Holographic quantum algorithms for simulating correlated spin systems

Abstract

We present a suite of "holographic" quantum algorithms for efficient ground-state preparation and dynamical evolution of correlated spin-systems, which require far-fewer qubits than the number of spins being simulated. The algorithms exploit the equivalence between matrix-product states (MPS) and quantum channels, along with partial measurement and qubit re-use, in order to simulate a $D$-dimensional spin system using only a ($D$-1)-dimensional subset of qubits along with an ancillary qubit register whose size scales logarithmically in the amount of entanglement present in the simulated state. Ground states can either be directly prepared from a known MPS representation, or obtained via a holographic variational quantum eigensolver (holoVQE). Dynamics of MPS under local Hamiltonians for time $t$ can also be simulated with an additional (multiplicative) $\mathrm{poly}(t)$ overhead in qubit resources. These techniques open the door to efficient quantum simulation of MPS with exponentially large bond-dimension, including ground-states of 2D and 3D systems, or thermalizing dynamics with rapid entanglement growth. As a demonstration of the potential resource savings, we implement a holoVQE simulation of the antiferromagnetic Heisenberg chain on a trapped-ion quantum computer, achieving within $10(3)\%$ of the exact ground-state energy of an infinite chain using only a pair of qubits.

13 pages, 9 figures

References in corpus (3)

• Demonstration of the trapped-ion quantum-CCD computer architecture
• Parallel Quantum Simulation of Large Systems on Small Quantum Computers
• Fermionic Matrix Product States and One-Dimensional Topological Phases

Cited by in corpus (65)

• A Race Track Trapped-Ion Quantum Processor
• Emerging quantum computing algorithms for quantum chemistry
• Hardware-efficient variational quantum algorithms for time evolution
• Fractal, logarithmic and volume-law entangled non-thermal steady states via spacetime duality
• Filtering variational quantum algorithms for combinatorial optimization
• The Variational Power of Quantum Circuit Tensor Networks
• Dynamical purification and the emergence of quantum state designs from the projected ensemble
• Barren plateaus in quantum tensor network optimization
• Entanglement dynamics in hybrid quantum circuits
• Holographic dynamics simulations with a trapped ion quantum computer
• Sequential generation of projected entangled-pair states
• Constant-depth preparation of matrix product states with adaptive quantum circuits
• Noise-assisted digital quantum simulation of open systems
• Characterizing a non-equilibrium phase transition on a quantum computer
• Algebraic Bethe Circuits
• Qubit-efficient entanglement spectroscopy using qubit resets
• Suppression of mid-circuit measurement crosstalk errors with micromotion
• Quantum algorithms for estimating quantum entropies
• Learning quantum states and unitaries of bounded gate complexity
• Entanglement from tensor networks on a trapped-ion QCCD quantum computer
• Quantum Magic and Multi-Partite Entanglement in the Structure of Nuclei
• Holographic quantum simulation of entanglement renormalization circuits
• Crystalline Quantum Circuits
• Probing Geometric Excitations of Fractional Quantum Hall States on Quantum Computers
• Holographic simulation of correlated electrons on a trapped ion quantum processor
• Variational quantum algorithm for unconstrained black box binary optimization: Application to feature selection
• Preparing quantum many-body scar states on quantum computers
• Isometric tensor network optimization for extensive Hamiltonians is free of barren plateaus
• Tensor networks for quantum computing
• Quantum algorithms for scientific computing
• Quantum-classical eigensolver using multiscale entanglement renormalization
• Tensor-network-assisted variational quantum algorithm
• Probing critical states of matter on a digital quantum computer
• Observation of a non-Hermitian supersonic mode on a trapped-ion quantum computer
• Universal structure of measurement-induced information in many-body ground states
• Exactly solvable many-body dynamics from space-time duality
• A tensor network discriminator architecture for classification of quantum data on quantum computers
• Fisher zeros and persistent temporal oscillations in non-unitary quantum circuits
• Simulating 2D topological quantum phase transitions on a digital quantum computer
• Optimal Parameter Configurations for Sequential Optimization of Variational Quantum Eigensolver
• Absence of barren plateaus and scaling of gradients in the energy optimization of isometric tensor network states
• Convergence and Quantum Advantage of Trotterized MERA for Strongly-Correlated Systems
• Quantum algorithm for calculation of transition amplitudes in hybrid tensor networks
• Accelerating two-dimensional electronic spectroscopy simulations with a probe qubit protocol
• Sequential quantum simulation of spin chains with a single circuit QED device
• Holographic Gaussian Boson Sampling with Matrix Product States on 3D cQED Processors
• Variational Quantum Simulation of Valence-Bond Solids
• Emergent unitary designs for encoded qubits from coherent errors and syndrome measurements
• Quantum Phase Transitions between Symmetry-Enriched Fracton Phases
• Inductive Construction of Variational Quantum Circuit for Constrained Combinatorial Optimization
• Variational Quantum Imaginary Time Evolution for Matrix Product State Ansatz with Tests on Transcorrelated Hamiltonians
• Two Dimensional Isometric Tensor Networks on an Infinite Strip
• Straddling-gates problem in multipartite quantum systems
• Solving the Hubbard model using density matrix embedding theory and the variational quantum eigensolver
• Quantum tensor network algorithms for evaluation of spectral functions on quantum computers
• Sequential Generation of Two-dimensional Super-area-law States with Local Parent Hamiltonian
• Pseudoentanglement from tensor networks
• Simulating Topological Order on Quantum Processors
• Measurement-Induced Entanglement in Conformal Field Theory
• Qubit recycling and the path counting problem
• Fractal decompositions and tensor network representations of Bethe wavefunctions
• Error detection without post-selection in adaptive quantum circuits
• Preparing the Gutzwiller wave function for attractive SU(3) fermions on a quantum computer
• Tri-unitary quantum circuits
• Non-invasive mid-circuit measurement and reset on atomic qubits