Fractional Chern insulators arise in topologically nontrivial flat bands, characterized by an integer Chern number C that corresponds to the number of dissipationless edge states in the noninteracting regime. Higher Chern numbers can replicate the physics of higher Landau levels and often confer enhanced topological robustness. However, realizing correlated fractional phases with higher Chern numbers in such flat band systems remains challenging. Here, we propose an interlayer coupling scheme to generate higher Chern numbers in a flat-band system, where the interlayer coupling transforms two C = 1 bands in a bilayer checkerboard lattice into a single flat band with C = 2 by lifting their degeneracy and merging their topological indices. Exact diagonalization calculations reveal that this engineered band hosts two fractional Chern insulator states with many-body Chern numbers C = 2/3 and 2/5 at fillings of nu = 1/3 and 1/5, respectively. An experimental setup is proposed to simulate these states using cold alkaline-earth-like atoms in an effective bilayer optical lattice. Our work provides a general and widely applicable strategy for constructing higher Chern number flat bands, opening a pathway to explore exotic fractional quantum phases.

A nanodiamond with an embedded nitrogen-vacancy (NV) center is one of the experimental systems that can be coherently manipulated within current technologies. Entanglement between NV center electron spin and mechanical rotation of the nanodiamond plays a fundamental role in building a quantum network connecting these microscopic and mesoscopic degrees of motions. Here we present a protocol to asymptotically prepare a highly entangled state of the total quantum angular momentum and electron spin by adiabatically boosting the external magnetic field.

Quantum distillation is a modern technology to decrease the von Neumann entropy of a subsystem by coherent system dynamics. Here we propose an active quantum distillation protocol, in which a bang-bang theme is applied to actively control the coherent dynamics of our system in order to obtain a subsystem with the von Neumann entropy as low as possible. For a bipartite Bosonic system, we derive the analytical expression of lower bound of the entropy of subsystem under any unitary transformation with conservation of particles. The lower bound is validated by numerical simulations on the Bose-Hubbard model, where the coherent evolution is controlled by tuning one interaction term of the Hamiltonian. Our protocol can be used to decrease the entropy of one subsystem lower than the total bipartite state and increase the number of Bosons or only distill out very few Bosons in the subsystem.

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.

As quantum technology rapidly advances, the need for efficient scalable methods to characterize quantum systems intensifies. Quantum state tomography and Hamiltonian learning are essential for interpreting and optimizing quantum systems, yet a unified approach remains elusive. Such an integration could enhance our understanding of the complex relationship between quantum states and Hamiltonians, contributing to the development of more efficient methodologies. In this paper, we present a method that integrates quantum state tomography and Hamiltonian learning, drawing inspiration from machine translation in the field of natural language processing (NLP). We demonstrate the effectiveness of our approach across a variety of quantum systems, successfully learning the complex relationships between quantum states and Hamiltonians. Furthermore, the scalability and few-shot learning capabilities of our method could potentially minimize the resources required for characterizing and optimizing quantum systems. Our research provides valuable insights into the relationship between quantum states and Hamiltonians, paving the way for further studies on quantum systems and advancing quantum computation and related technologies.

Hamiltonian Learning is a process of recovering system Hamiltonian from measurements, which is a fundamental problem in quantum information processing. In this study, we investigate the problem of learning the symmetric Hamiltonian from its eigenstate. Inspired by the application of group theory in block diagonal secular determination, we have derived a method to determine the number of linearly independent equations about the Hamiltonian unknowns obtained from an eigenstate. This number corresponds to the degeneracy of the associated irreducible representation of the Hamiltonian symmetry group. To illustrate our approach, we examine the XXX Hamiltonian and the XXZ Hamiltonian. We first determine the Hamiltonian symmetry group, then work out the decomposition of irreducible representation, which serves as foundation for analyzing the uniqueness of recovered Hamiltonian. Our numerical findings consistently align with our theoretical analysis.

Hamiltonian Learning (HL) is essential for validating quantum systems in quantum computing. Not all Hamiltonians can be uniquely recovered from a steady state. HL success depends on the Hamiltonian model and the steady state. Here, we analyze HL for a specific type of steady state composed of eigenstates with degenerate mixing weight, making these Hamiltonian's eigenstates indistinguishable. To overcome this challenge, we utilize the orthogonality relationship between the eigenstate space and its complement space, constructing the orthogonal space equation. By counting the number of linearly independent equations derived from a steady state, we determine the recoverability of a generic local Hamiltonian. Our scheme is applicable for generic local Hamiltonians under various steady state, therefore offering a way of measuring the degree to which a steady state characterizes a Hamiltonian.

Motivated by the recent experimental developments in ultracold molecules and atoms, we propose a simple theoretical model to address the disassociation, reflection, and transmission probability of a one-dimensional cold molecule via quantum scattering. First, we show the Born approximation results in the weak interaction regime. Then, by employing the Lippmann–Schwinger equation, we give the numerical solution and investigate the disassociation’s dependence on the injection momentum and the interaction strengths. We find that the maximum disassociation rate has a limit when increasing the interaction strengths and injection momentum.We expect that our model can be realized in experiments in the near future.

Quantum information distribution in a tripartite state plays a fundamental role in quantum information processes. Here we investigate how a bipartite unitary transformation $U_{AB}$ redistributes the quantum mutual information with the third party $C$ in a tripartite pure state $|\psi\rangle_{ABC}$ in a $d_A\times d_B\times d_C$ dimensional Hilbert space. In particular, we focus on finding out the optimal unitary transformation $U_{AB}^{\ast}$ that maximizes the quantum mutual entropy between party $A$ and party $C$, $I(A:C)=S(\rho_A)-S(\rho_B)+S(\rho_C)$. We show that the mutual entropy $I(A:C)$ is upper bounded by $2S(\rho_C)$ derived from the Araki-Lieb inequality. This upper bound can be realized via an optimal unitary transformation for any pure state with the rank $r_{C}$ of $\rho_C$ satisfying $r_C\le d_A$. For a generic pure state with $r_C> d_A$, the upper bound can not be realized by any bipartite unitary transformation. To maximize the mutual entropy in the latter case, we propose a fast numerical algorithm to produce an approximate optimal unitary transformation, where our optimization is transformed into a modified number partition problem. The validness of our algorithm is confirmed by its comparison with the results from the Adam algorithm for parameterized unitary transformations. Our approximate algorithm thus provides a practical protocol to implement redistribution of quantum mutual information for a tripartite quantum state with high dimensions.

An anyonic system not only has potential applications in the construction of topological quantum computers but also presents a unique property known as topological entanglement entropy (TEE) in quantum many-body systems. Recently, Bonderson et al. [Ann. Phys. (NY) 385, 399 (2017)] have formally defined the entropy of anyonic charge entanglement (ACE) in anyonic states that has been shown to be able to derive TEE. We give it operational meaning from the perspective of quantum information theory. Specifically, for an anyonic bipartite system, we define an operational measure of topological correlation based on the principle of maximum entropy, where the topological correlation is the information that cannot be accessed by local operations constrained by anyonic superselection rules (SSRs) and classical communication. For a given anyonic bipartite state with maximal rank, we prove that its topological correlation is equal to its entropy of ACE. This measure can be extended to measure nonlocal resources of other compound quantum systems in the presence of SSRs and can provide a more refined classification of correlations in a multipartite system with SSRs.

Schr\"odinger's equation serves as a fundamental component in characterizing quantum systems, wherein both quantum state tomography and Hamiltonian learning are instrumental in comprehending and interpreting quantum systems. While numerous techniques exist for carrying out state tomography and learning Hamiltonians individually, no method has been developed to combine these two aspects. In this study, we introduce a new approach that employs the attention mechanism in transformer models to effectively merge quantum state tomography and Hamiltonian learning. By carefully choosing and preparing the training data, our method integrates both tasks without altering the model's architecture, allowing the model to effectively learn the intricate relationships between quantum states and Hamiltonian. We also demonstrate the effectiveness of our approach across various quantum systems, ranging from simple 2-qubit cases to more involved 2D antiferromagnetic Heisenberg structures. The data collection process is streamlined, as it only necessitates a one-way generation process beginning with state tomography. Furthermore, the scalability and few-shot learning capabilities of our method could potentially minimize the resources required for characterizing and optimizing quantum systems. Our research provides valuable insights into the relationship between Hamiltonian structure and quantum system behavior, fostering opportunities for additional studies on quantum systems and the advancement of quantum computation and associated technologies.

Anyonic system not only has potential applications in the construction of topological quantum computer, but also presents a unique property known as topological entanglement entropy in quantum many-body systems. How to understand topological entanglement entropy is one of the most concerned problems for physicists. For an anyonic bipartite system, we define an operational measure of topological correlation based on the principle of maximal entropy, where the topological correlation is the information that cannot be accessed by local operations constrained by anyonic superselection rules and classical communication. This measure can be extended to measure non-local resources of other compound quantum systems in the presence of superselection rules. For a given anyonic bipartite state with maximal rank, we prove that its topological correlation is equal to its entropy of anyonic charge entanglement that has been shown in the literature to be able to derive topological entanglement entropy. This measure provides a more refined classification of correlations in a multipartite system with superselection rules and an illuminating approach to topological phase classification.

Anyons have been extensively investigated as information carriers in topological quantum computation. However, how to characterize the information flow in quantum networks composed of anyons is less understood, which motivates us to study quantum communication protocols in anyonic systems. Here we propose a general topologically protected protocol for quantum teleportation based on the Ising anyon model and prove that with our protocol an unknown anyonic state of any number of Ising anyons can be teleported from Alice to Bob. Our protocol naturally generalizes quantum state teleportation from systems of locally distinguishable particles to systems of Ising anyons, which may promote our understandings of anyonic quantum entanglement as a quantum resource. In addition, our protocol is expected to be realized with the Majorana zero modes, one of the possible physical realizations for the Ising anyon in experiments.

The quantum imaginary time evolution is a powerful algorithm for preparing the ground and thermal states on near-term quantum devices. However, algorithmic errors induced by Trotterization and local approximation severely hinder its performance. Here we propose a deep reinforcement learning-based method to steer the evolution and mitigate these errors. In our scheme, the well-trained agent can find the subtle evolution path where most algorithmic errors cancel out, enhancing the fidelity significantly. We verified the method’s validity with the transverse-field Ising model and the Sherrington-Kirkpatrick model. Numerical calculations and experiments on a nuclear magnetic resonance quantum computer illustrate the efficacy. The philosophy of our method, eliminating errors with errors, sheds light on error reduction on near-term quantum devices.

Coherence distillation is a basic information-theoretic task in the resource theory of coherence. In this paper, we present the necessary and sufficient conditions under which a mixed state can be distilled into a pure coherent state via stochastic incoherent operations (sIOs). With the help of this result, we further show the following: (i) Any two-dimensional coherent state is distillable via sIOs if and only if it is a pure coherent state; (ii) a state rho is n-distillable via sIOs if and only if it is 1-distillable; and (iii) the set of distillable states via stochastic maximally incoherent operations is identical to the set of distillable states via sIOs. Finally, we analyze the reason why sIO is stronger than stochastic strictly incoherent operations when we use them to distill a coherent state.

Group theory is extremely successful in characterizing the symmetries in quantum systems, which greatly simplifies and unifies our treatments of quantum systems. Here we introduce the concept of the symmetry for a quantum Boltzmann machine and develop a group theory to describe the symmetry. This symmetry implies not only that all the target states related with the symmetry transformations are equivalent, but also that for a given target state all the optimal solutions related with the symmetry transformations that keep the target state invariant are equivalent. For the Boltzmann machines built on qubits, we propose a systematic procedure to construct the group, and develop a numerical algorithm to verify the completeness of our construction. (C) 2021 Elsevier B.V. All rights reserved.

Anyonic states, which are topologically robust because of their peculiar structure of Hilbert space, have important applications in quantum computing and quantum communication. Here we investigate the capacity of the deterministic quantum one-time pad (DQOTP) that uses Fibonacci anyons as an information carrier. We find that the Fibonacci particle-antiparticle pair produced from vacuum can be used to asymptotically send 2 log(2) d(tau) bits of classical information (d(tau) is the quantum dimension of a Fibonacci anyon tau), which equals anyonic mutual information of the pair. Furthermore, by studying the DQOTP via a parameterized state of six Fibonacci anyons with trivial total charge, we give the analytical results of the maximum number of messages that can be sent for different parameters, which is a step function with every step corresponding to a regular simplex from the viewpoint of geometry. The results for the maximum number of messages sent by the DQOTP can be explained by anyonic accessible information.

Zheng An, 2 Chenfeng Cao, and D. L. Zhou 2, 4, 5, ∗ Institute of Physics, Beijing National Laboratory for Condensed Matter Physics, Chinese Academy of Sciences, Beijing 100190, China School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China Collaborative Innovation Center of Quantum Matter, Beijing 100190, China Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China (Dated: July 9, 2021)

With the development of quantum many-body simulator, Hamiltonian tomography has become an increasingly important technique for verification of quantum devices. Here we investigate recovering the Hamiltonians of two spin chains with 2-local interactions and 3-local interactions by measuring local observables. For these two models, we show that when the chain length reaches a certain critical number, we can recover the local Hamiltonian from its one steady state by solving the homogeneous operator equation (HOE) developed in Ref. [1]. To explain the existence of such a critical chain length, we develop an alternative method to recover Hamiltonian by solving the energy eigenvalue equations (EEE). By using the EEE method, we completely recovered the numerical results from the HOE method. Then we theoretically prove the equivalence between the HOE method and the EEE method. In particular, we obtain the analytical expression of the rank of the constraint matrix in the HOE method by using the EEE method, which can be used to determine the correct critical chain length in all the cases.

Manipulation and control of the complex quantum system with high precision are essential for achieving universal fault-tolerant quantum computing. For a physical system with restricted control resources, it is a challenge to control the dynamics of the target system efficiently and precisely under disturbances. Here we propose a multilevel dissipative quantum control framework and show that deep reinforcement learning provides an efficient way to identify the optimal strategies with restricted control parameters of the complex quantum system. This framework can be generalized to be applied to other quantum control models. Compared with the traditional optimal control method, this deep reinforcement learning algorithm can realize efficient and precise control for multilevel quantum systems with different types of disturbances.