Predicting the quantum dynamics of promising solid-state and molecular quantum technology candidates remains a formidable challenge. Yet, accessing these dynamics is key to understanding and controlling decoherence mechanisms-a prerequisite for designing better qubits, sensors, and memories. We leverage a matrix product state representation to introduce a numerically exact and scalable method to achieve this goal. We demonstrate that our method accurately predicts coherence and population dynamics of spin networks across a wide range of parameter regimes, encompassing nuclear spin sensors and qubits in solid-state semiconductors and molecular magnets. Our method further predicts spin dynamics under the influence of repeated light pulses, which are commonly used to mitigate decoherence and perform quantum sensing experiments. Our method thus provides reliable results for moderately sized spin platforms spanning molecular magnets and solid-state spins that can guide the development of approximate but efficient quantum dynamics methods and enable principled inquiry into decoherence mechanisms.
Predicting the quantum dynamics of promising solid-state and molecular quantum technology candidates remains a formidable challenge. Yet, accessing these dynamics is key to understanding and controlling decoherence mechanisms-a prerequisite for designing better qubits, sensors, and memories. We leverage a matrix product state representation to introduce a numerically exact and scalable method to achieve this goal. We demonstrate that our method accurately predicts coherence and population dynamics of spin networks across a wide range of parameter regimes, encompassing nuclear spin sensors and qubits in solid-state semiconductors and molecular magnets. Our method further predicts spin dynamics under the influence of repeated light pulses, which are commonly used to mitigate decoherence and perform quantum sensing experiments. Our method thus provides reliable results for moderately sized spin platforms spanning molecular magnets and solid-state spins that can guide the development of approximate but efficient quantum dynamics methods and enable principled inquiry into decoherence mechanisms.
The usefulness of solid-state spins in quantum technologies depends on how long they can remain in a coherent superposition of quantum states. This Colloquium discusses how first-principles simulations can predict spin dynamics for different types of solid-state electron spins, helping design novel and improved platforms for quantum computing, networking, and sensing. We begin by outlining the necessary concepts of the noise affecting generic quantum systems. We then focus on recent advances in predicting spin-phonon relaxation of the spin-defect qubits. Next, we discuss cluster methods as a means of simulating quantum decoherence induced by spin-spin interactions, emphasizing the critical role of validation in ensuring the accuracy of these simulations. We highlight how validated cluster methods can be instrumental in interpreting recent experimental results and, more importantly, predicting the coherence properties of novel spin-based quantum platforms, guiding the development of next-generation quantum technologies.
This paper explores the application of tensor network methods for simulating molecular dynamics on quantum computers. Traditional molecular dynamics simulations are computationally expensive, particularly for complex systems exhibiting strong quantum correlations. Tensor networks provide a powerful framework for representing and manipulating high-dimensional quantum states, potentially offering a pathway to efficiently simulate molecular dynamics by directly leveraging quantum computational resources. This work details the theoretical framework, outlining how tensor network techniques, specifically Matrix Product States (MPS) and Tree Tensor Networks (TTN), can be adapted for this purpose. We present a simplified model of a diatomic molecule to illustrate the core concept: the construction of a tensor network representation of the molecular wavefunction, followed by the application of time evolution operators to simulate dynamics. The focus is on demonstrating the potential of this approach rather than a fully optimized simulation, highlighting key challenges and future research directions. The efficiency gains compared to classical methods are discussed, acknowledging the significant technological hurdles involved in realizing this approach on near-term quantum devices. We investigate the scalability of the method, considering the limitations imposed by the bond dimension of the tensor network. The ultimate goal is to demonstrate how tensor networks can provide a viable strategy for tackling computationally intractable molecular dynamics problems, paving the way for a new era of quantum-enhanced molecular simulations.
Molecular spins are promising candidates for quantum information science, leveraging coherent electronic spin states for quantum sensing and computation. However, the practical application of these systems is hindered by electronic spin decoherence, driven by interactions with nuclear spins in the molecule and the surrounding environment at low temperatures. Predicting dephasing dynamics remains a formidable challenge due to the complexity of the spin bath. In this work, we develop a non-Markovian time-convolutionless master equation to treat an electronic spin coupled to a nuclear-spin bath. By relating ab initio electronic structure parameters directly to the decoherence dynamics, we provide a framework that accounts for pure dephasing in the low-temperature limit. We apply this method to a series of molecular qubit candidates and demonstrate good agreement with experimental relaxation trends. This approach offers a computationally efficient path for the prediction of low-temperature decoherence trends in molecular spin systems.
In this thesis I present contributions to the development, analysis and application of tensor network state methods for numerically exact quantum dynamics in one and two-dimensional lattice systems. The setting of numerically exact quantum dynamics is introduced in Chapter 2. This includes a discussion of exact diagonalization approaches and massively parallel implementations thereof as well as a brief introduction of tensor network states. In Chapter 3, I perform a detailed analysis of the performance of n-ary tree tensor network states for simulating the dynamics of two-dimensional lattices. This constitutes the first application of this class of tensor network to dynamics in two spatial dimensions, a long-standing challenge, and the method is found to perform on par with existing state-of-the-art approaches. Chapter 4 showcases the efficacy of a novel tensor network format I developed, tailored to electron-phonon coupled problems in their single-electron sector, through an application to the Holstein model. The applicability of the approach to a broad range of parameters of the model allows to reveal the strong influence of the spread of the electron distribution on the initial state of the phonons at the site where the electron is introduced, for which a simple physical picture is offered. I depart from method development in Chapter 5 and analyse the prospects of using tensor network states evolved using the time-dependent variational principle as an approximate approach to determine asymptotic transport properties with a finite, moderate computational effort. The method is shown to not yield the correct asymptotics in a clean, non-integrable system and can thus not be expected to work in generic systems, outside of finely tuned parameter regimes of certain models. Chapters 6 and 7 are concerned with studies of spin transport in long-range interacting systems using tensor network state methods. For the clean case, discussed in Chapter 6, we find that for sufficiently short-ranged interactions, the spreading of the bulk of the excitation is diffusive and thus dominated by the local part of the interaction, while the tail of the excitation decays with a powerlaw that is twice as large as the powerlaw of the interaction. Similarly, in the disordered case, analysed in Chapter 7, we find subdiffusive transport of spin and sub-linear growth of entanglement entropy. This behaviour is in agreement with the behaviour of systems with local interactions at intermediate disorder strength, but provides evidence against the phenomelogical Griffith picture of rare, strongly disordered insulating regions. We generalize the latter to long-ranged interactions and show that it predicts to diffusion, in contrast to the local case where it results in subdiffusive behaviour.
Predicting the properties of correlated materials and molecules often requires a many-body description that goes beyond single-particle and mean-field approximations. Tensor networks address this challenge by exploiting the entanglement structure of quantum states to construct compact, systematically improvable representations. Although developed largely for idealized model Hamiltonians, these methods are increasingly being integrated into material-specific calculations. This Perspective introduces their underlying principles and examines how network geometry, bond-dimension truncation, and approximate contraction determine the accuracy and computational reach of these approaches. We survey applications across regimes of increasing complexity, ranging from ground-state properties of quantum magnets and itinerant-fermion systems to excitation spectra, nonequilibrium dynamics, finite-temperature and open systems, and molecular electronic structure. We then examine four routes connecting these methods to real materials, including experimentally constrained models, downfolded Hamiltonians, dynamical mean-field theory with tensor network impurity solvers, and quantum embedding. Throughout, we evaluate the maturity of existing capabilities and their principal limitations, synthesizing this assessment into a practical method-selection guide. We argue that reliable materials predictions require quantifying uncertainties introduced at each stage, from constructing material-specific Hamiltonians to extracting experimentally accessible observables. Finally, we identify the algorithmic advances and reproducible computational practices needed to establish tensor networks as a routine tool for predictive materials science and quantum chemistry.
The control of open quantum systems has a fundamental relevance for fields ranging from quantum information processing to nanotechnology. Typically, the system whose coherent dynamics one wants to manipulate, interacts with an environment that smoothly degrades its quantum dynamics. Thus, a precise understanding of the inner mechanisms of this process, called "decoherence", is critical to develop strategies to control the quantum dynamics. In this thesis we solved the generalized Liouville-von Neumann quantum master equation to obtain the dynamics of many-spin systems interacting with a spin bath. We also solve the spin dynamics within the Keldysh formalism. Both methods lead to identical solutions and together gave us the possibility to obtain numerous physical predictions that contrast well with Nuclear Magnetic Resonance experiments. We applied these tools for molecular characterizations, development of new numerical methodologies and the control of quantum dynamics in experimental implementations. But, more important, these results contributed to fundamental physical interpretations of how quantum dynamics behaves in open systems. In particular, we found a manifestation of an environmentally induced quantum dynamical phase transition.