Transverse-field Model Research Articles

Toward Transparent and Controllable Quantum Generative Models.

Quantum generative models have shown promise in fields such as quantum chemistry, materials science, and optimization. However, their practical utility is hindered by a significant challenge: the lack of interpretability. In this work, we introduce model inversion to enhance both the interpretability and controllability of quantum generative models. Model inversion allows for tracing generated quantum states back to their latent variables, revealing the relationship between input parameters and generated outputs. We apply this method to models generating ground states for Hamiltonians, such as the transverse-field Ising model (TFIM) and generalized cluster Hamiltonians, achieving interpretability control without retraining the model. Experimental results demonstrate that our approach can accurately guide the generated quantum states across different quantum phases. This framework bridges the gap between theoretical models and practical applications by providing transparency and fine-tuning capabilities, particularly in high-stakes environments like drug discovery and material design.

Role of coherence in many-body Quantum Reservoir Computing

Quantum Reservoir Computing (QRC) offers potential advantages over classical reservoir computing, including inherent processing of quantum inputs and a vast Hilbert space for state exploration. Yet, the relation between the performance of reservoirs based on complex and many-body quantum systems and non-classical state features is not established. Through an extensive analysis of QRC based on a transverse-field Ising model we show how different quantum effects, such as quantum coherence and correlations, contribute to improving the performance in temporal tasks, as measured by the Information Processing Capacity. Additionally, we critically assess the impact of finite measurement resources and noise on the reservoir’s dynamics in different regimes, quantifying the limited ability to exploit quantum effects for increasing damping and noise strengths. Our results reveal a monotonic relationship between reservoir performance and coherence, along with the importance of quantum effects in the ergodic regime.

Impact of quantum information encoding and metallic leads on dynamical multipartite correlation formation in semiconductor quantum dot arrays.

This study investigates quantum information scrambling (QIS) in a semiconductor quantum dot array. Starting with the 1D Transverse Field Ising model, we expand to more relevant quasi-2D frameworks such as the Heisenberg chain, super-extended Fermi-Hubbard and hardcore Fermi-Hubbard models. Assessing their relevance to semiconductor spin-qubit quantum computers, simulations of multipartite entanglement formation examine qubit encoding strategies' fidelity, stability, and robustness, revealing trade-offs among these aspects. Furthermore, we investigate the weakly coupled metallic injector/detector (I/D) leads' significant impact on QIS behavior by employing Ω lead N-single orbital impurities weakly coupled Anderson models. We observe sign flips in spatiotemporal tripartite mutual information I3 which result in significant effects on dynamical quantum entanglement structures and their formation. Exploring carrier number effects, we identify optimal regions for QIS enhancement. Our findings emphasize the necessity of proper qubit encoding and I/D lead influence on quantum devices amidst noise and impurities.

Classification of dynamical Lie algebras of 2-local spin systems on linear, circular and fully connected topologies

Much is understood about 1-dimensional spin chains in terms of entanglement properties, physical phases, and integrability. However, the Lie algebraic properties of the Hamiltonians describing these systems remain largely unexplored. In this work, we provide a classification of all Lie algebras generated by the terms of 2-local spin chain Hamiltonians, or so-called dynamical Lie algebras, on 1-dimensional linear and circular lattice structures. We find 17 unique dynamical Lie algebras. Our classification includes some well-known models such as the transverse-field Ising model and the Heisenberg chain, and we also find more exotic classes of Hamiltonians that appear new. In addition to the closed and open spin chains, we consider systems with a fully connected topology, which may be relevant for quantum machine learning approaches. We discuss the practical implications of our work in the context of variational quantum computing, quantum control and the spin chain literature.

Confinement in the Transverse Field Ising Model on the Heavy Hex Lattice.

Inspired by a recent quantum computing experiment [Y. Kim etal., Nature (London), 618, 500-5 (2023)NATUAS0028-083610.1038/s41586-023-06096-3], we study the emergence of confinement in the transverse field Ising model on a decorated hexagonal lattice. Using an infinite tensor network state optimized with belief propagation we show how a quench from a broken symmetry state leads to striking nonthermal behavior underpinned by persistent oscillations and saturation of the entanglement entropy. We explain this phenomenon by constructing a minimal model based on the confinement of elementary excitations. Our model is in excellent agreement with our numerical results. For quenches to larger values of the transverse field and/or from nonsymmetry broken states, our numerical results display the expected signatures of thermalization: a linear growth of entanglement entropy in time, propagation of correlations, and the saturation of observables to their thermal averages. These results provide a physical explanation for the unexpected classical simulability of the quantum dynamics.

Quantum-coherence-assisted dynamical phase transition in the one-dimensional transverse-field Ising model

Quantum coherence will undoubtedly play a fundamental role in understanding the dynamics of quantum many-body systems; therefore, to be able to reveal its genuine contribution is of great importance. In this paper, we focus our discussions on the one-dimensional transverse field quantum Ising model initialized in the coherent Gibbs state, and investigate the effects of quantum coherence on dynamical quantum phase transition (DQPT). After quenching the strength of the transverse field, the effects of quantum coherence are studied using Fisher zeros and the rate function of the Loschmidt echo. We find that quantum coherence not only recovers DQPT destroyed by thermal fluctuations, but also generates some entirely new DQPTs, which are independent of the equilibrium quantum critical point. We also find that the Fisher zero cutting the imaginary axis is not sufficient to generate DQPT because it also requires the Fisher zeros to be tightly bound close enough to the neighborhood of the imaginary axis. It can be manifested that DQPTs are rooted in quantum fluctuations. This work reveals new information on the fundamental connection between quantum critical phenomena and quantum coherence.

Hybrid quantum-classical algorithm for the transverse-field Ising model in the thermodynamic limit

Hybrid quantum-classical algorithm for the transverse-field Ising model in the thermodynamic limit

Analytical derivation and extension of the anti-Kibble-Zurek scaling in the transverse field Ising model

Analytical derivation and extension of the anti-Kibble-Zurek scaling in the transverse field Ising model

Dynamical phase transitions, caustics, and quantum dark bands

Abstract We provide a new perspective on quantum dynamical phase transitions (DPTs) by explaining their origin in terms of caustics that form in the Fock space representation of the many-body state over time, using the fully connected transverse field Ising model as an example. In this way we establish a connection between DPTs in a quantum spin system and an everyday natural phenomenon: The dark band between the primary and secondary bows (caustics) in rainbows known as Alexander’s dark band. The DPT occurs when the Loschmidt echo crosses the switching line between the evanescent tails of two back-to-back Airy functions that dress neighbouring fold caustics in Fock space and is the time-dependent analogue of what is seen as a function of angle in the sky. The structural stability and universal properties of caustics, as described mathematically by catastrophe theory, explains the generic occurrence of DPTs in the model and suggests that our analysis has wide applicability. Based on our thorough analytical understanding we propose a protocol which can be used to verify the existence of a DPT in a finite system experiment.

Order-by-disorder in the antiferromagnetic J1−J2−J3 transverse-field Ising model on the ruby lattice

We investigate the quantum phase diagram of the J1−J2−J3 antiferromagnetic transverse-field Ising model on the ruby lattice. In the low-field limit we derive an effective quantum dimer model, analyzing how the extensive ground-state degeneracy at zero field is lifted by an order-by-disorder scenario. We support our analysis by studying the gap closing of the high-field phase using series expansions. For J2>J3, we find a columnar phase at low fields, followed by a clock-ordered phase stabilized by resonating plaquettes at intermediate field values, and an emergent three-dimensional (3D)-XY quantum phase transition to the polarized high-field phase. For J3>J2, an order-by-disorder mechanism stabilizes a distinct k=(0,0) order and a quantum phase transition in the 3D-Ising universality class is observed. Further, we discuss the possible implementation of the columnar- and clock-ordered phase in existing Rydberg atom quantum simulators. When taking into account the full algebraically decaying long-range interactions on the ruby lattice, we find that long-range interactions favor the same ground state as the quantum fluctuations induced by a transverse field, which could make the ruby lattice a promising candidate for the realization of a clock-ordered phase. Published by the American Physical Society 2024

Quantum neural network approach to Markovian dissipative dynamics of many-body open quantum systems.

Numerous variational methods have been proposed for solving quantum many-body systems, but they often face exponentially increasing computational complexity as the Hilbert space dimension grows. To address this, we introduce a novel approach using quantum neural networks to simulate the dissipative dynamics of many-body open quantum systems. This method combines neural-network quantum state representation with the time-dependent variational principle, both implemented via quantum algorithms. This results in accurate open quantum dynamics described by the Lindblad quantum master equation, exemplified by the spin-boson and transverse field Ising models. Our approach avoids the computational expense of classical algorithms and demonstrates the potential advantages of quantum computing for many-body simulations. To reduce measurement errors, we introduce a projection reset procedure, which could benefit other quantum simulations. In addition, our approach can be extended to simulate non-Markovian quantum dynamics.

Quantum-critical properties of the one- and two-dimensional random transverse-field Ising model from large-scale quantum Monte Carlo simulations

We study the ferromagnetic transverse-field Ising model with quenched disorder at T = 0T=0 in one and two dimensions by means of stochastic series expansion quantum Monte Carlo simulations using a rigorous zero-temperature scheme. Using a sample-replication method and averaged Binder ratios, we determine the critical shift and width exponents \nu_\mathrm{s}νs and \nu_\mathrm{w}νw as well as unbiased critical points by finite-size scaling. Further, scaling of the disorder-averaged magnetisation at the critical point is used to determine the order-parameter critical exponent \betaβ and the critical exponent \nu_{\mathrm{av}}νav of the average correlation length. The dynamic scaling in the Griffiths phase is investigated by measuring the local susceptibility in the disordered phase and the dynamic exponent z'z′ is extracted. By applying various finite-size scaling protocols, we provide an extensive and comprehensive comparison between the different approaches on equal footing. The emphasis on effective zero-temperature simulations resolves several inconsistencies in existing literature.

Robust Estimation of the Quantum Fisher Information on a Quantum Processor

We present the experimental measurement, on a quantum processor, of a series of polynomial lower bounds that to the quantum Fisher information (QFI), a fundamental quantity for certifying multipartite entanglement that is useful for metrological applications. We combine advanced methods of the randomized measurement toolbox to obtain estimators that are robust regarding drifting errors caused uniquely during the randomized measurement protocol. We estimate the QFI for Greenberger-Horne-Zeilinger states, observing genuine multipartite entanglement. Then we prepare the ground state of the transverse-field Ising model at the critical point using a variational circuit. We estimate its QFI and investigate the interplay between state optimization and noise induced by our increasing the circuit depth. Published by the American Physical Society 2024

Quantum Architecture Search with Neural Predictor Based on Graph Measures

AbstractQuantum architecture search (QAS) has attracted increasing attention owing to its remarkable ability to automate the design of quantum circuits for variational quantum algorithms (VQAs). However, evaluating the performance of numerous quantum circuits is essential to provide feedback for the search strategy, which inevitably renders QAS computationally expensive. Performance predictors have emerged as highly efficient evaluation methods to mitigate this challenge. However, the performance predictor faces a critical challenge in reducing the required number of circuit‐performance pairs for training. This study encodes circuit architecture by representing a quantum circuit as a relational graph that emphasizes message exchange. Subsequently, valuable information about circuit architecture is extracted through three types of graph measures, including distance‐based, degree‐based, and cluster‐based measures. The graph measures define a smooth space related to circuit performance, facilitating the training of the performance predictor. The effectiveness of the proposed method is assessed across three tasks within variational quantum eigensolvers (VQE): identifying the ground states of the Transverse Field Ising Model (TFIM), the Heisenberg model, and the molecule. The simulation results demonstrate notable enhancements in predictive accuracy achieved by our method, coupled with a substantial reduction in the required number of training samples for the predictor.

Quantum criticality in the infinite-range transverse field Ising model

Quantum criticality in the infinite-range transverse field Ising model

Deep neural networks as variational solutions for correlated open quantum systems

In this work we apply deep neural networks to find the non-equilibrium steady state solution to correlated open quantum many-body systems. Motivated by the ongoing search to find more powerful representations of (mixed) quantum states, we design a simple prototypical convolutional neural network and show that parametrizing the density matrix directly with more powerful models can yield better variational ansatz functions and improve upon results reached by neural density operator based on the restricted Boltzmann machine. Hereby we give up the explicit restriction to positive semi-definite density matrices. However, this is fulfilled again to good approximation by optimizing the parameters. The great advantage of this approach is that it opens up the possibility of exploring more complex network architectures that can be tailored to specific physical properties. We show how translation invariance can be enforced effortlessly and reach better results with fewer parameters. We present results for the dissipative one-dimensional transverse-field Ising model and a two-dimensional dissipative Heisenberg model compared to exact values.

Learning quantum phases via single-qubit disentanglement

Identifying phases of matter presents considerable challenges, particularly within the domain of quantum theory, where the complexity of ground states appears to increase exponentially with system size. Quantum many-body systems exhibit an array of complex entanglement structures spanning distinct phases. Although extensive research has explored the relationship between quantum phase transitions and quantum entanglement, establishing a direct, pragmatic connection between them remains a critical challenge. In this work, we present a novel and efficient quantum phase transition classifier, utilizing disentanglement with reinforcement learning-optimized variational quantum circuits. We demonstrate the effectiveness of this method on quantum phase transitions in the transverse field Ising model (TFIM) and the XXZ model. Moreover, we observe the algorithm's ability to learn the Kramers-Wannier duality pertaining to entanglement structures in the TFIM. Our approach not only identifies phase transitions based on the performance of the disentangling circuits but also exhibits impressive scalability, facilitating its application in larger and more complex quantum systems. This study sheds light on the characterization of quantum phases through the entanglement structures inherent in quantum many-body systems.

Global optimization in variational quantum algorithms via dynamic tunneling method

We present a global optimization routine for the variational quantum algorithms, which utilizes the dynamic tunneling flow. Originally designed to leverage information gathered by a gradient-based optimizer around local minima, we adapt the conventional dynamic tunneling flow to exploit the distance measure of quantum states, resolving issues of extrinsic degeneracy arising from the parametrization of quantum states. Our global optimization algorithm is applied to the variational quantum eigensolver for the transverse-field Ising model to demonstrate the performance of our routine while comparing it with the conventional dynamic tunneling method, which is based on the Euclidean distance measure on the parameter space.

Exact counterdiabatic driving in finite topological lattice models

Adiabatic protocols are often employed in state preparation schemes but require the system to be driven by a slowly varying Hamiltonian so that transitions between instantaneous eigenstates are exponentially suppressed. Counterdiabatic driving is a technique to speed up adiabatic protocols by including additional terms calculated from the instantaneous eigenstates that counter diabatic excitations. However, this approach requires knowledge of the full eigenspectrum meaning that the exact analytical form of counterdiabatic driving is only known for a subset of problems, e.g., the harmonic oscillator and transverse field Ising model. We extend this subset of problems to include the general family of one-dimensional noninteracting lattice models with open boundary conditions and arbitrary onsite potential, tunneling terms, and lattice size. We will derive a general analytical form for the counterdiabatic term for all states of lattice models, including bound and in-gap states which appear, e.g., in topological insulators. We also derive the general analytical form of targeted counterdiabatic driving terms which are tailored to enforce the dynamical state to remain in a specific state. As an example of the use of the derived analytical forms, we consider state transfer using the topological edge states of the Su-Schrieffer-Heeger model. The derived analytical counterdiabatic driving Hamiltonian can be utilized to inform control protocols in many-body lattice models or to probe the nonequilibrium properties of lattice models. Published by the American Physical Society 2024

Lieb-Robinson correlation function for the quantum transverse-field Ising model

The Lieb-Robinson correlation function is the norm of a commutator between local operators acting on separate subsystems at different times. This provides a useful state-independent measure for characterizing the specifically quantum interaction between spatially separated qubits. The finite propagation velocity for this correlator defines a “light cone” of quantum influence. We calculate the Lieb-Robinson correlation function for one-dimensional qubit arrays described by the transverse-field Ising model. Direct calculations of this correlation function have been limited by the exponential increase in the size of the state space with the number of qubits. We introduce a technique that avoids this barrier by transforming the calculation to a sum over Pauli walks which results in linear scaling with system size. We can then explore propagation in arrays of hundreds of qubits and observe the effects of the quantum phase transition in the system. We observe the emergence of two distinct velocities of propagation: a correlation front velocity, which is affected by the phase transition, and the Lieb-Robinson velocity which is not. The correlation front velocity is equal to the maximum group velocity of single quasiparticle excitations. The Lieb-Robinson velocity describes the extreme leading edge of correlations when the value of the correlation function itself is still very small. For the semi-infinite chain of qubits at the quantum critical point, we derive an analytical result for the correlation function. Published by the American Physical Society 2024