Holographic quantum simulation of entanglement renormalization circuits
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2022
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| _version_ | 1866911789693796352 |
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| author | Anand, Sajant Hauschild, Johannes Zhang, Yuxuan Potter, Andrew C. Zaletel, Michael P. |
| author_facet | Anand, Sajant Hauschild, Johannes Zhang, Yuxuan Potter, Andrew C. Zaletel, Michael P. |
| contents | 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 $D{\rm -}1$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_00886 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Holographic quantum simulation of entanglement renormalization circuits Anand, Sajant Hauschild, Johannes Zhang, Yuxuan Potter, Andrew C. Zaletel, Michael P. Quantum Physics Strongly Correlated Electrons 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 $D{\rm -}1$-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. |
| title | Holographic quantum simulation of entanglement renormalization circuits |
| topic | Quantum Physics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2203.00886 |