Qubit frugal entanglement determination with the deep multi-scale entanglement renormalization ansatz
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866912438905995264 |
|---|---|
| author | Garg, Kushagra Ahmed, Zeeshan Thomasen, Andreas |
| author_facet | Garg, Kushagra Ahmed, Zeeshan Thomasen, Andreas |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_08548 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Qubit frugal entanglement determination with the deep multi-scale entanglement renormalization ansatz Garg, Kushagra Ahmed, Zeeshan Thomasen, Andreas Quantum Physics 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. |
| title | Qubit frugal entanglement determination with the deep multi-scale entanglement renormalization ansatz |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2404.08548 |