Probing phases of quantum matter with an ion-trap tensor-network quantum eigensolver

Abstract

Tensor-Network (TN) states are efficient parametric representations of ground states of local quantum Hamiltonians extensively used in numerical simulations. Here we encode a TN ansatz state directly into a quantum simulator, which can potentially offer an exponential advantage over purely numerical simulation. In particular, we demonstrate the optimization of a quantum-encoded TN ansatz state using a variational quantum eigensolver on an ion-trap quantum computer by preparing the ground states of the extended Su-Schrieffer-Heeger model. The generated states are characterized by estimating the topological invariants, verifying their topological order. Our TN encoding as a trapped ion circuit employs only single-site addressing optical pulses - the native operations naturally available on the platform. We reduce nearest-neighbor crosstalk by selecting different magnetic sublevels with well-separated transition frequencies to encode even and odd qubits.

arXiv comment17 pages, 14 figures

References in corpus (86)

• Topological Insulators
• Topological insulators and superconductors
• Quantum Computing in the NISQ era and beyond
• Fault-tolerant quantum computation by anyons
• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• A variational eigenvalue solver on a quantum processor
• The density-matrix renormalization group in the age of matrix product states
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Quantum Simulation
• Area laws for the entanglement entropy - a review
• The theory of variational hybrid quantum-classical algorithms
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Noisy intermediate-scale quantum (NISQ) algorithms
• Experimental issues in coherent quantum-state manipulation of trapped atomic ions
• Entanglement spectrum of a topological phase in one dimension
• Quantum computation with ions in thermal motion
• Multi-particle entanglement of hot trapped ions
• Quantum Phases of Matter on a 256-Atom Programmable Quantum Simulator
• Effective quantum spin systems with ion traps
• Symmetry protection of topological order in one-dimensional quantum spin systems
• Probing Topological Spin Liquids on a Programmable Quantum Simulator
• Programmable Quantum Simulations of Spin Systems with Trapped Ions
• Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
• Scalable Quantum Simulation of Molecular Energies
• Experimental realization of a long-range antiferromagnet in the Hubbard model with ultracold atoms
• Matrix product states represent ground states faithfully
• Programmable quantum simulation of 2D antiferromagnets with hundreds of Rydberg atoms
• Quantum optimization using variational algorithms on near-term quantum devices
• Deterministic entanglement of two trapped ions
• Tensor renormalization group approach to 2D classical lattice models
• Probing entanglement entropy via randomized measurements
• Self-Verifying Variational Quantum Simulation of the Lattice Schwinger Model
• Quantum Simulators: Architectures and Opportunities
• Quantum dynamics of cold trapped ions, with application to quantum computation
• Efficient Z-Gates for Quantum Computing
• Quantum state estimation
• Observation of the topological soliton state in the Su-Schrieffer-Heeger model
• Quantum chemistry calculations on a trapped-ion quantum simulator
• A class of ansatz wave functions for 1D spin systems and their relation to DMRG
• Entropy scaling and simulability by Matrix Product States
• qubit-ADAPT-VQE: An adaptive algorithm for constructing hardware-efficient ansatze on a quantum processor
• A compact ion-trap quantum computing demonstrator
• Experimental realisation of Shor's quantum factoring algorithm using qubit recycling
• Sequential generation of entangled multi-qubit states
• A quantum information processor with trapped ions
• Maximum-likelihood estimation of the density matrix
• Detection of Symmetry Protected Topological Phases in 1D
• Mixed-state entanglement from local randomized measurements
• Towards Quantum Machine Learning with Tensor Networks
• Fast quantum logic gates with trapped-ion qubits
• Bad metallic transport in a cold atom Fermi-Hubbard system
• Topological order in an exactly solvable 3D spin model
• Real- and imaginary-time evolution with compressed quantum circuits
• Optimal metrology with programmable quantum sensors
• Process tomography of ion trap quantum gates
• Imaging magnetic polarons in the doped Fermi-Hubbard model
• Optimal quantum control of multi-mode couplings between trapped ion qubits for scalable entanglement
• Choreographed entangle dances: topological states of quantum matter
• Photonic tensor networks produced by a single quantum emitter
• Spin Transport in a Mott Insulator of Ultracold Fermions
• Precision measurement and compensation of optical Stark shifts for an ion-trap quantum processor
• Realising the Symmetry-Protected Haldane Phase in Fermi-Hubbard Ladders
• How to realize a universal quantum gate with trapped ions
• Towards simulating 2D effects in lattice gauge theories on a quantum computer
• Time-Resolved Observation of Spin-Charge Deconfinement in Fermionic Hubbard Chains
• Crossing a topological phase transition with a quantum computer
• Deterministic entanglement of ions in thermal states of motion
• Parallel Quantum Simulation of Large Systems on Small Quantum Computers
• Exploring corner transfer matrices and corner tensors for the classical simulation of quantum lattice systems
• An order parameter for symmetry-protected phases in one dimension
• Many-body topological invariants from randomized measurements
• Theoretical and Experimental Perspectives of Quantum Verification
• Demonstration of two-atom entanglement with ultrafast optical pulses
• Observation of Pauli Crystals
• Isometric Tensor Network representation of string-net liquids
• Sequentially generated states for the study of two dimensional systems
• Scalable and Parallel Tweezer Gates for Quantum Computing with Long Ion Strings
• Sequential generation of projected entangled-pair states
• Realization of a Bosonic Antiferromagnet
• Entanglement from tensor networks on a trapped-ion QCCD quantum computer
• Experimental Bayesian calibration of trapped ion entangling operations
• Generation of Photonic Matrix Product States with Rydberg Atomic Arrays
• Doppler-free, Multi-wavelength Acousto-optic deflector for two-photon addressing arrays of Rb atoms in a Quantum Information Processor
• Variational quantum state preparation via quantum data buses
• Generation of photonic tensor network states with Circuit QED

Cited by in corpus (7)

• Quantum Computing for High-Energy Physics: State of the Art and Challenges. Summary of the QC4HEP Working Group
• Efficient Information Retrieval for Sensing via Continuous Measurement
• Variational quantum simulation of U(1) lattice gauge theories with qudit systems
• Constructing the spin-1 Haldane phase on a qudit quantum processor
• Quantum simulation of extended electron-phonon coupling models in a hybrid Rydberg atom setup
• Learning quantum phases via single-qubit disentanglement
• Photonic variational quantum eigensolver for NISQ-compatible quantum technology