Entanglement Hamiltonian of Many-Body Dynamics in Strongly Correlated Systems

Construction of Antisymmetric Variational Quantum States with Real Space Representation

Electronic state calculations using quantum computers are mostly based on the second quantized formulation, which is suitable for qubit representation. Another way to describe electronic states on a quantum computer is based on the first quantized formulation, which is expected to achieve smaller scaling with respect to the number of basis functions than the second quantized formulation. Among basis functions, a real space basis is an attractive option for quantum dynamics simulations in the fault-tolerant quantum computation (FTQC) era. A major difficulty in the first quantized algorithm with a real space basis is state preparation for many-body electronic systems. This difficulty stems from the antisymmetry of electrons, and it is not straightforward to construct antisymmetric quantum states on a quantum circuit. In this study, we provide a design principle for constructing variational quantum circuits to prepare an antisymmetric quantum state. The proposed circuit generates the superposition of exponentially many Slater determinants, that is, multiconfiguration state, which provides a systematic approach to approximating the exact ground state. We performed the variational quantum eigensolver (VQE) to obtain the ground state of a one-dimensional hydrogen molecular system. As a result, the proposed circuit well reproduced the exact antisymmetric ground state and its energy, whereas the conventional variational circuit yielded neither the antisymmetric nor the symmetric state. Furthermore, we analyzed the many-body wave functions based on the quantum information theory, which illustrated the relation between the electron correlation and the quantum entanglement.

Persistent Ballistic Entanglement Spreading with Optimal Control in Quantum Spin Chains

Entanglement propagation provides a key routine to understand quantum many-body dynamics in and out of equilibrium. Entanglement entropy (EE) usually approaches to a subsaturation known as the Page value S[over ˜]_{P}=S[over ˜]-dS (with S[over ˜] the maximum of EE and dS the Page correction) in, e.g., the random unitary evolutions. The ballistic spreading of EE usually appears in the early time and will be deviated far before the Page value is reached. In this work, we uncover that the magnetic field that maximizes the EE robustly induces persistent ballistic spreading of entanglement in quantum spin chains. The linear growth of EE is demonstrated to persist until the maximal S[over ˜] (along with a flat entanglement spectrum) is reached. The robustness of ballistic spreading and the enhancement of EE under such an optimal control are demonstrated, considering particularly perturbing the initial state by random pure states (RPSs). These are argued as the results from the endomorphism of the time evolution under such an entanglement-enhancing optimal control for the RPSs.

Exploring large-scale entanglement in quantum simulation

Entanglement is a distinguishing feature of quantum many-body systems, and uncovering the entanglement structure for large particle numbers in quantum simulation experiments is a fundamental challenge in quantum information science1. Here we perform experimental investigations of entanglement on the basis of the entanglement Hamiltonian (EH)2 as an effective description of the reduced density operator for large subsystems. We prepare ground and excited states of a one-dimensional XXZ Heisenberg chain on a 51-ion programmable quantum simulator3 and perform sample-efficient 'learning' of the EH for subsystems of up to 20 lattice sites4. Our experiments provide compelling evidence for a local structure of the EH. To our knowledge, this observation marks the first instance of confirming the fundamental predictions of quantum field theory by Bisognano and Wichmann5,6, adapted to lattice models that represent correlated quantum matter. The reduced state takes the form of a Gibbs ensemble, with a spatially varying temperature profile as a signature of entanglement2. Our results also show the transition from area- to volume-law scaling7 of von Neumann entanglement entropies from ground to excited states. As we venture towards achieving quantum advantage, we anticipate that our findings and methods have wide-ranging applicability to revealing and understanding entanglement in many-body problems with local interactions including higher spatial dimensions.

Unlocking the general relationship between energy and entanglement spectra via the wormhole effect

Based on the path integral formulation of the reduced density matrix, we develop a scheme to overcome the exponential growth of computational complexity in reliably extracting low-lying entanglement spectrum from quantum Monte Carlo simulations. We test the method on the Heisenberg spin ladder with long entangled boundary between two chains and the results support the Li and Haldane's conjecture on entanglement spectrum of topological phase. We then explain the conjecture via the wormhole effect in the path integral and show that it can be further generalized for systems beyond gapped topological phases. Our further simulation results on the bilayer antiferromagnetic Heisenberg model with 2D entangled boundary across the (2 + 1)D O(3) quantum phase transition clearly demonstrate the correctness of the wormhole picture. Finally, we state that since the wormhole effect amplifies the bulk energy gap by a factor of β, the relative strength of that with respect to the edge energy gap will determine the behavior of low-lying entanglement spectrum of the system.

Thermalization of Gauge Theories from their Entanglement Spectrum

Using dual theories embedded into a larger unphysical Hilbert space along entanglement cuts, we study the entanglement structure of Z_{2} lattice gauge theory in (2+1) spacetime dimensions. We demonstrate Li and Haldane's conjecture, and show consistency of the entanglement Hamiltonian with the Bisognano-Wichmann theorem. Studying nonequilibrium dynamics after a quench, we provide an extensive description of thermalization in Z_{2} gauge theory which proceeds in a characteristic sequence: Maximization of the Schmidt rank and spreading of level repulsion at early times, self-similar evolution with scaling coefficients α=0.8±0.2 and β=0.0±0.1 at intermediate times, and finally thermal saturation of the von Neumann entropy.