Holographic quantum simulation of entanglement renormalization circuits

Abstract

While standard approaches to quantum simulation require a number of qubits proportional to the number of simulated particles, current noisy quantum computers are limited to tens of qubits. With the technique of holographic quantum simulation, a $D$-dimensional system can be simulated with a $D-1$-dimensional subset of qubits, enabling the study of systems significantly larger than current quantum computers. Using circuits derived from the multiscale entanglement renormalization ansatz (MERA), we accurately prepare the ground state of an $L=32$ critical, non-integrable perturbed Ising model and measure long-range correlations on the 10 qubit Quantinuum trapped ion computer. We introduce generalized MERA (gMERA) networks that interpolate between MERA and matrix product state networks and demonstrate that gMERA can capture far longer correlations than a MERA with the same number of qubits, at the expense of greater circuit depth. Finally, we perform noisy simulations of these two network ansätze and find that the optimal choice of network depends on noise level, available qubits, and the state to be represented.

References in corpus (26)

• Quantum Computing in the NISQ era and beyond
• A variational eigenvalue solver on a quantum processor
• Entanglement renormalization
• Thermodynamic limit of the density matrix renormalization for the spin-1 Heisenberg chain
• An Area Law for One Dimensional Quantum Systems
• A class of quantum many-body states that can be efficiently simulated
• Matrix product states represent ground states faithfully
• Quantum optimization using variational algorithms on near-term quantum devices
• Demonstration of the trapped-ion quantum-CCD computer architecture
• Optimal Quantum Circuits for General Two-Qubit Gates
• Efficient numerical simulations with Tensor Networks: Tensor Network Python (TeNPy)
• Sequential generation of entangled multi-qubit states
• Algorithms for entanglement renormalization
• The computational complexity of PEPS
• Tensor network decompositions in the presence of a global symmetry
• Real- and imaginary-time evolution with compressed quantum circuits
• Encoding of Matrix Product States into Quantum Circuits of One- and Two-Qubit Gates
• Isometric Tensor Network States in Two Dimensions
• Parallel Quantum Simulation of Large Systems on Small Quantum Computers
• Phase Diagram of the Interacting Majorana Chain Model
• Holographic quantum algorithms for simulating correlated spin systems
• Finding purifications with minimal entanglement
• Isometric Tensor Network representation of string-net liquids
• Scaling of entanglement entropy in the (branching) multi-scale entanglement renormalization ansatz
• Sequential generation of projected entangled-pair states
• Matrix product state renormalization

Cited by in corpus (16)

• Tensor networks for quantum computing
• Automatic quantum circuit encoding of a given arbitrary quantum state
• Probing critical states of matter on a digital quantum computer
• Random insights into the complexity of two-dimensional tensor network calculations
• Holographic deep thermalization for secure and efficient quantum random state generation
• Charge and Spin Sharpening Transitions on Dynamical Quantum Trees
• Emergent unitary designs for encoded qubits from coherent errors and syndrome measurements
• Variational Quantum Imaginary Time Evolution for Matrix Product State Ansatz with Tests on Transcorrelated Hamiltonians
• Tomonaga-Luttinger Liquid Behavior in a Rydberg-encoded Spin Chain
• Exploring nontrivial topology at quantum criticality in a superconducting processor
• One-half reflected entropy is not a lower bound for entanglement of purification
• Holographic Classical Shadow Tomography
• Sequential Generation of Two-dimensional Super-area-law States with Local Parent Hamiltonian
• Pseudoentanglement from tensor networks
• Fractal decompositions and tensor network representations of Bethe wavefunctions
• Qubit frugal entanglement determination with the deep multi-scale entanglement renormalization ansatz