Holographic quantum simulation of entanglement renormalization circuits
- URL: http://arxiv.org/abs/2203.00886v1
- Date: Wed, 2 Mar 2022 05:58:19 GMT
- Title: Holographic quantum simulation of entanglement renormalization circuits
- Authors: Sajant Anand, Johannes Hauschild, Yuxuan Zhang, Andrew C. Potter,
Michael P. Zaletel
- Abstract summary: 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 $Drm -1$-dimensional subset of qubits.
- Score: 14.385064176392595
- License: http://creativecommons.org/licenses/by/4.0/
- 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 $D{\rm
-}1$-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 ans\"atze and find that the optimal choice of network depends
on noise level, available qubits, and the state to be represented.
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