parameters suppress high frequency components and yield lower simulation errors, and (iii) the variational manifold exhibits dynamical selectivity, maintaining mapping fidelity even as the exact solution's sensitivity to q increases.

DOI
10.48550/arxiv.2505.12013

Related papers

Variational quantum simulation of thermal relaxation in open qubit systems with nonadditive dissipation

Lucas Queiroz Galvão, A. C. P. Rosa, Marcelo Albano Moret +1 more

In this paper, we present an application of the variational quantum simulation (VQS) framework to capture finite temperature open system dynamics on near-term quantum hardware. By embedding the generalized amplitude damping channel into the VQS algorithm, we model energy exchange with a thermal bath through its Lindblad representation and thereby simulate realistic dissipative effects. To explore a wide range of activation behaviors, we introduce a nonadditive relaxation time model using a generalized form of the Arrhenius law, based on the phenomenological parameter q. We compare our method on driven qubit systems subject to both static and composite time-dependent fields, comparing population evolution and trace distance errors against reference numerical solutions. Our results demonstrate that (1) VQS accurately maps the effective nonunitary generator under GAD, (2) smoother drive envelopes induced by nonaddtive parameters suppress high-frequency components and yield lower simulation errors, and (3) the variational manifold exhibits dynamical selectivity, maintaining mapping fidelity even as the reference numerical solution's sensitivity to q increases.

Physical review. E•Nov 20, 2025•0 citations

Variational Quantum Simulation of Lindblad Dynamics via Quantum State Diffusion

Jianming Luo, Kaihan Lin, Xing Bao Gao

Quantum simulation of dynamics in open quantum systems is crucial but poses a significant challenge due to the non-Hermitian nature leading to nonunitary evolution and the limited quantum resources on current quantum computers. Here we introduce a variational hybrid quantum-classical algorithm designed for simulating the time evolution governed by the Lindblad master equation. Our approach involves on a stochastic unveiling of the density matrix, transforming the Lindblad equation into a wave function-based quantum state diffusion (QSD) method with the aim of reducing qubit requirements. We then apply variational quantum simulation (VQS) to efficiently capture the nonunitary evolution in QSD. We demonstrate our QSD-VQS algorithm by investigating the quantum dynamics in a two-level system subjected to an amplitude damping channel and a four-level transverse field Ising model within a dissipative environment including time-independent and periodic Hamiltonian cases. The results reveal its promising utility with upcoming hardware in the near future.

The Journal of Physical Chemistry Letters•Mar 22, 2024•21 citations

Energy relaxation via quantum thermalization: A superconducting qubit coupled to an interacting many-body two-level system

Xue-Yi Guo

Two-level systems (TLS) are widely recognized as a dominant source of energy relaxation in superconducting qubits, limiting coherence times and device performance. While TLS-induced dissipation is often modeled as independent channels, interacting TLS can form finite many-body environments whose dynamical role in qubit relaxation remains insufficiently understood. Building on the information-erasure-based framework for irreversible thermalization developed in our previous work, we present a microscopic model and numerical simulations of a superconducting qubit coupled to a finite interacting many-body TLS environment as a concrete physical realization of this mechanism. We show that effective irreversible energy relaxation can emerge from intrinsic many-body dynamics without invoking external baths or phenomenological dissipation. The introduction of information erasure drives a transition from coherent oscillatory energy exchange to nonoscillatory exponential relaxation of the qubit. The relaxation times exhibit the scaling $T_1, T_2 \propto J_{q,τ}^{-2}$ with respect to the qubit-TLS coupling strength, consistent with Fermi's golden rule and Lindblad-type descriptions. Importantly, both exponential decay and its scaling behavior arise directly from microscopic many-body dynamics. These results provide quantitative insight into TLS-induced decoherence mechanisms and establish a microscopic link between information erasure, many-body thermalization, and irreversible relaxation in superconducting quantum systems.

quant-pharXiv:2603.13322•APS Open Science•Mar 5, 2026•0 citations

Variational quantum simulation of dynamical quantum phase transition in Markovian open quantum systems

Yukai Guo, Jinjian Yu, Xing Bao Gao

We investigate dynamical quantum phase transitions (DQPTs) in Markovian open quantum systems using a variational quantum simulation (VQS) algorithm based on quantum state diffusion (QSD). This approach reformulates the Lindblad master equation as an ensemble of pure-state trajectories, enabling efficient simulation of dissipative quantum dynamics with effectively reduced quantum resources. Focusing on the one-dimensional transverse-field Ising model (TFIM), we simulate quench dynamics under both local and global Lindblad dissipation. The QSD-VQS algorithm accurately captures the nonanalytic cusps in the Loschmidt rate function, and reveals their modulation by dissipation strength and system size. Notably, DQPTs are gradually suppressed under strong local dissipation, while they persist under strong global dissipation due to collective environmental effects. Benchmarking against exact Lindblad solutions confirms the high accuracy and scalability of our method.

Chinese Journal of Chemical Physics•Aug 1, 2025•0 citations

A Davydov Ansatz approach to accurate system–bath dynamics in the presence of multiple baths with distinct temperatures

Chi Ma, Fulu Zheng, Kewei Sun +2 more

We perform benchmark simulations using the time-dependent variational approach with the multiple Davydov Ansatz (mDA) to study real-time nonequilibrium dynamics in a single qubit model coupled to two thermal baths with distinct temperatures. A broad region of the parameter space has been investigated, accompanied by a detailed analysis of the convergence behavior of the mDA method. In addition, we have compared our mD2 results to those from two widely adopted, numerically "exact" techniques: the methods of hierarchical equations of motion (HEOM) and the quasi-adiabatic path integral (QUAPI). It is found that the mDA approach in combination with thermal field dynamics yields numerically accurate, convergent results in nearly all regions of the parameter space examined, including those that pose serious challenges for QUAPI and HEOM. Our results reveal that mDA offers a highly adaptable framework capable of capturing long-time dynamics, even in challenging regimes where other methods face limitations. These findings underscore the potential of mDA as a versatile tool for exploring quantum thermodynamics, energy transfer processes, and non-equilibrium quantum systems.

arXiv:2510.09029•The Journal of Chemical Physics•Sep 28, 2025•1 citation

Characterization of a damping channel as a mixture of amplitude damping and anti-damping channels of different parameters

Vijay Pathak, R. Srikanth

Non-unital noise is a fundamental feature of open quantum systems, governing energy exchange and inducing state translations on the Bloch sphere. While such translations can be useful for tasks such as state preparation and channel capacity, unital dynamics where no translation occurs are often preferred in quantum information processing, particularly for error correction. Phase-covariant dynamics provide a general framework encompassing dissipation, excitation, and dephasing processes in qubit systems; however, commonly used models such as the generalized amplitude damping (GAD) channel offer only limited control over these features. In this work, we present a constructive framework for generating a broader class of phase-covariant dynamics by mixing amplitude-damping and anti-damping channels with unequal decay parameters and time-dependent mixing probabilities. This approach enables independent control over contraction and translation, allows continuous tuning between non-unital and unital regimes, and yields an effective dephasing contribution absent in GAD. To characterize these dynamics, we employ the general theorem for P-divisibility and show that it can be used constructively by evaluating it in suitably chosen Hilbert space bases, leading to simplified conditions for both unital and non-unital cases. The framework captures a wide range of behaviors, including CP-divisible, P-divisible but not CP-divisible, and non-P-divisible dynamics. We further show that appropriate mixing can reduce the deviation from the ideal noiseless evolution and that such improvement persists even after tuning the dynamics to the unital regime. Our results provide a flexible approach to engineering open system dynamics beyond standard thermal models, with potential applications in noise control and quantum information processing.

quant-pharXiv:2608.20178•Aug 21, 2026•0 citations
In this paper, we present an application of the variational quantum simulation (VQS) framework to capture finite-temperature open-system dynamics on near-term quantum hardware. By embedding the generalized amplitude-damping channel into the VQS algorithm, we modeled the energy exchange with a thermal bath through its Lindblad representation and thereby simulated realistic dissipative effects. To explore a wide range of activation behaviors, we introduce a nonadditive relaxation-time model using a generalized form of the Arrhenius law, based on the phenomenological parameter q. We compare our method on a driven qubit subject to both static and composite time-dependent fields, comparing population evolution and trace distance errors against exact solutions. Our results demonstrate that (i) VQS accurately maps the effective nonunitary generator under generalized amplitude damping, (ii) smoother drive envelopes induced by nonaddtive parameters suppress high frequency components and yield lower simulation errors, and (iii) the variational manifold exhibits dynamical selectivity, maintaining mapping fidelity even as the exact solution's sensitivity to q increases. Our results demonstrate that (i) VQS accurately maps the effective nonunitary generator under generalized amplitude damping, (ii) smoother drive envelopes induced by nonaddtive parameters suppress high frequency components and yield lower simulation errors, and (iii) the variational manifold exhibits dynamical selectivity, maintaining mapping fidelity even as the exact solution's sensitivity to q increases.
In this paper, we present an application of the variational quantum simulation (VQS) framework to capture finite temperature open system dynamics on near-term quantum hardware. By embedding the generalized amplitude damping channel into the VQS algorithm, we model energy exchange with a thermal bath through its Lindblad representation and thereby simulate realistic dissipative effects. To explore a wide range of activation behaviors, we introduce a nonadditive relaxation time model using a generalized form of the Arrhenius law, based on the phenomenological parameter q. We compare our method on driven qubit systems subject to both static and composite time-dependent fields, comparing population evolution and trace distance errors against reference numerical solutions. Our results demonstrate that (1) VQS accurately maps the effective nonunitary generator under GAD, (2) smoother drive envelopes induced by nonaddtive parameters suppress high-frequency components and yield lower simulation errors, and (3) the variational manifold exhibits dynamical selectivity, maintaining mapping fidelity even as the reference numerical solution's sensitivity to q increases.
Quantum simulation of dynamics in open quantum systems is crucial but poses a significant challenge due to the non-Hermitian nature leading to nonunitary evolution and the limited quantum resources on current quantum computers. Here we introduce a variational hybrid quantum-classical algorithm designed for simulating the time evolution governed by the Lindblad master equation. Our approach involves on a stochastic unveiling of the density matrix, transforming the Lindblad equation into a wave function-based quantum state diffusion (QSD) method with the aim of reducing qubit requirements. We then apply variational quantum simulation (VQS) to efficiently capture the nonunitary evolution in QSD. We demonstrate our QSD-VQS algorithm by investigating the quantum dynamics in a two-level system subjected to an amplitude damping channel and a four-level transverse field Ising model within a dissipative environment including time-independent and periodic Hamiltonian cases. The results reveal its promising utility with upcoming hardware in the near future.
Two-level systems (TLS) are widely recognized as a dominant source of energy relaxation in superconducting qubits, limiting coherence times and device performance. While TLS-induced dissipation is often modeled as independent channels, interacting TLS can form finite many-body environments whose dynamical role in qubit relaxation remains insufficiently understood. Building on the information-erasure-based framework for irreversible thermalization developed in our previous work, we present a microscopic model and numerical simulations of a superconducting qubit coupled to a finite interacting many-body TLS environment as a concrete physical realization of this mechanism. We show that effective irreversible energy relaxation can emerge from intrinsic many-body dynamics without invoking external baths or phenomenological dissipation. The introduction of information erasure drives a transition from coherent oscillatory energy exchange to nonoscillatory exponential relaxation of the qubit. The relaxation times exhibit the scaling T1,T2∝Jq,τ−2T_1, T_2 \propto J_{q,τ}^{-2}T1​,T2​∝Jq,τ−2​ with respect to the qubit-TLS coupling strength, consistent with Fermi's golden rule and Lindblad-type descriptions. Importantly, both exponential decay and its scaling behavior arise directly from microscopic many-body dynamics. These results provide quantitative insight into TLS-induced decoherence mechanisms and establish a microscopic link between information erasure, many-body thermalization, and irreversible relaxation in superconducting quantum systems.
We investigate dynamical quantum phase transitions (DQPTs) in Markovian open quantum systems using a variational quantum simulation (VQS) algorithm based on quantum state diffusion (QSD). This approach reformulates the Lindblad master equation as an ensemble of pure-state trajectories, enabling efficient simulation of dissipative quantum dynamics with effectively reduced quantum resources. Focusing on the one-dimensional transverse-field Ising model (TFIM), we simulate quench dynamics under both local and global Lindblad dissipation. The QSD-VQS algorithm accurately captures the nonanalytic cusps in the Loschmidt rate function, and reveals their modulation by dissipation strength and system size. Notably, DQPTs are gradually suppressed under strong local dissipation, while they persist under strong global dissipation due to collective environmental effects. Benchmarking against exact Lindblad solutions confirms the high accuracy and scalability of our method.
We perform benchmark simulations using the time-dependent variational approach with the multiple Davydov Ansatz (mDA) to study real-time nonequilibrium dynamics in a single qubit model coupled to two thermal baths with distinct temperatures. A broad region of the parameter space has been investigated, accompanied by a detailed analysis of the convergence behavior of the mDA method. In addition, we have compared our mD2 results to those from two widely adopted, numerically "exact" techniques: the methods of hierarchical equations of motion (HEOM) and the quasi-adiabatic path integral (QUAPI). It is found that the mDA approach in combination with thermal field dynamics yields numerically accurate, convergent results in nearly all regions of the parameter space examined, including those that pose serious challenges for QUAPI and HEOM. Our results reveal that mDA offers a highly adaptable framework capable of capturing long-time dynamics, even in challenging regimes where other methods face limitations. These findings underscore the potential of mDA as a versatile tool for exploring quantum thermodynamics, energy transfer processes, and non-equilibrium quantum systems.
Non-unital noise is a fundamental feature of open quantum systems, governing energy exchange and inducing state translations on the Bloch sphere. While such translations can be useful for tasks such as state preparation and channel capacity, unital dynamics where no translation occurs are often preferred in quantum information processing, particularly for error correction. Phase-covariant dynamics provide a general framework encompassing dissipation, excitation, and dephasing processes in qubit systems; however, commonly used models such as the generalized amplitude damping (GAD) channel offer only limited control over these features. In this work, we present a constructive framework for generating a broader class of phase-covariant dynamics by mixing amplitude-damping and anti-damping channels with unequal decay parameters and time-dependent mixing probabilities. This approach enables independent control over contraction and translation, allows continuous tuning between non-unital and unital regimes, and yields an effective dephasing contribution absent in GAD. To characterize these dynamics, we employ the general theorem for P-divisibility and show that it can be used constructively by evaluating it in suitably chosen Hilbert space bases, leading to simplified conditions for both unital and non-unital cases. The framework captures a wide range of behaviors, including CP-divisible, P-divisible but not CP-divisible, and non-P-divisible dynamics. We further show that appropriate mixing can reduce the deviation from the ideal noiseless evolution and that such improvement persists even after tuning the dynamics to the unital regime. Our results provide a flexible approach to engineering open system dynamics beyond standard thermal models, with potential applications in noise control and quantum information processing.