Qubit frugal entanglement determination with the deep multi-scale entanglement renormalization ansatz

Abstract

We study the deep multi-scale entanglement renormalization ansatz (DMERA) on quantum hardware and the causal cone of a subset of the qubits which make up the ansatz. This causal cone spans $O(M+\log N)$ physical qubits on a quantum device, where $M$ and $N$ are the subset size and the total number qubits in the ansatz respectively. This allows for the determination of the von Neumann entanglement entropy of the $N$ qubit wave-function using $O(M+\log N)$ qubits by diagonalization of the reduced density matrix (RDM). We show this by randomly initializing a 16-qubit DMERA and diagonalizing the resulting RDM of the $M$-qubit subsystem using density matrix simulation. As an example of practical interest, we also encode the variational ground state of the quantum critical long-range transverse field Ising model (LRTIM) on 8 spins using DMERA. We perform density matrix simulation with and without noise to obtain entanglement entropies in separate experiments using only 4 qubits. Finally we repeat the experiment on the IBM Kyoto backend reproducing simulation results.

arXiv comment9 pages, 4 figures

References in corpus (29)

• Entanglement in quantum critical phenomena
• Scaling of Entanglement close to a Quantum Phase Transitions
• The Variational Quantum Eigensolver: a review of methods and best practices
• An adaptive variational algorithm for exact molecular simulations on a quantum computer
• Unitary-projective entanglement dynamics
• Relating the Resource Theories of Entanglement and Quantum Coherence
• Variational Quantum State Diagonalization
• A perspective on the current state-of-the-art of quantum computing for drug discovery applications
• Entanglement renormalization and topological order
• Probing real-space and time resolved correlation functions with many-body Ramsey interferometry
• A Non-Orthogonal Variational Quantum Eigensolver
• Drug design on quantum computers
• Variational Quantum Fidelity Estimation
• Fault-tolerant resource estimate for quantum chemical simulations: Case study on Li-ion battery electrolyte molecules
• Barren plateaus in quantum tensor network optimization
• Analyzing the barren plateau phenomenon in training quantum neural networks with the ZX-calculus
• Critical behavior of quantum magnets with long-range interactions in the thermodynamic limit
• Fidelity and criticality of quantum Ising chain with long-range interactions
• Simulating key properties of lithium-ion batteries with a fault-tolerant quantum computer
• Quantum algorithm for estimating Renyi entropies of quantum states
• ADAPT-QSCI: Adaptive Construction of an Input State for Quantum-Selected Configuration Interaction
• Quantum algorithms for estimating quantum entropies
• Quantum computation of silicon electronic band structure
• Non-local scaling operators with entanglement renormalization
• Holographic quantum simulation of entanglement renormalization circuits
• A randomized measurement toolbox for an interacting Rydberg-atom quantum simulator
• A Quantum Computing Implementation of Nuclear-Electronic Orbital (NEO) Theory: Towards an Exact pre-Born-Oppenheimer Formulation of Molecular Quantum Systems
• Demonstrating Quantum Computation for Quasiparticle Band Structures
• Constructing Local Bases for a Deep Variational Quantum Eigensolver for Molecular Systems